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Famous Mathematicians

List and Biographies of Great Mathematicians

15 Famous Indian Mathematicians and Their Contributions

January 23, 2017 By admin

13. Bhāskara I Born in the district of Mysore, this small town lad grew up to be the shining star. His contributions are mainly his proof of the fact that zero stood for ‘nothing’(the idea initially introduced by Bhramagupta). He made many calculations to prove so; division, permutation and combination theories. He also proved how the earth appears to be flat even though it’s a sphere.

14. Bhaskara II Bhaskara II so called to avoid any confusion with the first. His work represented significant mathematical and astronomical knowledge. He is most known for his work in calculus and how it is applied to astronomical problems and computations. Not only did he deal with calculus but had vast knowledge over arithmetic, algebra, mathematics of planets and spheres.

15. Hemachandra His most significant contribution in mathematics was his initial version of the Fibonacci sequence. He was not only a mathematician but also a scholar, polymath, poet who wrote on grammar, philosophy and contemporary history. Therefore his contributions are not only restricted to math but over all the various different fields that he had mastered over.

Indian Mathematicians

Table of Contents

Srinivasa ramanujan, brahmagupta, shakuntala devi, c.p. ramanujan, p.c. mahalanobis, anil kumar gain, ganesh prasad, c.s. seshadri, radhanath sikdar, dattathreya ramchandra kaprekar.

Srinivasa Ramanujan was a brilliant mathematician who gets credited even today for his contributions in the field of mathematics.

Born in the year 1887 in Tamil Nadu, Ramanujan was an exceptionally brilliant child who would outshine other children of his age in solving equations. The circumstances of his family were not good and they lived in poverty for most part of their lives, thereby not giving the young Ramanujan an opportunity to pursue his passion-mathematics-due to lack of proper resources.

However the laborious Ramanujan found his inspiration in the book 'Synopsis of elementary results in pure mathematics' by George S. Carr. A brilliant mathematician, Srinivasa Ramanujan is credited today for his contributions in the field of mathematics.

It was due to sheer strength of determination and devotion that the immensely talented mathematician could  invent some of the most crucial equations for the field of mathematical studies- game theory and infinite series. The infinite series for π is used in arithmetical calculations even today.

The year 1914 was the turning point in the struggling life the genius mathematician. He was invited to Cambridge by the very eminent mathematician, G.H.Hardy. Hardy after going through Ramanujan's papers was perplexed by the geniousness of his work. The papers that the young mind had brought along, from home to  Cambridge, were written between the years 1903-14. While some equations had already been discovered, the remainder were entirely new for even G.H.Hardy. He was amazed at Ramanujan's insight into algebraical formulae, transformations of infinite series, etc. In the year 1916, he was awarded his Ph.D. by the university.

The story of this mathematical genius is truly inspiring as Ramanujan had to practice in circumstances that didn't even let him afford enough papers to practice the equations.  A slate and chalk were his most trusted aids. At a very young age, Ramanuj bid goodbye to the world in the year 1920 due to the dreaded disease, Tuberculosis.

Brahmagupta was a seventh century Indian mathematician and astronomer, best known for his book 'Brāhmasphuṭasiddhānta'. The book was the first text that treated zero as a number and gave references for using it in calculations.

Born in the state of Rajasthan, most of his works were in the Sanskrit language, which was the prominent language then. Known also as Bhillamalacarya, the genius mathematician made immense contribution in the field of Arithmetic by not only explaining how to calculate cube and the cube-root of an integer but also providing rules for computation of square and square root.

Brahmagupta could not complete the use of zero in calculations relating to division but he offered other calculations, such as (1 + 0 = 1; 1 - 0 = 1; and 1 x 0 =0), for using the digit zero.

Interestingly, previously calculations such as 3-4 entailed the answer called meaningless. Brahmagupta gave such calculations a meaning by inventing the concept of negative numbers.

Brahmagupta made immense contributions in the field of geometry and trigonometry by establishing √10 (3.162277) as an approximation for π (3.141593).  The other contributions of the accomplished mathematician were the Brahmagupta's Formula and Brahmagupta's Theorem. The former provided a formula for the area of a cyclic quadrilateral while the latter related to the diagonals of a cyclic quadrilateral.

Bhaskara I (c.600 CE-680) was a seventh century Indian mathematician and astronomer credited with the invention of Hindu decimal system. Born in Maharashtra,

Bhaskara's commentary Aryabhatiyabhasya, written in 629 CE, is the oldest known work, in Sanskrit language, on mathematics and astronomy. He was a follower of Aryabhat.

His most notable books were Laghubhāskarīya and Mahabhaskariya

The latter book, divided into eight chapters, dwells into mathematical astronomy. The book is also credited to have given the approximation formula for sin x. Relations between sine and cosine, and also between the sine of an angle >90° >180° or >270° to the sine of an angle <90°  have been given in this book.

The book also discusses about longitudes of the planets, conjunctions of the planets with each other and with bright stars, eclipses of the sun and the moon, risings and settings, and the lunar crescent. Bhaskara I is also known for the Pell Equation ( 8x² + 1 = y² ).

Not much is known about Bhaskara I except that he was born in Parbhani, Maharashtra and died in Andhra Pradesh. He is called Bhaskara I to distinguish from another 12th century mathematician of the same name. It is believed that Bhaskara I's father was his earliest teacher and the book,  Laghubhāskarīya, is an abridged version of his earlier book, Aryabhatiyabhasya. However Bhaskara I along with Brahmagupta is considered to be the greatest ancient Indian mathematicians of all time.

Shakuntala Devi was a remarkable lady known for superfast calculations, something that had earned her the title of 'human computer'.

Born in Bangalore in the year 1929, Shakuntala's talent was first observed by her father when he was training her for remembering numbers on the card for the circuses. Shakuntala's father used to work in a circus. Soon after the father - daughter duo were traveling to do street shows based on a young Shakuntala's calculations' talent.

Shakuntala had by the end of year 1944 moved to London thereby traveling across the world doing shows. After all the young prodigy was known to solve the most complex equations within seconds. So much so that the professor of psychology at California University, Arthur Jensen, had called her to the university in the year 1988 to study her exceptional capabilities.

The world was stunned with Shakuntala Devi's talent. In the year 1980, her name was recorded in the Guinness Book of World Record for calculating thirteen digit numbers- 7,686,369,774,870 × 2,465,099,745,779- which were picked at random at the Computer Department of Imperial College, London. She gave the correct answer – 18,947,668,177,995,426,462,773,730- in just 28 seconds.

Shakuntala Devi was also a successful astrologer and author of several books on the subject. She also wrote texts on mathematics for children and puzzles. The immensely gifted mathematician bid her adieu to the world in year 2013.

Famously also called Aryabhata I (476-550 CE) or Aryabhata The Elder, in order to distinguish him from another tenth century mathematician of the same name, Aryabhata flourished in Patliputra during Gupta dynasty

Aryabhata was a Scientist, Mathematician as well as an Astronomer. This is so because not only had he discovered that the Earth is spherical, which revolves around the Sun but also that the number of days in a year is 365.

The two most prominent works composed by Aryabhata are Aryabhatiya and the Aryabhatasiddhanta.

The latter is a lost work now while Aryabhatiya was divided into three sections- Ganita (Mathematics), Kala-kriya (Time Calculations), and Gola (Sphere).

In Ganita, Aryabhata has named the first 10 decimal places and given algorithms for obtaining the square and cubic roots by using the decimal number system. Aryabhata had also developed using one of the two methods for creating the table of sines by using Pythagorean theorem. He also realized that second-order sine difference is proportional to sine.

In Kala-kriya Aryabhata discusses about astronomy such as planetary motions, definitions of various units of time, etc.

In Gola, Aryabhata has applied trigonometry to spherical geometry. This also became the apparent basis for prediction of solar and lunar eclipse. The equation in Gola was used by Aryabhata to explain that the rotation of the Earth about its axis was the reason for westward motion of the stars. He also referred to reflections from the Sun for luminosity of the Moon and the planets.

Calyampudi Radhakrishna Rao, considered the doyen of Indian Statistics, has works that have influenced various fields from economics to demography to medicine.

Born in 1879 in Karnataka, Rao had developed interest in the subject mathematics from a very early age. Evident as this is from his earlier account narrating how his father brought for him to solve a book titled 'Problems for Leelavathi' that contained questions by a mathematician for his daughter Leelavathi to solve. He explains how his father would motivate the then eleven years old Rao to try solving five to ten problems every day.

Rao had always keen interest in the subject and this is the reason why he could win for himself the Chandrasekara Iyer Scholarship for both the years at intermediate level. Even M.A, he graduated with first class honours from Andhra University in the year 1940. However it was his year at the Indian Statistical Institute that proved to be a turning point in the life of young Roy. Here he got to publish six papers, jointly (with top researcher K.R. Nair) as well as indepently in the year 1941.

C.R. Rao received gold medal and a first class M.A. degree in Statistics from the Indian Statistical Institute (Kolkata) in the year 1943. Rao' work focussed on four areas- multivariate analysis, linear model, designs in experiments, characterisation of probability distributions- and this focus continued to be his area of specialisation for the rest of his career.

Rao has made important contributions to combinatorial mathematics and a number of  technical terms in statistics such as Cramér-Rao Inequality or Bound (CRB), Rao-Blackwell Theorem, Fisher-Rao Metric, and Rao Distance have been  named after him.

Rao score test  was also created by hi as an alternative to Pearson’s chi-squared test and Wald’s test. C.R. Rao was also instrumental in introducing the concept of ‘quadratic entropy’ — a diversity measure, which could be used to carry out an analysis of diversity of any order.

C.R. Rao under the guidance of his mentor P.C. Mahalanobis has  contributed to the establishment of  statistical bureaus across India. He was conferred the Padma Vibhushan by the Government of India in the year 2001, and the National Medal of Science by President George W Bush in 2002. Aside from the various other awards, the legendary C.R. Rao has been has been awarded thirty-three honorary degrees by universities in eighteen countries if the world.

Chakravarthi Padmanabhan Ramanujam was a gifted Indian mathematician, known for his works on number theory and algebraic geometry.

Born in the year 1938 in Madras (now Chennai), Ramanujan joined the prestigious Loyola college in Madras (now Chennai) for finishing intermediate and college studies after finishing his high school in the year 1952.

C.P. Ramanujan is well known for his rejection of promotion to the position of an Associate Professor at Tata Institute of Fundamental Research (TIFR), Mumbai. Believing this elevation to a higher  position to be  undeserving in nature, he later accepted this post after persuasions by several of his friends and colleagues.

Passionate about the subject mathematics, the young Ramanujan was appreciated well by his doctoral supervisor for in-depth knowledge of the subject.

Ramanujan's personal library had books based in other languages as he was trying to teach himself other languages such as French, German, Russian and Italian to study mathematics in their original forms.

During his stint as a professor at TIFR, Ramanujan published his first two papers in the year 1963, on Waring’s problem for algebraic number fields. The second paper was based on the algebraic half of Siegel’s problem. The paper provided such results that had never been proved. The brilliant mathematician also received great praises for  preparing lecture notes, for highly established mathematicians, that were to be imparted as notes for various courses at TIFR, Mumbai.

Ramanujam had also made significant contributions in the field of algebraic geometry, especially providing clarification on the Kodaira Vanishing Theorem.

Ramanujan had made remarkable contributions in the field of mathematics and these were well appreciated by the international community. However just like S.Ramanujan, C.P. Ramanujan died very early at the young age of only 37. Immediately after his death, a commemorative hall was named after him in the Institute of Mathematics at the University of Genoa.

P.C. Mahalanobis was an Indian Mathematician, Statistician and Scientist. Not only is he considered the father of Statistics in India but also the hand behind the establishment of Indian Statistical Institute (ISI) in India in the year 1931. He was also instrumental in shaping up of the Planning Commission of India.

Prasanta Chandra Mahalanobis was born in Kolkata in the year 1893. After completing his school education, he received his B.Sc in Physics from Presidency College, Kolkata. Later he went to Cambridge for further studies in Mathematics and Physics.

Mahalanobis is best known for his Mahalanobis Distance or D2-statistic- measure of comparison between two different data sets. In simple words, it is a measurement used for studies in population distribution.

Indian Statistical Institute (ISI) credits all the major statistical work done up till the 1930s to P.C.Mahalanobis. Many  findings of his early studies were of great impact for agricultural development and control of floods.

For Mahalanobis, statistics was a kind of new technology that aided greatly in increasing the efficiency of human effort. The sixty years of flood data, in Odisha, so analysed and published by him in 1926, laid the foundation for installation of Hirakud dam on Mahanadi river, some three decades later.

So great was the influence of his work that not only Statistics was soon recognised as a key discipline but also students majoring in Physics had begun to take interest in Statistics.

Satyendra Nath Bose was an Indian physicist and mathematician, known most famously for Bose-Einstein Condensate. Bose had worked directly with Albert Einstein for this project. A certain type of particle named 'boson' or the 'God Particle' was assigned to Bose in recognition of the contributions made by Bose. Bose is therefore often referred to as “The Father of the God Particle”.

Born in the year 1894 in Kolkata , Bose had always been an intelligent child excelling in education at every turn. By the years 1913 and 1915 respectively, he had finished his B.Sc and M.Sc in Mathematics while also at the same time outperforming his other classmates.

S.N.Bose enrolled himself at the University College of Science in the year 1917 for further studies. It is during his tenure as a student there that Bose got to study theories of Statistical Mechanics by American mathematician J.Willard Gibbs and theory of relativity by Albert Einstein. Bose in collaboration with another bright fellow from his batch started translating the works of Einstein into English from German and French languages. This of course only after getting permission from Einstein.

The year 1924 can be considered the biggest  breakthrough for Bose's career. During this year was published a paper in which Bose had derived Planck’s 'quantum radiation law' without making any reference to the classical theories of physics. This work got all the more importance because Planck’s law had yet not been proved. This paper was submitted by Bose to Einstein for a review. Einstein was impressed with Bose's research. A translated copy of the research, in German language, was submitted to the European Physics Journal by Einstein himself along with a letter of personal recommendation. Einstein soon used the basic concept by Bose for further research into the field of material physics.

Further research by Peter Higgs and Francois Englert, in the field of God particle so clearly set by Bose, led them to winning the Nobel Prize in physics in the year 2013. Though Bose was never awarded this honour, many noted scientists believe Bose rightly deserved the award.

From the years 1927, when Bose was made the head of the physics department in University of Kolkata, till 1945 Bose was working in his field of expertise. During later years Bose moved towards literature, philosophy and Indian independence movement.

Bose had received not only Padma Vibhushan for his notable works but also been appointed for various prestigious positions at different universities. For instance,  being an adviser to the Council of Scientific and Industrial Research or the presidentship of Indian Physical Society and the National Institute of Science. He was also awarded the fellowship for the Royal Society in London in 1958. Satyendra Nath Bose died in the year 1974.

Anil Kumar Gain was an Indian mathematician, statistician and educationist. Gain was the founder of Vidyasagar University, named after the social reformer, Ishwar Chand Vidyasagar.

Born in Bengal in the year 1919, Gain as a young learner had always had great interest in subjects mathematics and english. He was a gold medalist in M.A. from the University of Calcutta degree before getting a doctorate in mathematics in the year 1950, from the University of Cambridge.

Gain's most significant contribution is his works on Pearson product-moment correlation coefficient in the field of applied statistics, along with his colleague Ronald Fisher.

Gain was the president of the statistics section of the Indian Science Congress Association. He also served as the head of the Department of Mathematics at the Indian Institute of Technology, Kharagpur. The eminent mathematician was also was honoured by the Royal Statistical Society and the Cambridge Philosophical Society. He died in the year 1978 in Bengal.

Mahavira was a ninth century Indian mathematician known for separating astrology from mathematics. No exact information is available as to where he was exactly born, but it is mentioned that it was probably the Mysuru state of Southern India.

Mahavira made significant contributions in the field of algebra. The book written by him, Ganitasarasangraha, is composed of mathematical procedures such as basic operations, reductions of fractions, miscellaneous problems involving a linear or quadratic equation with one unknown, the rule of three (involving proportionality), mixture problems, geometric computations with plane figures, ditches (solids), and shadows (similar right-angled triangles).

His work was highly acclaimed because of his contributions to the establishment of terminology for concepts such as equilateral and isosceles triangle; rhombus; circle and semicircle.

Mahavira was the first mathematician to explain that negative numbers don't have square roots.

The brilliant mathematician's works were highly recognised in Southern India and his texts were referred to by many scholars from southern India.

Ganesh Prasad, an eminent Indian mathematician, specialised in the theory of potentials, theory of functions of a real variable, Fourier series and the theory of surfaces.

Born in the year 1876, in the state of Uttar Pradesh, Ganesh Prasad's notable works include 'A Treatise on Spherical Harmonics' and the 'Functions of Bessel and Lame'.

After obtaining his M.A. and D.Sc degrees from Allahabad University, he had, in the year 1899, moved to Cambridge for further research and training as a Government of India scholar. He returned to India in 1904 and that is when he started laying the foundations for developing a culture  of research in India.

This is the reason why Ganesh Prasad is also known as the "father of mathematical researches in India."

Ganesh Prasad had also served as professor at Banaras Hindu University, Muir Central College (Allahabad). In the year 1923, he went to Kolkata to occupy the chair of Hardinge Professor of Mathematics. He was also elected the president of Calcutta Mathematical Society in 1924 and vice-president of Indian Association for the Advancement of Science, Kolkata. He held both these offices till his last. Dr Ganesh Prasad was also the founder member of National Institute of Sciences, India (which is now Indian National Science Academy). He was also one of the founders of the Agra University. Dr Prasad died in the year 1935.

C.S. Seshadri is an eminent mathematician, known for the Seshadri Constant (named after him). The well known Indian mathematician was awarded the Padma Bhushan in the year 2009 for his outstanding contributions in the field of mathematics.

Born in the year 1932, Chennai, Seshadri completed his graduation in the subject Mathematics in the year 1953, from Madras University before attending Bombay (now Mumbai) University for a Ph.D in the subject. He completed his doctorate in the year 1958 and later on got elected as a fellow at the Indian Academy of Sciences in 1971. From the years 1953-1984, Seshadri also worked as a research scholar and senior professor, in the later years, at Tata Institute of Fundamental Research (TIFR), Mumbai.

C.S. Seshadri's area of specialisation is algebraic geometry. The Narasimhan–Seshadri theorem, created in collaboration with M.S. Narsimhan, has held a great influence in the field of mathematical studies. Equally well recognised are his works on the Geometric Invariant Theory,  Schubert Varieties, and Standard Monomial Theory.

Seshadri, from the years 1957-1960, was sent to France by TIFR, Mumbai. There he was quite fascinated by French tastes in not just wine and cuisine but also mathematics. Influenced greatly by mathematical geniuses such as Chevalley, Cartan, Schwartz, Grothendieck and Serre, Seshadri returned to India only to become one of the pioneers for starting the School of Mathematics, Tata Institute.

In a career spanning around five decades, C.S. Seshadri has been not only an inspiring teacher for many but also a leader of a whole generation of mathematicians. His contributions have been considered highly critical for development of Moduli problems,  Geometric Invariant Theory as well as Representation Theory of Algebraic Groups. The widely acclaimed mathematician is also the recipient of several prestigious awards such as TWAS Science Award, Honorary D.Sc. from Banaras Hindu University, Shanti Swarup Bhatnagar Award, Fellow of IAS, INSA and a Fellow of the Royal Society, Honorary degree, Université Pierre et Marie Curie (UPMC), Paris, Fellow of the American Mathematical Society, Srinivasa Ramanujan Medal from the Indian Academy of Sciences, etc.

Radhanath Sikdar is most famously known for his calculation of the height of Mt Everest. He was one of the first two Indians to read Newton’s Principia (the other Indian was Rajnarayan Basak). By the year 1932, the talented mathematician had studied Euclid’s Elements, Jephson’s Fluxion and Analytical Geometry and Astronomy by Windhouse.

Born in Kolkata in the year 1813, Sikdar's first job was conducting geodetic surveys under the then Surveyor General of India, George Everest. He got this job in the year 1931 at the Great Trigonometric Survey.

By the year 1852, Sikdar had started working at the Dehradun headquarters under the student of George Everest, Colonel Andrew Waugh. Here Sikdar was tasked with calculating the height of different peaks for different mountains in the Himalayas. How Radhanath Sikdar came across this reading for the highest peak is interesting. Till date Kanchenjunga was considered the highest peak but a study by James Nicolson had concluded that there might be a higher peak, called the peak XV. This study however had to be left midway as Nicolson contracted malaria.

Sikdar basing his readings on the above calculations calculated the distance of peak XV. It is said that when he found out the measurements, he burst into Waugh's office exclaiming, "Sir, I have discovered the highest mountain in the world."

The peak was later on named Mt Everest and the height, 29002 ft, so calculated by Radhanath Sikdar, was the official height till the year 1955 in India, before an Indian survey recalculated it to 29,092 ft.

George Everest had retired in the year 1843, but the letter he wrote to Radhanath's father back then in appreciation of his work was testimony to the brilliance and unique capabilities of the young Bengali mathematician.

Dattathreya Ramchandra Kaprekar (1905–1986), also known as 'Ganitananda', was a recreational mathematician. After receiving his  education from a school in Thane and later from Fergusson College in Pune, Kaprekar, in the year 1927, won the Wrangler R. P. Paranjpe Mathematical Prize for an original piece of work in mathematics.

Though he had received, from the University of Mumbai , his bachelor's degree in the year 1929, yet Kaprekar he could never get any postgraduate training in the subject for himself. He was a teacher at a school on Nashik (Maharashtra), and had worked tirelessly to publish extensively on topics such as recurring decimals, magic squares, and integers with special properties.

Due to his extensive publications he had become a well known in the recreational mathematics circles.

He had described in his works several classes of natural numbers as well as the Kaprekar, Harshad and Self numbers. The Kaprekar constant, named after him, was also discovered by Kaprekar. 6174 is the number, which is also called the Kaprekar Constant.

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Biography of Srinivasa Ramanujan, Mathematical Genius

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Srinivasa Ramanujan (born December 22, 1887 in Erode, India) was an Indian mathematician who made substantial contributions to mathematics—including results in number theory, analysis, and infinite series—despite having little formal training in math.

Fast Facts: Srinivasa Ramanujan

• Full Name: Srinivasa Aiyangar Ramanujan
• Known For: Prolific mathematician
• Parents’ Names: K. Srinivasa Aiyangar, Komalatammal
• Born: December 22, 1887 in Erode, India
• Died: April 26, 1920 at age 32 in Kumbakonam, India
• Spouse: Janakiammal
• Interesting Fact: Ramanujan's life is depicted in a book published in 1991 and a 2015 biographical film, both titled "The Man Who Knew Infinity."

Early Life and Education

Ramanujan was born on December 22, 1887, in Erode, a city in southern India. His father, K. Srinivasa Aiyangar, was an accountant, and his mother Komalatammal was the daughter of a city official. Though Ramanujan’s family was of the Brahmin caste , the highest social class in India, they lived in poverty.

Ramanujan began attending school at the age of 5. In 1898, he transferred to Town High School in Kumbakonam. Even at a young age, Ramanujan demonstrated extraordinary proficiency in math, impressing his teachers and upperclassmen.

However, it was G.S. Carr’s book, "A Synopsis of Elementary Results in Pure Mathematics," which reportedly spurred Ramanujan to become obsessed with the subject. Having no access to other books, Ramanujan taught himself mathematics using Carr’s book, whose topics included integral calculus and power series calculations. This concise book would have an unfortunate impact on the way Ramanujan wrote down his mathematical results later, as his writings included too few details for many people to understand how he arrived at his results.

Ramanujan was so interested in studying mathematics that his formal education effectively came to a standstill. At the age of 16, Ramanujan matriculated at the Government College in Kumbakonam on a scholarship, but lost his scholarship the next year because he had neglected his other studies. He then failed the First Arts examination in 1906, which would have allowed him to matriculate at the University of Madras, passing math but failing his other subjects.

For the next few years, Ramanujan worked independently on mathematics, writing down results in two notebooks. In 1909, he began publishing work in the Journal of the Indian Mathematical Society, which gained him recognition for his work despite lacking a university education. Needing employment, Ramanujan became a clerk in 1912 but continued his mathematics research and gained even more recognition.

Receiving encouragement from a number of people, including the mathematician Seshu Iyer, Ramanujan sent over a letter along with about 120 mathematical theorems to G. H. Hardy, a lecturer in mathematics at Cambridge University in England. Hardy, thinking that the writer could either be a mathematician who was playing a prank or a previously undiscovered genius, asked another mathematician J.E. Littlewood, to help him look at Ramanujan’s work.

The two concluded that Ramanujan was indeed a genius. Hardy wrote back, noting that Ramanujan’s theorems fell into roughly three categories: results that were already known (or which could easily be deduced with known mathematical theorems); results that were new, and that were interesting but not necessarily important; and results that were both new and important.

Hardy immediately began to arrange for Ramanujan to come to England, but Ramanujan refused to go at first because of religious scruples about going overseas. However, his mother dreamed that the Goddess of Namakkal commanded her to not prevent Ramanujan from fulfilling his purpose. Ramanujan arrived in England in 1914 and began his collaboration with Hardy.

In 1916, Ramanujan obtained a Bachelor of Science by Research (later called a Ph.D.) from Cambridge University. His thesis was based on highly composite numbers, which are integers that have more divisors (or numbers that they can be divided by) than do integers of smaller value.

In 1917, however, Ramanujan became seriously ill, possibly from tuberculosis, and was admitted to a nursing home at Cambridge, moving to different nursing homes as he tried to regain his health.

In 1919, he showed some recovery and decided to move back to India. There, his health deteriorated again and he died there the following year.

Personal Life

On July 14, 1909, Ramanujan married Janakiammal, a girl whom his mother had selected for him. Because she was 10 at the time of marriage, Ramanujan did not live together with her until she reached puberty at the age of 12, as was common at the time.

Honors and Awards

• 1918, Fellow of the Royal Society
• 1918, Fellow of Trinity College, Cambridge University

In recognition of Ramanujan’s achievements, India also celebrates Mathematics Day on December 22, Ramanjan’s birthday.

Ramanujan died on April 26, 1920 in Kumbakonam, India, at the age of 32. His death was likely caused by an intestinal disease called hepatic amoebiasis.

Legacy and Impact

Ramanujan proposed many formulas and theorems during his lifetime. These results, which include solutions of problems that were previously considered to be unsolvable, would be investigated in more detail by other mathematicians, as Ramanujan relied more on his intuition rather than writing out mathematical proofs.

His results include:

• An infinite series for π, which calculates the number based on the summation of other numbers. Ramanujan’s infinite series serves as the basis for many algorithms used to calculate π.
• The Hardy-Ramanujan asymptotic formula, which provided a formula for calculating the partition of numbers—numbers that can be written as the sum of other numbers. For example, 5 can be written as 1 + 4, 2 + 3, or other combinations.
• The Hardy-Ramanujan number, which Ramanujan stated was the smallest number that can be expressed as the sum of cubed numbers in two different ways. Mathematically, 1729 = 1 3 + 12 3 = 9 3 + 10 3 . Ramanujan did not actually discover this result, which was actually published by the French mathematician Frénicle de Bessy in 1657. However, Ramanujan made the number 1729 well known. 1729 is an example of a “taxicab number,” which is the smallest number that can be expressed as the sum of cubed numbers in n different ways. The name derives from a conversation between Hardy and Ramanujan, in which Ramanujan asked Hardy the number of the taxi he had arrived in. Hardy replied that it was a boring number, 1729, to which Ramanujan replied that it was actually a very interesting number for the reasons above.
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• Singh, Dharminder, et al. “Srinvasa Ramanujan's Contributions in Mathematics.” IOSR Journal of Mathematics , vol. 12, no. 3, 2016, pp. 137–139.
• “Srinivasa Aiyangar Ramanujan.” Ramanujan Museum & Math Education Centre , M.A.T Educational Trust, www.ramanujanmuseum.org/aboutramamujan.htm.
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Srinivasa Ramanujan

(1887-1920)

Who Was Srinivasa Ramanujan?

After demonstrating an intuitive grasp of mathematics at a young age, Srinivasa Ramanujan began to develop his own theories and in 1911, he published his first paper in India. Two years later Ramanujan began a correspondence with British mathematician G. H. Hardy that resulted in a five-year-long mentorship for Ramanujan at Cambridge, where he published numerous papers on his work and received a B.S. for research. His early work focused on infinite series and integrals, which extended into the remainder of his career. After contracting tuberculosis, Ramanujan returned to India, where he died in 1920 at 32 years of age.

Srinivasa Ramanujan was born on December 22, 1887, in Erode, India, a small village in the southern part of the country. Shortly after this birth, his family moved to Kumbakonam, where his father worked as a clerk in a cloth shop. Ramanujan attended the local grammar school and high school and early on demonstrated an affinity for mathematics.

When he was 15, he obtained an out-of-date book called A Synopsis of Elementary Results in Pure and Applied Mathematics , Ramanujan set about feverishly and obsessively studying its thousands of theorems before moving on to formulate many of his own. At the end of high school, the strength of his schoolwork was such that he obtained a scholarship to the Government College in Kumbakonam.

A Blessing and a Curse

However, Ramanujan’s greatest asset proved also to be his Achilles heel. He lost his scholarship to both the Government College and later at the University of Madras because his devotion to math caused him to let his other courses fall by the wayside. With little in the way of prospects, in 1909 he sought government unemployment benefits.

Yet despite these setbacks, Ramanujan continued to make strides in his mathematical work, and in 1911, published a 17-page paper on Bernoulli numbers in the Journal of the Indian Mathematical Society . Seeking the help of members of the society, in 1912 Ramanujan was able to secure a low-level post as a shipping clerk with the Madras Port Trust, where he was able to make a living while building a reputation for himself as a gifted mathematician.

Around this time, Ramanujan had become aware of the work of British mathematician G. H. Hardy — who himself had been something of a young genius — with whom he began a correspondence in 1913 and shared some of his work. After initially thinking his letters a hoax, Hardy became convinced of Ramanujan’s brilliance and was able to secure him both a research scholarship at the University of Madras as well as a grant from Cambridge.

The following year, Hardy convinced Ramanujan to come study with him at Cambridge. During their subsequent five-year mentorship, Hardy provided the formal framework in which Ramanujan’s innate grasp of numbers could thrive, with Ramanujan publishing upwards of 20 papers on his own and more in collaboration with Hardy. Ramanujan was awarded a bachelor of science degree for research from Cambridge in 1916 and became a member of the Royal Society of London in 1918.

Doing the Math

"[Ramanujan] made many momentous contributions to mathematics especially number theory," states George E. Andrews, an Evan Pugh Professor of Mathematics at Pennsylvania State University. "Much of his work was done jointly with his benefactor and mentor, G. H. Hardy. Together they began the powerful "circle method" to provide an exact formula for p(n), the number of integer partitions of n. (e.g. p(5)=7 where the seven partitions are 5, 4+1, 3+2, 3+1+1, 2+2+1, 2+1+1+1, 1+1+1+1+1). The circle method has played a major role in subsequent developments in analytic number theory. Ramanujan also discovered and proved that 5 always divides p(5n+4), 7 always divides p(7n+5) and 11 always divides p(11n+6). This discovery led to extensive advances in the theory of modular forms."

But years of hard work, a growing sense of isolation and exposure to the cold, wet English climate soon took their toll on Ramanujan and in 1917 he contracted tuberculosis. After a brief period of recovery, his health worsened and in 1919 he returned to India.

The Man Who Knew Infinity

Ramanujan died of his illness on April 26, 1920, at the age of 32. Even on his deathbed, he had been consumed by math, writing down a group of theorems that he said had come to him in a dream. These and many of his earlier theorems are so complex that the full scope of Ramanujan’s legacy has yet to be completely revealed and his work remains the focus of much mathematical research. His collected papers were published by Cambridge University Press in 1927.

Of Ramanujan's published papers — 37 in total — Berndt reveals that "a huge portion of his work was left behind in three notebooks and a 'lost' notebook. These notebooks contain approximately 4,000 claims, all without proofs. Most of these claims have now been proved, and like his published work, continue to inspire modern-day mathematics."

A biography of Ramanujan titled The Man Who Knew Infinity was published in 1991, and a movie of the same name starring Dev Patel as Ramanujan and Jeremy Irons as Hardy, premiered in September 2015 at the Toronto Film Festival.

QUICK FACTS

• Name: Srinivasa Ramanujan
• Birth Year: 1887
• Birth date: December 22, 1887
• Birth City: Erode
• Birth Country: India
• Gender: Male
• Best Known For: Srinivasa Ramanujan was a mathematical genius who made numerous contributions in the field, namely in number theory. The importance of his research continues to be studied and inspires mathematicians today.
• Education and Academia
• Astrological Sign: Sagittarius
• University of Madras
• Cambridge University
• Nacionalities
• Death Year: 1920
• Death date: April 26, 1920
• Death City: Kumbakonam
• Death Country: India

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• Last Updated: September 10, 2019
• Original Published Date: September 10, 2015

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Srinivasa Ramanujan (1887-1920) was an Indian mathematician who made great and original contributions to many mathematical fields, including complex analysis , number theory , infinite series , and continued fractions . He was "discovered" by G. H. Hardy and J. E. Littlewood, two world-class mathematicians at Cambridge, and enjoyed an extremely fruitful period of collaboration with them from 1914 to 1919. Unfortunately, his mathematical career was curtailed by health problems; he returned to India and died when he was only 32 years old.

Hardy, who was a great mathematician in his own right, recognized Ramanujan's genius from a series of letters that Ramanujan sent to mathematicians at Cambridge in 1913. Like much of his writing, the letters contained a dizzying array of unique and difficult results, stated without much explanation or proof. The contrast between Hardy, who was above all concerned with mathematical rigor and purity, and Ramanujan, whose writing was difficult to read and peppered with mistakes but bespoke an almost supernatural insight, produced a rich partnership.

Since his death, Ramanujan's writings (many contained in his famous notebooks) have been studied extensively. Some of his conjectures and assertions have led to the creation of new fields of study. Some of his formulas are believed to be true but as yet unproven.

There are many existing biographies of Ramanujan. The Man Who Knew Infinity , by Robert Kanigel, is an accessible and well-researched historical account of his life. The rest of this wiki will give a brief and light summary of the mathematical life of Ramanujan. As an appetizer, here is an anecdote from Kanigel's book.

In 1914, Ramanujan's friend P. C. Mahalanobis gave him a problem he had read in the English magazine Strand . The problem was to determine the number \( x \) of a particular house on a street where the houses were numbered \( 1,2,3,\ldots,n \). The house with number \( x \) had the property that the sum of the house numbers to the left of it equaled the sum of the house numbers to the right of it. The problem specified that \( 50 < n < 500 \).

Ramanujan quickly dictated a continued fraction for Mahalanobis to write down. The numerators and denominators of the convergents to that continued fraction gave all solutions \( (n,x) \) to the problem \((\)not just the particular one where \( 50 < n < 500). \) Mahalanobis was astonished, and asked Ramanujan how he had found the solution.

Ramanujan responded, "...It was clear that the solution should obviously be a continued fraction; I then thought, which continued fraction? And the answer came to my mind."

This is not the most illuminating answer! If we cannot duplicate the genius of Ramanujan, let us at least find the solution to the original problem. What is \( x \)?

\(\) Bonus: Which continued fraction did Ramanujan give Mahalanobis?

This anecdote and problem is taken from The Man Who Knew Infinity , a biography of Ramanujan by Robert Kanigel.

Taxicab numbers, nested radicals and continued fractions, ramanujan primes, ramanujan sums, the ramanujan \( \tau \) function and ramanujan's conjecture.

Many of Ramanujan's mathematical formulas are difficult to understand, let alone prove. For instance, an identity such as

\[\frac1{\pi} = \frac{2\sqrt{2}}{9801}\sum_{k=0}^{\infty} \frac{(4k)!(1103+26390k)}{(k!)^4 396^{4k}}\]

is not particularly easy to get a handle on. Perhaps this is why the most famous mathematical fact about Ramanujan is trivial and uninteresting, compared to the many brilliant theorems he proved.

The story goes that Hardy was visiting Ramanujan in the hospital, and remarked offhandedly that the taxi he had taken had a "dull number," 1729. Instantly Ramanujan replied, "No, it is a very interesting number! It is the smallest positive integer expressible as the sum of two positive cubes in two different ways."

That is, \( 1729 = 1^3+12^3 = 9^3+10^3 \).

Hardy and Wright proved in 1938 that for every \( n \), there is a positive integer \( \text{Ta}(n) \) that is expressible as the sum of two positive cubes in \( n \) different ways. So \( \text{Ta}(2) = 1729 \). \((\)The value of \( \text{Ta}(2) \) had been known since the \(17^\text{th}\) century, which is in some sense characteristic of Ramanujan as well: as he was largely self-taught, he was often rediscovering theorems that were already well-known at the same time as he was constructing entirely new ones.\()\) The numbers \( \text{Ta}(n) \) are called taxicab numbers in honor of Hardy and Ramanujan.

Ramanujan developed several formulas that allowed him to evaluate nested radicals such as \[ 3 = \sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{\cdots}}}}. \] This is a special case of a result from his notebooks, which is proved in the wiki on nested functions .

He also contributed greatly to the theory of continued fractions . One of the identities in his letter to Hardy was \[ 1+\frac{e^{-2\pi}}{1+\frac{e^{-4\pi}}{1+\frac{e^{-6\pi}}{\cdots}}} = \left( \sqrt{\frac{5+\sqrt{5}}2} - \frac{1+\sqrt{5}}2 \right)e^{2\pi/5}. \] This and several others along these lines were among the results that convinced Hardy that Ramanujan was a brilliant mathematician. This result is in fact a special case of the Rogers-Ramanujan continued fraction , which is of the form \[ R(q) = \frac{q^{1/5}}{1+\frac{q}{1+\frac{q^2}{1+\frac{q^3}{\cdots}}}} \] and is related to the theory of modular forms, a deep branch of modern number theory.

Ramanujan's work with modular forms produced the following celebrated divisibility results involving the partition function \( p(n) \): \[ \begin{align} p(5k+4) &\equiv 0 \pmod 5 \\ p(7k+5) &\equiv 0 \pmod 7 \\ p(11k+6) &\equiv 0 \pmod{11}. \end{align} \] Ramanujan commented in the paper in which he proved these results that there did not appear to be any other simple results of the same type. But in fact there are similar congruences of the form \( p(ak+b) \equiv 0 \pmod n \) for any \( n \) relatively prime to \( 6\); this is due to Ken Ono (2000). (Even for small \( n\), the values of \( a \) and \( b \) in the congruences are quite large.) The topic remains the subject of much contemporary research.

Ramanujan proved a generalization of Bertrand's postulate , as follows: Let \( \pi(x) \) be the number of positive prime numbers \( \le x \); then for every positive integer \( n \), there exists a prime number \( R_n \) such that \[ \pi(x)-\pi(x/2) \ge n \text{ for all } x \ge R_n. \] \((\)The case \( n = 1 \), \( R_n = 2 \) is Bertrand's postulate.\()\)

The \( R_n \) are called Ramanujan primes .

The sum \( c_q(n) \) of the \(n^\text{th}\) powers of the primitive \( q^\text{th}\) roots of unity is called a Ramanujan sum . It can be shown that these are multiplicative arithmetic functions , and in fact that \[c_q(n) = \frac{\mu\left(\frac qd\right)\phi(q)}{\phi\left(\frac qd\right)},\] where \( d = \text{gcd}(q,n)\), and \( \mu \) and \( \phi \) are the Mobius function and Euler's totient function , respectively.

Let \(c_{2015}(n)\) be the sum of the \(n^\text{th}\) powers of all the primitive \(2015^\text{th}\) roots of unity, \(\omega.\) Find the minimal value of \(c_{2015}(n)\) for all positive integers \(n\).

This year's problem

Ramanujan found nice infinite sums of the form \( \sum a_n c_q(n) \) or \( \sum a_q c_q(n) \) representing the standard arithmetic functions that are important in number theory. For instance, \[ d(n) = -\frac1{2\gamma+\ln(n)} \sum_{q=1}^{\infty} \frac{\ln(q)^2}{q} c_q(n), \] where \( \gamma \) is the Euler-Mascheroni constant .

Another example: the identity \[ \sum_{q=1}^{\infty} \frac{c_q(n)}{q} = 0 \] turns out to be equivalent to the prime number theorem .

Sums involving \( c_q(n) \) are known as Ramanujan sums ; these were also used in applications including the proof of Vinogradov's theorem that every sufficiently large odd positive integer is the sum of three primes.

Ramanujan's \( \tau \) function is defined by the formula \[ \sum_{n=1}^{\infty} \tau(n) q^n = q\prod_{n=1}^{\infty} (1-q^n)^{24} \] and is related to the theory of modular forms.

Ramanujan conjectured several properties of the \( \tau \) function, including \[ |\tau(p)| \le 2p^{11/2} \text{ for all primes } p. \] This turned out to be an extremely important and deep result, which was proved in 1974 by Pierre Deligne in his Fields-medal-winning proofs of the Weil conjectures on points on algebraic varieties over finite fields.

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Aryabhata the elder.

... no final verdict can be given regarding the locations of Asmakajanapada and Kusumapura.

... Aryabhata was an author of at least three astronomical texts and wrote some free stanzas as well.

... it is extremely likely that Aryabhata knew the sign for zero and the numerals of the place value system. This supposition is based on the following two facts: first, the invention of his alphabetical counting system would have been impossible without zero or the place-value system; secondly, he carries out calculations on square and cubic roots which are impossible if the numbers in question are not written according to the place-value system and zero.

Add four to one hundred, multiply by eight and then add sixty-two thousand. the result is approximately the circumference of a circle of diameter twenty thousand. By this rule the relation of the circumference to diameter is given.

Aryabhata I's value of π is a very close approximation to the modern value and the most accurate among those of the ancients. There are reasons to believe that Aryabhata devised a particular method for finding this value. It is shown with sufficient grounds that Aryabhata himself used it, and several later Indian mathematicians and even the Arabs adopted it. The conjecture that Aryabhata's value of π is of Greek origin is critically examined and is found to be without foundation. Aryabhata discovered this value independently and also realised that π is an irrational number. He had the Indian background, no doubt, but excelled all his predecessors in evaluating π. Thus the credit of discovering this exact value of π may be ascribed to the celebrated mathematician, Aryabhata I.

Aryabhata is the master who, after reaching the furthest shores and plumbing the inmost depths of the sea of ultimate knowledge of mathematics, kinematics and spherics, handed over the three sciences to the learned world.

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Additional Resources ( show )

Other pages about Aryabhata:

• See Aryabhata on a timeline
• Astronomy: The Structure of the Solar System
• Heinz Klaus Strick biography

Other websites about Aryabhata:

• Dictionary of Scientific Biography
• Google books
• Sci Hi blog

Honours ( show )

Honours awarded to Aryabhata

• Lunar features Crater Aryabhata
• Popular biographies list Number 37

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• Student Projects: Indian Mathematics - Redressing the balance: Chapter 10
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Life of Srinivasa Ramanujan

• First Online: 31 May 2021

Cite this chapter

• K. Srinivasa Rao 2  

Srinivasa Ramanujan, the brilliant twentieth-century Indian mathematician, has been compared with all-time great Leonhard Euler, Carl Friedrich Gauss and Carl Gustav Jacob Jacobi, for his natural mathematical genius. This book is a biography of the life and work of Ramanujan.

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Carl Friedrich Gauss, April 30, 1777–February 23, 1855.

Carl Gustav Jacob Jacobi, December 10, 1804–February 18, 1851.

“Relevance of Srinivasa Ramanujan at the Dawn of the New Millennium”, K. Srinivasa Rao, (2002) in A.K. Agarwal, B.C. Berndt, C.F. Krattenthaler, G.L. Mullen, K. Ramachandra, M. Waldschmidt (eds), Number Theory and Discrete Mathematics , Hindustan Book Agency, Gurgaon (2002) 261–268.

It is unfortunate that there is no photograph of the father of Srinivasa Ramanujan. A close look at the photographs of Ramanujan and his mother Komalathammal reveals the strong resemblance between the mother and son.

“Naalayiram” in Tamizh means four thousand, “Divya Prabhandam” means Divine collection of hymns in praise of the god Narayana, the sustainer of all creations in the Universe—composed and sung by His devotees, referred to as Azhwars, in the Tamizh language.

In Sanskrit, “Akshara” means letter and “abhyasa” means practising (to read/write).

“Vijayadashami”, also known as Dasara or Dusshera, reveres victory of good over evil—Rama’s victory over Ravana, in the epic Ramayana, and the day the Pandava’s came out of their 13th year of banishment, spent incognito, in the epic Mahabharata.

At the beginning of the twentieth century, India was under the British rulers. Indians tried to master the English language to impress their superior officers, to gain an advantage in the form of favours and recommendations to positions of importance. Some of the important books published in England were available within a short time in Indian libraries also.

The Fourth Form corresponds to the current IX standard in schools.

Reminiscences of my esteemed Teacher , K.S. Viswanatha Sastri, in Ramanujan Letters and Reminiscences , Edited by P.K. Srinivasan, (1968), Vol. I, pp. 89–93.

To this intriguing question of 0∕0, the Hindu ancient mathematician Bhaskara proved the answer to be infinity.

My Association with Ramanujan , in Ramanujan: Letters and Reminiscences , Memorial Number 1 (1968), Ed. P.K. Srinivasan, The Muthialpet High School, Madras-1, Volume 1, p.83–88.

Notebooks of Srinivasa Ramanujan , (facsimile edition) 2 volumes, Tata Institute of Fundamental Research, Bombay, 1957; Narosa, New Delhi, 1987. Reprinted in 2012 by the National Board for Higher Mathematics (NBHM).

Oxford University Press Warehouse, 1895—as pointed out by N. Hari Rao, a classmate of Ramanujan in Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, Muthialpet High School (1968) pp. 120–123.

We two together in the college , in Ramanujan: Letters and Reminiscences, Memorial Number , Vol. 1, The Muthialpet High School, 1968, p. 120–123.

Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work , G.H. Hardy, Chelsea (1940) and Reprinted by the Am. Math. Soc. and the London Math. Soc. (1999).

An excellent exposition of the Mathematical Tripos of Cambridge, a coveted examination which Hardy took but in later years denounced, can be found in Robert Kanigel’s The Man Who Knew Infinity , Charles Scribner’s, New York (1991).

Private communication to the author, when Prof. Askey visited India on the occasion of the Birth centenary of Ramanujan in December 1987.

Ref. Kanigel’s The Man Who Knew Infinity , Charles Scribner’s, New York (1991) p. 57.

There are several teachers now in our country who are capable of propagating the nuances of creating even and odd magic squares, date magic squares, rectangular magic squares, squares which include negative numbers as well or even fractions and even create 100 × 100 squares. One such person who is a Railway Station Master, who can be contacted, is T.R. Jothilingam, Retired Railway Superintendent, Madurai. He was selected by the All India Ramanujan Maths Club, New Delhi, for the Ramanujan Award for 2016. The author provided him with all the dates of relevance in the life of Ramanujan, with which he formed a large magic sqaure. The interested reader may contact him at: [email protected].

Note: Social reformers like Raja Ram Mohan Roy, Kandukuri Veeresalingam Panthulu and E.V. Ramaswami Naicker were yet to awaken the public to protest against child marriages, which, in later years, became illegal under the Hindu Marriages Act.

K.S. Viswanatha Sastri, whose article can be found in Ramanujan: Letters and Reminiscences , ed. P.K. Srinivasan, Publisher: The Muthialpet High School, Madras, Vol. 1 (1968).

Sri Ramaswamy Iyer was a lover of Mathematics, and when he received a reply from London with the cover addressing him as Professor Ramaswamy Iyer, his friends started calling him, and addressing him as ‘Professor’ from then on, though he never was a Professor in any educational institution!

Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, The Muthialpet High School, Madras, Vol. 1 (1968) p. 129.

Ref.: Extract from late Dewan Bahadur Ramachandra Rao’s reminiscences, in Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, The Muthialpet High School, Madras, Vol. 1 (1968) pp. 126–127.

Perhaps due to the reluctance with which he was given an audience (on the fifth visit) by the status conscious Dewan Bahadur Ramachandra Rao, Ramanujan initially did not avail himself of this dole. But later reluctantly did accept the same for a short period of time, till he got the first ever research scholarship of the University of Madras.

Notebooks of Srinivasa Ramanujan , (facsimile edition), 2 Volumes, Tata Institute of Fundamental Research, Bombay, 1957; reprinted by Noarsa, New Delhi, 1987.

Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, Muthialpet High School, Madras, Vol. 1 (1968) p. 125.

Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, Muthialpet High School, Madras, Vol. 1 (1968) p. 112.

Ref. Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, Muthialpet High School, Madras-1, Vol. 1 (1968) p. 115.

Griffith to Sir Francis Spring: To keep Ramanujan happily employed , Letter dated 12 Nov. 1912; in Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, Muthialpet High School, Madras Vol. 1 (1968) p. 50.

M.J.M. Hill to C.L.T. Griffith: Fallen into pitfalls , dated 3 Dec. 1912; in Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, Muthialpet High School, Madras, Vol. 1 (1968) p. 53.

Ramanujan: Letters and Commentary , by Bruce C. Berndt and Robert A. Rankin, AMS-LMS (1995). Also, Indian Edition with a Preface, Additions to the Indian Edition and Errata, by K. Srinivasa Rao, published by Affiliated East West Press Pvt. Ltd. (1997).

The first 25 prime numbers are: 2,3,5,7; 11,13,17,19; 23,29; 31,37; 41,43,47; 53,59; 61,67; 71,73,79; 83,89; 97 and from this one can say that there are 4 prime numbers below 10; 8 below 20; 10 below 30; 13 below 50; 15 below 60; 17 below 70; 20 below 80; 22 below 90 and below 100 there are 25 prime numbers which we can write as: p (10) = 4, p (20) = 8, p (30) = 10, p (40) = 12, p (50) = 15, p (60) = 17, p (70) = 19, p (80) = 22, p (90) = 24 and p (100) = 25. One of the significant contributions of Ramanujan was to discover an exact formula for p ( n ). Only the asymptotic formula \(p(n)\sim n/\log n\) was known to Gauss.

Collected Papers of Ramanujan , Ed. G.H. Hardy, P.V. Seshu Aiyar and B.M. Wilson, AMS Chelsea Publishing (2000), p. xxii.

Godfrey Harold Hardy, was born on February 7, 1877, more than 10 years before Ramanujan was born, on December 22, 1887. In early 1947, a confirmed bachelor, Hardy tried to kill himself, by swallowing too many barbiturates, which made him vomit. He was possibly driven to this extreme since he was virtually an invalid for about a year by then and died on December 1, 1947, the day he was to receive the highest honour, the Copely Medal, from the Royal Society of London.

I am thankful to Mr. Pacha Nambi, s/o Mr. Nambi Iyengar (who was the Personal Assistant of Professor Alladi Ramakrishnan) for sending me a copy of this book in September 1998, which was brought out as an Indian Edition, by M/s. Allied Publisher (India) Pvt. Ltd., after I got the required permission of Prof. Bruce Berndt and all concerned.

Reprinted in Ramanujan: Letters and Commentary , by Bruce C. Berndt and Robert A. Rankin, with Additions to the Indian edition and errata, by K. Srinivasa Rao, Affiliated East-West Press Pvt. Ltd. (1997).

Ramanujan: Letters and Commentary , Bruce C. Berndt and Robert A. Rankin, Am. Math. Soc. and London Math. Soc. (1995) p. 44.

This reference is most probably to Prof. M.J.M. Hill. Ref. M.J.M. Hill to C.L.T. Griffith, in Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, Memorial Number, vol. 1, Muthialpet High School, Chennai-1 (1968) p. 53.

Ramanujan: Letters and Commentary , Ed. Bruce C. Berndt and Robert A. Rankin, AMS-LMS (1995) p. 17.

The Riemann zeta-function is defined as: \(\zeta (s)=\sum _{n=0}^\infty \frac {1}{n^s}, Re\ s>1\) . The ζ function has a unique analytic continuation to the point s  = −1, and it is known that ζ (−1) = −1∕12. With hind sight, in the modern day notation, we may say that Ramanujan combined the series definition of: ζ (−1) = 1 + 2 + 3 + 4 + ⋯ with its value ζ (−1) = −1∕12, equated the two right hand sides into the one equation of his, viz. that the sum of the series: 1 + 2 + 3 + 4 + ⋯ is equal to − 1∕12.

S. Ramanujan, Notebooks (2 Volumes), Tata Institute of Fundamental Research, Bombay (1957).

C.P. Snow, in his Foreword to G.H. Hardy’s: A Mathematician’s Apology , Cambridge University Press (1967) p. 30.

p.10 in C.P. Snow’s Introduction in A Mathematician’s Apology , G.H. Hardy, ‘Orders of Infinity’, Cambridge Univ. Press, Cambridge (1910).

Allied Publishers, New Delhi, 1980.

Also see, Bruce C. Berndt, Ramanujan Notebooks , Part I, Springer-Verlag (1985) p. 3.

S. Narayana Iyer, M.A.(Maths.), was one who can be considered the foremost among the benefactors of Ramanujan. He not only supported Ramanujan all through and was indeed a friend, philosopher, guide and perhaps, even a scribe, on occasions for letters written to Hardy, but also continued to support Mrs. Ramanujan throughout his lifetime.

Ramanujan: Letters and Reminiscences , Memorial Vol. No.1, Ed. P.K. Srinivasan, The Muthialpet High School, Madras, Vol. 1 (1968), p. 55.

Ramanujan was getting a salary of Rs. 25/- per month when he was in the Accountant General’s Office and Rs. 30/- per month when he was at the Madras Port Trust. The salary of a Professor in those days was Rs. 225/- per month.

The quotations are from the Introduction to the Collected Papers of Srinivasa Ramanujan , Ed. G.H. Hardy, P.V. Seshu Aiyar and B.M. Wilson, Cambridge the University Press, Cambridge (1927), Second edition, Chelsea, New York (1962).

C.P. Snow in his Foreword to G.H. Hardy’s A Mathematician’s Apology , Cambridge University Press (1967) p. 30.

The Meteorological Observatory has been shifted to Pune, in later years.

Ramanujan was getting a salary of Rs. 25/- per month when he was in the Accountant General’s Office and Rs. 30/- per month when he was at the Madras Port Trust.

Ramanujan’s Notebooks , Bruce C. Berndt, Springer-Verlag, Part I (1985)–Part V (1997).

Ref. Bruce C. Berndt and Robert A. Rankin, Ramanujan: Letters and Commentary , AMS-LMS (1999), for these and other letters referred to in this article.

Crossing the oceans was considered a sacrilege by the Hindu Brahmins, and people who did so were, on their return to India, treated as out-castes. All relationships with such foreign returned individual and even their families were shunned!

From Obscurity to Fame , E.H. Neville, in Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, Muthialpet High School, Madras (1968) pp. 138–141.

E.H. Neville to Dewsbury: The Discovery of the Genius of Ramanujan , in Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, Muthialpet High School, Madras (1968) p.59.

Littlehailes to Dewsbury: First Research Student in Mathematics , in Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, Muthialpet High School, Madras (1968) pp. 61–63.

The second class fare between London and Bombay was £32/- in 1914, or about Rs. 480/-.

Sir Francis Spring to C.B. Cotterell, in Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, Muthialpet High School publication, (1968) pp. 64–65.

Traditionally April 14 is the Tamil New Year’s day, in India.

Letter to R. Krishna Rao: ’Letter 2. Arrival in London on 14-4-1914 and settling done at Trinity College’, dated 11 June 1914, in Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, Muthialpet High School, Madras-1 publication, (1968) pp. 5–7.

From the article ‘My Father and Ramanujan’ of Mr. Narayana Iyer’s son, N. Subbanarayanan, in Ramanujan: Letters and reminiscences , Ed. P.K. Srinivasan, Muthialpet High School, Madras-1, publication, (1968) pp. 112–115.

‘Srinivasa Ramanujan’, J.R. Newman in ‘Mathematics in the Modern World’, W.H. Freeman & Co., (1968) pp. 73–76.

Collected papers of Srinivasa Ramanujan , Ed. G.H. Hardy, P.V. Seshu Aiyar and B.M. Wilson, AMS Chelsea Publishing (2000), p. xxx.

The Man Who Knew Infinity: A Life of the Genius Ramanujan , Robert Kanigel, Rupa & Co, 1994, p. 226.

Outbreak of First World War , dated Nov.13, 1914, in Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, Muthialpet High School, Madras (1968), pp. 12–19.

Letter to S.M. Subramanian, (a classmate of Ramanujan during his School days) in Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, Muthialpet High School, Madras (1968) pp. 21–27.

My friendship with Ramanujan in England , P.C. Mahalanobis—who became later the eminent mathematician of India who started the Indian Statistical Institute in Calcutta—in Ramanujan: Letters and Commentary , Ed. P.K. Srinivasan, Muthialpet High School, Madras-1, (1968) pp. 145–148.

‘Hardy to Dewsbury’, in Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, Muthialpet High School, Madras-1, (1968) pp. 76–77.

Ramanujan: Letters and Commentary, B.C. Berndt and R.A. Rankin, AMS-LMS (1995) p. 137.

Collected Papers of Srinivasa Ramanujan , Ed. by G.H. Hardy, P.V. Seshu Aiyar and B.M. Wilson, AMS Chelsea Publishing, AMS, Providence, Rhode Island (2000) p. xxxiv.

Robert Kanigel, The Man Who Knew Infinity: A Life of the Genius Ramanujan , Charles Scribner’s Sons, New York (1991) p. 233.

S. R. Ranganathan, Ramanujan: The Man and the Mathematician , Asia Publishing House (1967).

Robert Kanigel, The Man Who Knew Infinity: A Life of the Genius Ramanujan , Charles Scribner’s Sons, New York (1991), Indian edition published by Rupa & Co. (1994).

R.A. Rankin, Ramanujan as a patient , Proc. Indian Acad. Sci., Math. Sci. 93 (1984) 79–100.

Dr. D.A.B. Young, Ramanujan’s illness , Current Science, 67 (1994) 967–972.

This word “medicography” is coined by the author as an abbreviation for medical biography. While “Discography” is in the Dictionaries, this word Medicography is yet to find its place in the Dictionaries!

The first case of amoebiasis was documented in 1875, and in 1891 the disease was described in detail, resulting in the terms amoebic dysentery and amoebic liver abscess. Amoebiasis, also known as amoebic dysentery, is an infection caused by any of the amoebae of the Entamoeba group. Amoebiasis can be mild and asymptomatic. Symptoms may include abdominal pain, diarrhoea or bloody diarrhoea.

Mr. P.K. Srinivasan, was a Fulbright Scholar for 2 years in the USA, and a Mathematics Teacher at the Muthialpet High School, Chennai, when he formed a Number Friends Society and an Old Boys’ Committee, to acquire, from 1962 to 1967, articles which are the contents of two Ramanujan Memorial Numbers: Ramanujan: Letters and Reminiscences and Ramanujan: An Inspiration. An Appreciation by Bharat Ratna, Dr. S. Radhakrishnan, Former President of India, is a fitting tribute to this stupendous effort, which has been the main source for several later day biographers, including the present author, who acquired copies of these volumes, for the Library of the IMSc, and for himself, in 1967.

Private communication by e-mail, dated 29 March 1996.

In Srinivasa Ramanujan, 1887–1920: A Tribute , Ed. K.R. Nagarajan and T. Soudararajan, Macmillan India Ltd. (1988) and articles therein by K. Srinivasa Rao, G.E. Andrews, R. Askey, B.C. Berndt, R.P. Agarwal, A. Verma, S. Bhargava, M.V. Subbba Rao and T. Soundararajan. All these articles were obtained on request by the present author.

One Stone weight is equal to 14 pounds, or about 6.6 kg.

D.A.B. Young, Ramanujan’s illness , Current Sci. 67 (1994) 967–972.

Hardy in his letter to Dewsbury, the Registrar of the University of Madras—refer Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, in Ramanujan Memorial No. 1, Muthialpet High School, Chennai, pp. 76–77.

S.R. Ranganathan, Ramanujan: The Man and the Mathematician , Asia Pub. House (1967).

D.A.B. Young, Ramanujan’s illness , Current Science, 67 (1994) 967–972.

G.H. Hardy, A Mathematician’s Apology , Cambridge Univ. Press (1976) p. 71.

A few examples which can be cited which explode The Myth of the Young Mathematician are: Newton’s Principia was written when he was in his mid-40s; Euler, despite his blindness, produced his three volumes on integral calculus when he was in his 60s; Gauss at 34 proposed his theory of analytic functions; and in more recent times, Elie Cartan, Poincaré, Siegel, Kolmogorov and Erdös exhibited creativity in mathematics in their later years—ref. Susan Landau, Notices of the Am. Math. Soc. 44 (1997) 1284.

The street names in Madras (officially renamed Chennai, in 1966) have been renamed by the caste conscious State Government regimes. So ridiculous were some of the changes that Netaji Subhash Chandra Bose Road, or N.S.C. Bose Road, Krishnamachari Road and Dr. Nair Road, were renamed, respectively as N.S.C. Road, Krishnama Road and Doctor Road! Needless to say, the Government turned a deaf year to appeals, in 1987, by the author and several others, to rename the Wallajah Road, where the Ramanujan Institute for Advanced Study in Mathematics of the University of Madras eventually moved to its own premises, as Ramanujan Road.

Bombay has been renamed as Mumbai .

The author accompanied each one of them and some others also, when they expressed their desire to meet the gracious lady, as a mark of respect to her husband. When Professor Askey asked her whether she had conjugal relationships with her husband, her answer was in the affirmative and there was a shy smile on her face. The Ramanujans had no children, and it is this fact that, perhaps, prompted Prof. Askey to raise the question.

E.H. Neville, in Ramanujan: Letters and Reminiscences , Memorial Number, vol.1, Ed. P.K. Srinivasan, Muthialpet High School (1968) pp. 59–60.

G.H. Hardy Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work , Chelsea, New York (1940).

G.H. Hardy to Subramanian, in Ramanujan: Letters and Reminiscences , Ed. P.K. Srinivasan, Muthialpet High School, Chennai-1 (1968), pp. 68–75.

‘Notes’ of S. Narayana Iyer, CAC, Madras Port Trust, 15-4-1915.

Letter to the Registrar from Sir Francis Spring, undated and handwritten on plain paper.

This was probably Ramanujan’s way of explaining away his incomparable intuition and success of his discoveries, to those who are unable to comprehend his ability to churn out continuously new theorems, persisted in questioning him as to how he discovered those results!

K. Ananda Rao, in Ramanujan: Letters and Reminiscences , Memorial Number, Vol.1, Ed. P.K. Srinivasan, Muthialpet High School, Madras (1968) p. 143.

Copy of the letter of Ramanujan to the Registrar, University of Madras, is in the list of Plates of S.R. Ranganathan Ramanujan: The Man and the Mathematician , Asia Publishing House (1967).

It is unfortunate that in the movie based on the book of Robert Kanigel, The Man Who Knew Infinity: A Life of the Genius Ramanujan , Charles Scribner’s Sons, New York (1991), Ramanujan is portrayed as an angry youngman, by an actor, who, in one scene, even shouts at Hardy and asks: “Who are you, Hardy?”, unthinkable and inexplicable from the writings of any of Ramanujan’s contemporaries—our only reliable sources of information available on any aspect of the life of Ramanujan, which inspired the author of this book.

Ramanujan’s letter to S. Narayana Iyer, in Ramanujan: Letters and Reminiscences , Memorial Number, Vol.1, Ed. P.K. Srinivasan, Muthialpet High School, Madras (1968) p. 32.

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UPSC IAS Exam: List of Indian Mathematicians and their Contributions

In UPSC Exam, there have been questions related to poets, saints of Ancient Indian History, Medieval Indian History and that too on foreign travellers from the section of Modern Indian History. Similarly, questions can be asked on the Indian Mathematicians from Ancient Indian to Modern Indian times in IAS Exam .

This article will provide you with a list of Indian Mathematicians and their contributions in India.

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It is essential to know about the ancient, medieval and modern time Indian mathematicians and their contribution to Science and Mathematics. Ancient Indian mathematicians have contributed immensely to the field of mathematics. The invention of zero is attributed to Indians and this contribution outweighs all other made by any other nation since it is the basis of the decimal number system, without which no advancement in mathematics would have been possible. The number system used today was invented by Indians and it is still called Indo-Arabic numerals because Indians invented them and the Arab merchants took them to the western world.

Here we are giving the list of important Indian mathematicians from ancient to modern times.

Famous Indian Mathematicians and their Contributions

1. Bhaskara

• He is also known as Bhaskaracharya.
• He was born in 1114.
• He was the one who acknowledged that any number divided by zero is infinity and that the sum of any number and infinity is also infinity.
• The famous book “Siddhanta Siromani” was written by him.

2. Aryabhata

• He was born in 476 CE at Kusumapura.
• He was regarded as the first of the major mathematician-astronomers from the classical age.
• Aryabhaṭiya and Arya-Siddhanta were his known works.
• He worked on the ‘place value system’ using letters to signify numbers and stating qualities.
• He discovered the position of the 9 planets and found that these planets revolve around the sun.
• He also described the number of days in a year to be 365.

3. Brahmagupta

• He was born in 598 CE near present-day Rajasthan.
• The most important contribution of Brahmagupta to mathematics was introducing the concept and computing methods of zero (0).

4. Srinivasa Ramanujan

• He was born on 1887.
• Hardy-Ramanujan-Littlewood circle method in number theory
• Roger-Ramanujan’s identities in the partition of numbers
• Work on the algebra of inequalities
• Elliptic functions
• Continued fractions
• Partial sums and products of hypergeometric series

5. P.C. Mahalanobis

• P.C. Mahalanobis was born in 1893.
• Mahalanobis distance
• Feldman–Mahalanobis model

6. Calyampudi Radhakrishna Rao

• R Rao was born in 1920.
• He is a well-known statistician.
• He is famous for his ‘Theory of estimation’.
• Cramer–Rao bound
• Rao–Blackwell theorem
• Orthogonal arrays

7. D. R. Kaprekar

• D. R. Kaprekar was a recreational mathematician.
• He discovered several results in number theory, comprising a class of numbers and a constant named after him.

8. Satyendranath Bose

• He was born in 1894.
• He is known for his collaboration with Albert Einstein.
• He is best known for his work on quantum mechanics.
• Bose-Einstein correlations
• Bose-Einstein condensate
• Bose-Einstein distribution
• Bose-Einstein statistics
• Ideal Bose equation of state.

9. Shakuntala Devi

• Known as the ‘Human Computer’ she was famous for solving the most complex maths equations without needing calculators.
• She was famous for setting many world records in mathematics with her superior intellect

10. Narendra Karamkar

• Best known for his work regarding polynomial algorithms. He is listed as an ISI highly cited researcher.
• Narendra Karamkar one of the first provably polynomial time algorithms for linear programming, which is generally referred to as an interior point method. The algorithm is a cornerstone in the field of Linear Programming.

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List of Top 10 Most Famous Indian Mathematicians and Their Contributions

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Many of you may find Mathematics confusing, while others love ( fall in love meaning and origin ) playing with numbers. However, no matter if you like or dislike maths, it plays an essential role in our everyday things. But you know there numerous Indian mathematicians who have received recognition from all around the globe. Can you think of any Indian mathematicians names? If you can’t, then after reading this article, you will always remember the great mathematicians of India. Here is the list of famous Indian mathematicians with pictures and names for you all.

Here is a list of the Great Indian Mathematicians and Their Contributions

1. srinivasa ramanujan.

1887 born, Srinivasa Ramanujan was a splendid Indian mathematician who gets credited even today for his commitments in the field of maths. Srinivasa Ramanujan mathematician was an astoundingly brilliant child who might dominate different kids of his age in maths. He belonged from Tamil Nadu, where his family was not well enough to support his passion for Mathematics.

George S. Carr’s book, ‘Synopsis of elementary results in pure mathematics, became his inspiration to follow his passion. Today, Ramanujan mathematician, remembered for inventions of important equations, the infinite series of π, and game theory. The year 1914 was the defining moment in the striving life of the virtuoso mathematician. G.H.Hardy, the great mathematician, invited him to Cambridge. In 1916, he was granted his PhD by the institution. Ramanujan died at an early age because of Tuberculosis in 1920. Although the great mathematician Ramanujan deceased at a young age, he is one of the top 5 Indian mathematicians.

2. Bhaskara I

Bhaskara, the 7 th -century famous Indian mathematician, was born in c.600 and died in CE 680. He is one of the ancient Indian mathematicians who is known for his contribution to maths. Bhaskara mathematician is famous for inventing the Hindu decimal system. This Aryabhata follower wrote a critique, ‘Aryabhatiyabhasya’ in CE 629, which is considered the oldest known Sanskrit language work in the mathematics & astronomy field. In addition, his other works include Mahabhaskariya and Laghubhāskarīya.

Mahabhaskariya comprises 8 chapters, dwelling on mathematical astronomy. The book discusses the relationship between cosine and sine and gives the sin x approximation formula. The book likewise examines about longitudes of the planets, conjunctions of the planets with one another and with eclipses of the sun & the moon, shining stars, the lunar crescent, risings and settings. Furthermore, the book explains the relationship between the sine of a point >90° >180° or >270° to the sine of a point <90°. Pell Equation ( 8x² + 1 = y² ) is given by Bhaskara I. Brahmagupta and Bhaskara I are the two great mathematicians of Ancient India.

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3. aryabhatta.

476-550 CE, the golden period of India in which Aryabhatta, the scientist, astronomer and mathematician, lived. Aryabhatta, Indian mathematician’s contributions include the discovery of the spherical shape of the earth, the number of days in 1 year and notable works are Aryabhatasiddhanta and Aryabhatiya. The former work is lost, and Aryabhatiya has three sections. These sections are:

• Ganita (Mathematics): This section has the names of the first 10 decimal places and provides algorithms for finding cube and square roots through decimals. In this second, he noticed the second-order sine difference and sine numbers are proportional. Aryabhatta is known for involving one of the two strategies for making the table of sines by utilizing the Pythagorean hypothesis.
• Kala-kriya (Time Calculations): Aryabhata examines cosmology like planetary movements, meanings of different units of time ( race against time phrase meaning ) so forth.
• Gola (Sphere): In this section, the mathematician used trigonometry for spherical geometry.

4. Brahmagupta

7 th -century Rajasthan astronomer and mathematician, Brahmagupta is famous for his work Brāhmasphuṭasiddhānta.’ The book is related to the use of 0 as a number in calculations. A large portion of his works was in the Sanskrit language. Brahmagupta, mathematician of Ancient India, also known as Bhillamalacarya, is recognized for his contribution to Arithematics, Trigonometry (Sine Table and Interpolation formula), and solutions to general linear equation, Brahmagupta’s Theorem and Brahmagupta’s Formula. Brahmagupta couldn’t finish the utilization of 0 in calculations with respect to division; however, he offered calculations, for example, (1 + 0 = 1; 1 – 0 = 1; and 1 x 0 =0), for utilizing the digit 0. The reason why he is known as the best mathematician in the world is the discovery of negative numbers and their calculations. Further, the establishment of √10 (3.162277) by Brahmagupta gave new dimensions to trigonometry and geometry.

5. P.C. Mahalanobis

In the list of the famous Indian mathematicians, P.C.Mahalanobis is one of them. In 1893, he was born in Kolkata. Mahalanobis completed his graduation from Presidency College in Physics and went to Cambridge for higher education in Physics and Mathematics. He is known as a Mathematician, Scientist and Statistician, and also an Indian Father of Statistics. In the year 1913, he was one of the people who contributed to the foundation of Indian Statistical Institute (ISI) in India. His contribution to the forming of Planning Commission of India is unquestionable, and in 1926, he laid the establishment of Hirakund Dam in Odisha on Mahanadi river. One of his best-known works is D2-statistic or Mahalanobis Distance. This distance is the measurement proportion of correlation between two distinct data sets.

6. Satyendra Nath Bose

S.N.Bose, famously known for Bose-Einstein Condensate, is among the top 10 mathematicians of India. Satyendra Nath Bose was an Indian mathematician and physicist who worked with Albert Einstein on the Bose-Einstein Condensate project. Among the Indian mathematicians’ names, Bose is one such who was felicitated with Padma Vibhushan. Bose is also referred to as the ‘Father of the God Particles’ for his contribution to Boson particle. Boson particle is also known as the God particle.

The best mathematician in India, S.N.Bose was born in Kolkata in 1894 and completed his graduation and post-graduation, majoring in mathematics. From his school day, he outperformed every year till his M.Sc. In 1915, he completed his master’s and decided to pursue higher education in 1917. During this tenure, Bose and his batchmate started translating French and German works of Albert Einstein, after getting the green flag from Einstein. Untill 1924, Planck’s Law was not proved, but this year, Bose published a paper deriving Planck’s Theory: quantum radiation law without referring to any classical physics theories. This publishing made him famous among the great mathematicians of world. Even Einstein was impressed by Bose’s work, and he translated the same into German language and was sent to European Physic Journal with Einstein’s recommendation. He died in 1974, but before that, he held several prestigious positions, including presidentship and adviser at the National Institute of Science and Council of Scientific and Industrial Research, respectively.

7. D R Kaprekar

In 1905, famous with the name ‘Ganitananda’, a future Indian mathematician was born; he was Dattathreya Ramchandra Kaprekar. In 1927, he won the Wrangler R. P. Paranjpe Mathematical Prize for his notable work in the field of mathematics. After graduating from the University of Mumbai in 1929, he started teaching in Nashik school. During his period of imparting lessons at a school, Kaprekar persistently published covering various topics like magic squares, recurring decimals and integers having special properties. The number 6174 is called Kaprekar Constant and is named after him. Kaprekar described numerous classes of natural numbers.

8. Shakuntala Devi

When asked for any female mathematicians of India, Shakuntala Devi is one name that is always on the list of the top 10 Indian mathematicians. A charismatic lady from India is recognized for her exceptional calculating speed. For this reason, she got the title of the ‘human computer.’ She was born in 1929 in Banglore. Her journey was a bit different from other famous Indian mathematicians. Shakuntala Devi, a mathematician, started her journey from memorizing cards for the show in the circuses to getting her name into the Guinness Book of World Record.

Her father acknowledged her talent, and later the entire world shouted out loud for her accomplishments. This Indian mathematician’s biography inspires and elates the motivation of everyone who thrives to do wonders as a mathematician.

9. Mahavira

In the list of Indian mathematicians, 9th-century mathematician, Mahavira is the one who is known for setting mathematics and astrology apart. He was mainly famous in the Southern region of India, and his work helped many other South Indian mathematicians to refer. He was the first Indian mathematician in the world who explained the fact that square roots don’t exist in the case of negative numbers. His work ‘Ganitasarasangraha’ includes various mathematical procedures. These vary from basic operations to miscellaneous problems of linear and quadratic equations, mixed problems, proportionality-based rule of 3, geometric calculations and reduction of fractions.

Mahavira mathematician is also known for his contribution to naming the concepts of a semicircle, circle, isosceles triangle, rhombus and equilateral triangle.

10. Narendra Karmarkar

Karmarkar procured his four-year certification in electrical engineering from IIT Bombay and proceeded to seek his PhD in the United States. He is renowned for his contribution to inventing the algorithms of the polynomial. This helped in solving the direct programming queries of linear.

After reading these Indian mathematicians’ names, you will never be able to stay dumbstruck when anyone asks Indian mathematicians and their contributions. Moreover, you will find all mathematicians’ photos with names so that in the future the changes to get confused will be a cypher.

11. C.R.Rao

Indian Mathematician, an influencer in many fields like medicine, economics and demography and the legend of statistics is C.R.Rao. Popular for the ‘Theory of Estimation’, Calyampudi Radhakrishna Rao was born in Karnataka in the year 1879. His father motivated him in the initial stage of his life, which developed Rao’s interest in mathematics. His father bought ‘Problems for Leelavathi’ for him, which comprises mathematics questions. His daily problem-solving practice later made him a famous Indian mathematician. He won Chandrasekara Iyer Scholarship and bagged a gold medal in MD in Statistics in 1943 while studying at Indian Statistical Institute. In 2001, he was felicitated with Padma Vibhushan, and the following year, George W Bush rewarded him with the National Medal of Science.

12. Harish Chandra

Harish Chandra was born in the year 1923 and is known for doing the fundamental work in representation theory. He was an Indian American physicist and mathematician. Among his numerous contributions, semisimple lie groups’ harmonic analysis is the most known. He was honored with Padma Bhusan (1977), Cole Prize (American Mathematical Society) and Srinivasa Ramanujan Medal (Indian National Science Academy).

13. Ashutosh Mukherjee

Ashutosh Mukherjee is another great mathematician of India who identified the talents of famous mathematicians like S.Radhakrishan and C.V.Raman. His contribution broadened the spectrum of maths in India. His notable contributions and numerous research papers in physics and mathematics made him achieve the zenith position in the list of eminent mathematicians. Ashutosh Mukherjee was a part of various national and international academic societies. In 1908, Ashutosh Mukherjee was the founder of the Calcutta Mathematical Society.

14. Ganesh Prasad

Ganesh Prasad, a famous Indian mathematician was born in 1876. Ganesh Prasad’s prominent works include ‘Functions of Bessel and Lame’ and ‘A Treatise for Spherical Harmonics’. He had expertise in the hypothesis of functions of a real variable, theory of potentials, Fourier series and the hypothesis of surfaces. After completing his M.A. and D.Sc. he moved to Cambridge in 1899 to pursue a higher degree. In 1904, he returned to India and initiated the development of the research culture in India. Hence, he is called the ‘father of mathematical research in India’.

List of Famous Female Mathematicians of India

Here is the list of Famous female mathematicians of India you should know:

• Raman Parimala
• Neena Gupta
• Shakuntala Devi
• Sujhata Ramdorai
• Mangala Narlikar
• Vanaja Iyengar
• Renuka Ravindra
• Ajit Iqbal Singh
• T. A. Sarasvati Amma
• Bhama Srinivasan

Famous Indian Mathematicians and their Inventions

Here are some of the great mathematicians of India and their inventions:

List of the Best Mathematicians in the World

Mathematicians from all over the world who have made their contributions in the field of Mathematics are:

• Thales of Miletus
• Eratosthenes
• Hero of Alexandria
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Srinivasa Ramanujan – Tale of the great Indian Mathematician

Imagine a little boy aged not more than 11, mastering advanced mathematics of the university level on his own. Unbelievable, right? This boy turned out to be the great Indian Mathematician, Srinivasa Ramanujan. Known as the ‘Man who knew Infinity’, he is not just the pride of India but also an inspiration for every maths lover worldwide.

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This is a tale of how a young boy born in the Madras Presidency during the British Raj left a mark in the history of Mathematics. We dedicate this article on the occasion of his 131st birthday.

Ramanujan was born on 22nd December 1887 to a Tamil Brahmin Family. His father was a clerk and mother, a housewife. He spent most of his childhood under the care of his mother, as his father was mostly busy with work. Initially, Ramanujan hated going to school. He would often avoid attending his classes. Finally, the family had to enlist a local constable to make sure he attended school.

The Beginning

This changed after he was 10 years old, when he first met with his life-long love, ‘Mathematics’. He had mastered advanced mathematics at an early age of 11. At the age of 14, he was discovering sophisticated theorems on his own.

At 15, He borrowed a library copy of  A Synopsis of Elementary Results in Pure and Applied Mathematics , G. S. Carr’s collection of 5,000 theorems. Ramanujan regarded this book as the one that envoked the genius in him.

Srinivasa Ramanujan was already famous as the prodigy. By the age of 16, he was assisting high school and university students along with teachers.

He received a scholarship which led him to study in the Government Arts College, Kumbakonam. He was so engrossed in mathematics that he topped the subject and finished the exam in half of the time. But, he failed in all other subjects which resulted in losing the scholarship.

He dropped out from there and enrolled in Pachaiyappa’s College in Madras. Here also, he would easily ace the Mathematics but struggled with other subjects like English, Sanskrit, and Physiology. He failed his Fellow of Arts exam twice, after which he started pursuing Mathematics independently. But, due to lack of money, he would lead a life of extreme poverty and often on the brink of starvation.

The Incredible Mathematician

In 1910, the founder of the Indian Mathematical Society, V. Ramaswamy Aiyer met with 23 years old Srinivasa Ramanujan. The genius showed Professor Aiyer his notes on mathematics in the hopes of getting a job in the revenue department.

“I was struck by the extraordinary mathematical results contained in [the notebooks]. I had no mind to smother his genius by an appointment in the lowest rungs of the revenue department.” – V. Ramaswamy Aiyer

Professor Aiyer was so impressed and surprised by the findings of Ramanujan that he sent him to his mathematician friends in Madras, with letters of introduction. Here he met other mathematicians who helped him find financial support. With Aiyer’s guide, Ramanujan had his work published in the  Journal of the Indian Mathematical Society.

Towards Infinity

The secretary of the Indian Mathematical Society, R. Ramachandra Rao, and other established men tried to present Ramanujan’s research work to the British Mathematicians like M. J. M. Hill, G. H. Hardy, and others. Initially, they thought that Ramanujan was a fraud but after thoroughly going through his work, Hardy said –

Ramanujan was “a mathematician of the highest quality, a man of altogether exceptional originality and power ”

Hardy along with E. H. Neville, persuaded Ramanujan to come to Cambridge.

Hardy and Ramanujan worked together for 5 years in Cambridge where the latter published 5 of his findings. Even though both were good friends, theirs was a partnership of complete opposites. Hardy was an atheist while Ramanujan was a religious man. Both of them had a very contrasting personality too.

{Replying to G. H. Hardy’s suggestion that the number of a taxi (1729) was ‘dull’, showing off his spontaneous mathematical genius.} No, it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways, the two ways being 13 + 123 and 93 + 103.” ― Srinivasa Ramanujan

• Ramanujan was the first Indian to be elected a Fellow of Trinity College, Cambridge.
• He was awarded the Bachelor of Science degree by research (this degree was later renamed Ph.D.) in March 1916.
• In 1918, he was elected a Fellow of the Royal Society, the second Indian admitted to the Royal Society.
• In 2011, on the 125th anniversary of his birth, the Indian Government declared that 22 December will be celebrated every year as  National Mathematics Day .
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Ramanujan | 10 Major Contributions And Achievements

Srinivasa Ramanujan FRS (1887 – 1920) was a self-taught Indian mathematical genius who made numerous contributions in several mathematical fields including mathematical analysis, infinite series, continued fractions, number theory and game theory . Ramanujan provided solutions to mathematical problems that were then considered unsolvable. Moreover, some of his work was so ahead of his time that mathematicians are still understanding its relevance . In 1914, Ramanujan found a formula for computing π (pi) that is currently the basis for the fastest algorithms used to calculate π. The circle method , which he developed with G. H. Hardy , constitute a large area of current mathematical research. Moreover, Ramanujan discovered K3 surfaces which play key roles today in string theory and quantum physics; while his mock modular forms are being used in an effort to unlock the secret of black holes. Know more about the achievements of Srinivasa Ramanujan through his 10 major contributions to mathematics.

#1 HE WAS THE SECOND INDIAN TO BE ELECTED A FELLOW OF THE ROYAL SOCIETY

A self-taught genius, Ramanujan moved to England in March 1914 after his talent was recognized by British mathematician G. H. Hardy . In 1916, Ramanujan was awarded a Bachelor of Science by Research degree (later named Ph.D.) by Cambridge even though he was not an undergraduate. The Ph.D. was awarded in recognition of his work on ‘Highly composite numbers’ . In 1918, Ramanujan became one of the youngest Fellows of the Royal Society and only the second Indian member . The same year he was elected a Fellow of Trinity College, Cambridge , the first Indian to be so honored . During his short lifespan of 32 years, Ramanujan independently compiled around 3,900 results . Apart from the below mentioned achievements his contributions include developing the relationship between partial sums and hyper-geometric series ; independently discovering Bernoulli numbers and using these numbers to formulated the value of Euler’s constant up to 15 decimal places ; discovering the Ramanujan prime number and the Landau–Ramanujan constant ; and coming up with Ramanujan’s sum and the Ramanujan’s master theorem.

#2 THE FASTEST ALGORITHMS FOR CALCULATION OF PI ARE BASED ON HIS SERIES

Finding an accurate approximation of π (pi) has been one of the most important challenges in the history of mathematics. In 1914, Srinivasa Ramanujan found a formula for computing pi that converges rapidly . His formula computes a further eight decimal places of π with each term in the series . It was in 1989, that Chudnovsky brothers computed π to over 1 billion decimal places on a supercomputer using a variation of Ramanujan’s infinite series of π. This was a world record for computing the most digits of pi . Moreover, the Ramanujan series is currently the basis for the fastest algorithms used to calculate π.

#3 RAMANUJAN CONJECTURE PLAYED A KEY ROLE IN THE FAMOUS LANGLANDS PROGRAM

In 1916 , Ramanujan published his paper titled “On certain arithmetical functions” . In the paper, Ramanujan investigated the properties of Fourier coefficients of modular forms . Though the theory of modular forms was not even developed then , he came up with three fundamental conjectures that served as a guiding force for its development . His first two conjectures helped develop the Hecke theory , which was formulated 20 years after his paper, in 1936, by German mathematician Erich Hecke . However, it was his last conjecture, known as the Ramanujan conjecture , that created a sensation in in 20th century mathematics . It played a pivotal role in the Langlands program , which began in 1970 through the proposal of American-Canadian mathematician Robert Langlands . The Langlands program aims to relate representation theory and algebraic number theory , two seemingly different fields of mathematics . It is widely viewed as the single biggest project in modern mathematical research . “On certain arithmetical functions” by Ramanujan thus effectively changed the course of 20th century mathematics .

#4 HE DEVELOPED THE INFLUENTIAL CIRCLE METHOD IN PARTITION NUMBER THEORY

A partition for a positive integer n is the number of ways the integer can be expressed as a sum of positive integers . For example p(4) = 5 . That means 4 can be expressed as a sum of positive integers in 5 ways: 4, 3+1, 2+2, 2+1+1 and 1+1+1 +1. Ramanujan, along with G. H. Hardy, invented the circle method which gave the first approximations of the partition of numbers beyond 200 . This method was largely responsible for major advances in the 20th century of notoriously difficult problems such as Waring’s conjecture and other additive questions. The circle method is now one of the central tools of analytic number theory . Moreover, circle method and its refinements constitute a large area of current mathematical research.

#5 HE DISCOVERED THE THREE RAMANUJAN’S CONGRUENCES

Related to the Partition Theory of Numbers, Ramanujan also came up with three remarkable congruences for the partition function p(n) . They are p(5n+4) = 0(mod 5); p(7n+4) = 0(mod 7); p(11n+6) = 0(mod 11) . For example, the first congruence means that if an integer is 4 more than a multiple of 5, then number of its partitions is a multiple of 5 . The study of Ramanujan type congruence is a popular research topic of number theory. It was in 2011, that a conceptual explanation for Ramanujan’s congruences was finally discovered . Ramanujan’s work on partition theory has applications in a number of areas including particle physics (particularly quantum field theory) and probability .

#6 NUMBER 1729 IS NAMED HARDY–RAMANUJAN NUMBER

In a famous incident British mathematician G. H. Hardy while visiting Ramanujan had ridden in a taxi cab with the number 1729 . He remarked to Ramanujan that the number “seemed to me rather a dull one, and that I hoped it was not an unfavorable omen” . “No,” Ramanujan replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.” The two different ways are: 1729 = 1 3 + 12 3 = 9 3 + 10 3 . 1729 is now known as the Hardy–Ramanujan number . Moreover, numbers that are the smallest number that can be expressed as the sum of two cubes in n distinct ways are now referred to as taxicab numbers due to the incident. The relevance of 1729 has recently come to light as it was part of a much larger theory that Ramanujan was developing . Theorems have been established in theory of elliptic curves that involve this fascinating number.

#7 HE DID GROUNDBREAKING RESEARCH RELATED TO FERMAT’S LAST THEOREM

In 2013 famous Japanese American Mathematician Ken Ono , along with Sarah Trebat-Leder , found an equation by Ramanujan had clearly showed that he had been working on Fermat’s last theorem, one of the most notable and difficult to prove theorems in the history of mathematics. In 1637, French mathematician Pierre de Fermat had asserted that: if n is a whole number greater than 2 , then there are no positive whole number triples x, y and z , such that x n + y n = z n . This means that there are no numbers which satisfy the equations: x 3 + y 3 = z 3 ; x 4 + y 4 = z 4 ; and so on . The equation of Ramanujan illustrates that he had found an infinite family of positive whole number triples x, y and z that very nearly, but not quite, satisfy Fermat’s equation for n=3 . They are off only by plus or minus one . Among them is 1729 , which misses the mark by 1 for x=9, y=10 and z=12 . Moving forward, Ramanujan also considered the equations of the form: y 2 =x 3 + ax + b . If you plot the points (x,y) for this equation you get an elliptic curve . Elliptic curves played a key role when English mathematician Sir Andrew Wiles finally proved Fermat’s last theorem in 1994, a feat described as a “stunning advance” in mathematics.

#8 RAMANUJAN WAS THE FIRST TO DISCOVER K3 SURFACES

Ken Ono also found that Ramanujan went on to discover an object more complicated than elliptic curves. When it was re-discovered in 1958 by Andre Weil , it was named K3 surface . Thus it has come to light that Ramanujan was using 1729 and elliptic curves to develop formulas for a K3 surface. “Elliptic curves and K3 surfaces form an important next frontier in mathematics and Ramanujan gave remarkable examples illustrating some of their features that we didn’t know before.” Moreover, K3 surfaces play key roles today in string theory and quantum physics . Like, string theory suggests that the world consists of more than the three dimensions that we can see . These extra dimensions are rolled up tightly in tiny little spaces too small for us to perceive . These tiny spaces have a particular geometric structure. Calabi–Yau manifold is a class of geometric objects that have similar structure and one of the simplest classes of Calabi-Yau manifolds comes from K3 surfaces.

#9 HIS THETA FUNCTION LIES AT THE HEART OF STRING THEORY IN PHYSICS

In mathematics, theta functions are special functions of several complex variables . German Mathematician Carl Gustav Jacob Jacobi came up with several closely related theta functions known as Jacobi theta functions . Theta functions were studied extensively by Ramanujan. He came up with the Ramanujan theta function , which generalizes the form of Jacobi theta functions while also capturing their general properties . In particular, the Jacobi triple product takes on an elegant form when written in terms of the Ramanujan theta function . Ramanujan theta function has several important applications. It is used to determine the critical dimensions in Bosonic string theory, superstring theory and M-theory .

#10 HIS MOCK MODULAR FORMS MAY UNLOCK THE SECRET OF BLACK HOLES

In a 1920 letter to Hardy, Ramanujan described several new functions that behaved differently from known theta functions , or modular forms , and yet closely mimicked them. These were the first ever examples of mock modular forms . More than 80 years later, in 2002 , a description for these functions was provided by Sander Zwegers . Further, Ramanujan predicted that his mock modular forms corresponded to ordinary modular forms producing similar outputs for roots of 1 . Ken Ono ultimately showed that a mock modular form could be computed just as Ramanujan predicted . It was found as the output of mock modular forms shoot off to enormous numbers, the corresponding ordinary modular form expand at a similar rate and thus their difference is a relatively small number. Expansion of mock modular forms is now used to compute the entropy, or level of disorder, of black holes. Thus even through black holes were virtually unknown during his time, Ramanujan was able to do mathematics which may unlock their secret.

4 thoughts on “Ramanujan | 10 Major Contributions And Achievements”

A major method for computation of Feynman integrals is the bracket integration method, a direct result from his Master Theorem ( https://en.wikipedia.org/wiki/Ramanujan%27s_master_theorem )

What is plus and minus infinity, he used in his theta function? Infinity in two opposite directions?

very useful information but no that much recognition

awesome pic. loved it

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India's contributions to pathbreaking discoveries made by mathematics date back to ancient and medieval times. From formulating geometric principles in the ancient era to pioneering concepts of calculus centuries before Europe, Indian mathematicians like Ramanujan made profound contributions to mathematical analysis in the modern period.

Contemporary Indian mathematicians are expanding frontiers in diverse domains, garnering global recognition, exploring the enduring legacy and monumental contributions of mathematicians from India across different eras, and highlighting their timeless influence on the evolution of mathematical knowledge.

List of Famous Indian Mathematicians and their Contributions

The origins of Indian mathematics date back to the Indus Valley Civilization around 3000 BCE . Concepts of geometry, arithmetic, and algebra saw systematic development starting from this period through the classical age around 500 CE. Here is the list of Indian mathematicians and their key contributions:

Applications of Indian Mathematics

Discoveries by Indian mathematicians continue to find novel applications decades and centuries later, proving the timelessness of their work. Some examples:

• Satellite Navigation - Uses formulae for spherical geometry and trigonometry derived by mathematicians like Aryabhata and Brahmagupta.
• Computer Graphics - Infinite series properties studied by Madhava and solutions using Pell's equations aid 3D modelling and animation.School
• Fluid Dynamics - Equations formulated by classical Indian mathematicians help accurately model phenomena like turbulence for applications in aerospace engineering.
• Cryptography - Number theory results, infinite series and combinatorics tools devised centuries ago are applied in cryptography and cybersecurity today.
• Modeling - Ancient mathematical techniques form the basis for epidemiological and weather prediction models . They also find use in artificial intelligence and data science algorithms.

The universal nature of mathematical truth enabled Indian geniuses to make contributions that continued to hold relevance centuries later. The foundation laid by them ushered in an era of modern mathematics globally.

FAQs on Indian Mathematicians

Who is called the father of indian mathematics.

Aryabhata, the 5th-century Indian mathematician, is considered the father of Indian mathematics and astronomy.

Name the Ancient Indian Mathematicians who calculated the value of Pi.

Aryabhata first calculated the value of Pi in the 5th century. Madhava of Sangamagrama and Nilakantha Somayaji computed Pi to more accurate decimal places in Kerala schools.

Who discovered the Pythagoras Theorem before Pythagoras?

Baudhayana, an ancient Indian mathematician in the Sulba Sutras text formulated special cases of the Pythagorean theorem in 800 BCE - before Pythagoras.

Name some modern Indian Mathematicians who won the Fields Medal.

Mathematicians Shafi Goldwasser (2014), Manjul Bhargava (2014) and Akshay Venkatesh (2018) are Indian-origin winners of the prestigious Fields Medal prize.

Which areas did Srinivasa Ramanujan make major contributions to?

Ramanujan made pathbreaking contributions in areas like number theory, continued fractions, infinite series, partitions of numbers, mock theta functions, and mathematical analysis.

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Srinivasa Ramanujan and his contribution to mathematics

• Ramanujan compiled around 3,900 results consisting of equations and identities. One of his most treasured findings was his infinite series for pi. This series forms the basis of many algorithms we use today. He gave several fascinating formulas to calculate the digits of pi in many unconventional ways.
• He discovered a long list of new ideas to solve many challenging mathematical problems, which gave a significant impetus to the development of game theory. His contribution to game theory is purely based on intuition and natural talent and remains unrivalled to this day.
• He elaborately described the mock theta function, which is a concept in the realm of modular form in mathematics. Considered an enigma till sometime back, it is now recognized as holomorphic parts of mass forms.
• One of Ramanujan’s notebooks was discovered by George Andrews in 1976 in the library at Trinity College. Later the contents of this notebook were published as a book.
• 1729 is known as the Ramanujan number. It is the sum of the cubes of two numbers 10 and 9. For instance, 1729 results from adding 1000 (the cube of 10) and 729 (the cube of 9). This is the smallest number that can be expressed in two different ways as it is the sum of these two cubes. Interestingly, 1729 is a natural number following 1728 and preceding 1730.
• Ramanujan’s contributions stretch across mathematics fields, including complex analysis, number theory, infinite series, and continued fractions.

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