# Srinivasa Ramanujan

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**Srinivasa Aiyangar Ramanujan** (Tamil: ஸ்ரீனிவாஸ ஐயங்கார் ராமானுஜன்) (22 December 1887 – 26 April 1920) was a Indian mathematician and autodidact, noted for his extraordinary achievements in the field of mathematical analysis, number theory, infinite series, and continued fractions. In his uniquely self-developed mathematical research he not only rediscovered known theorems but also produced brilliant new work, prompting his mentor G. H. Hardy to compare his brilliance to that of Euler and Gauss. He became a Fellow of the Royal Society, and India now observes his birthday as National Mathematics Day.

## Quotes[edit]

- One day he was explaining a relation to me; then he suddenly turned round and said, "
**Sir, an equation has no meaning for me unless it expresses a thought of GOD**."- Shiyali Ramamrita Ranganathan, in
*Ramanujan, the Man and the Mathematician*(1967), p. 88 - Variant:
**An equation means nothing to me unless it expresses a thought of God.**

- Shiyali Ramamrita Ranganathan, in

- I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office at Madras... I have no University education but I have undergone the ordinary school course. After leaving school I have been employing the spare time at my disposal to work at Mathematics. I have not trodden through the conventional regular course which is followed in a University course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as "startling". ...Very recently I came across a tract published by you styled
*Orders of Infinity*in page 36 of which I find a statement that no definite expression has been as yet found for the number of prime numbers less than any given number. I have found an expression which very nearly approximates to the real result, the error being negligible. I would request that you go through the enclosed papers. Being poor, if you are convinced that there is anything of value I would like to have my theorems published. I have not given the actual investigations nor the expressons that I get but I have indicated the lines on which I proceed. Being inexperienced I would very highly value any advice you give me. Requesting to be excused for the trouble I give you. I remain, Dear Sir, Yours truly...- Letter to Hardy, (Jan16, 1913)
*Ramanujan: Letters and Commentary*American Mathematical Society (1995)*History of Mathematics*, Vol.9

- Letter to Hardy, (Jan16, 1913)

## Quotes about Ramanujan[edit]

- Sorted alphabetically by author

**Ramanujan lived in a tiny hut in India. No formal education, no access to other works.**But he came across an old math book and from this basic text he was able to extrapolate theories that had baffled mathematicians for years. …**Ramanujan's genius was unparalleled.**- Ben Affleck and Matt Damon, in
*Good Will Hunting*(1997)

- Ben Affleck and Matt Damon, in

- Paul Erdős has passed on to us Hardy's personal ratings of mathematicians. Suppose that we rate mathematicians on the basis of pure talent on a scale from 0 to 100, Hardy gave himself a score of 25, Littlewood 30, Hilbert 80 and
**Ramanujan 100**.- Bruce C. Berndt in
*Ramanujan's Notebooks : Part I*(1994), "Introduction", p. 14

- Bruce C. Berndt in

- He began to focus on mathemtics at an early age, and, at the age of about fifteen, borrowed a copy of G. S. Carr's
*Synopsis of Pure and Applied Mathematics*, which served as his primary source for learning mathematics. Carr was a tutor and compiled this compendium of approximately 4000-5000 results (with very few proofs) to facilitate his tutoring.- Bruce C. Berndt, "An Overview of Ramanujan's Notebooks,"
*Ramanujan: Essays and Surveys*(2001) Berndt & Robert Alexander Rankin

- Bruce C. Berndt, "An Overview of Ramanujan's Notebooks,"

- At about the time Ramanujan entered college, he began to record his mathematical discoveries in notebooks... Ramanujan devoted all of his efforts to mathematics and continued to record his discoveries without proofs in notebooks for the next six years.
- Bruce C. Berndt, "An Overview of Ramanujan's Notebooks,"
*Ramanujan: Essays and Surveys*(2001) Berndt & Robert Alexander Rankin

- Bruce C. Berndt, "An Overview of Ramanujan's Notebooks,"

- After Ramanujan died, Hardy strongly urged that Ramanujan's notebooks be edited and published. By "editing," Hardy meant that each claim made by Ramanujan in his notebooks should be examined. If a theorem is known, sources providing proofs should be provided; if an entry is known, then an attempt should be made to prove it.
- Bruce C. Berndt, "An Overview of Ramanujan's Notebooks,"
*Ramanujan: Essays and Surveys*(2001) Berndt & Robert Alexander Rankin

- Bruce C. Berndt, "An Overview of Ramanujan's Notebooks,"

- Ramanujan's approach to the theory of theta functions does not appear to have been influenced by any other writer.
- Bruce C. Berndt, "An Overview of Ramanujan's Notebooks,"
*Ramanujan: Essays and Surveys*(2001) Berndt & Robert Alexander Rankin

- Bruce C. Berndt, "An Overview of Ramanujan's Notebooks,"

**He could remember the idiosyncrasies of numbers in an almost uncanny way.**It was Littlewood who said that every positive integer was one of Ramanujan's personal friends. I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "**it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.**"- G. H. Hardy, in
*Ramanujan : Twelve Lectures on Subjects Suggested by His Life and Work*(1940), the number 1729 is now known as the Hardy–Ramanujan number after this famous anecdote (1729 = 1^{3}+ 12^{3}= 9^{3}+ 10^{3}).

- G. H. Hardy, in

- The formulae (1.10) - (1.13) are on a different level and obviously both difficult and deep... (1.10) - (1.12) defeated me completely;
**I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written by a mathematician of the highest class. They must be true because, if they were not true, no one would have the imagination to invent them.**- G. H. Hardy as quoted by Edward O. Wilson,
*Biophilia*(2009)

- G. H. Hardy as quoted by Edward O. Wilson,

**Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science.**He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33, like Riemann before him.- Michio Kaku,
*Hyperspace : A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension*(1995), p. 172

- Michio Kaku,

- The number 24 appearing in Ramanujan's function is also the origin of the miraculous cancellations occurring in string theory. ...each of the 24 modes in the Ramanujan function corresponds to a physical vibration of a string. Whenever the string executes its complex motions in space-time by splitting and recombining, a large number of highly sophisticated mathematical identities must be satisfied. These are precisely the mathematical identities discovered by Ramanujan. ...The string vibrates in ten dimensions because it requires... generalized Ramanujan functions in order to remain self-consistent.
- Michio Kaku, in
*Hyperspace : A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension*(1995) Ch.7 Superstrings

- Michio Kaku, in

- Graduating from high school in 1904, he entered the University of Madras on a scholarship. However, his excessive neglect of all subjects except mathematics caused him to lose the scholarship after a year, and Ramanujan dropped out of college. He returned to the university after some traveling through the countryside, but never graduated. ...His marriage in 1909 compelled him to earn a living. Three years later, he secured a low-paying clerk's job with the Madras Port Trust.
- Thomas Koshy,
*Catalan Numbers with Applications*(2008)

- Thomas Koshy,

**Every positive integer is one of Ramanujan's personal friends.**- John Littlewood, as recalled in G. H. Hardy (1921), "Obituary Notices: Srinivasa Ramanujan",
*Proceedings of the London Mathematical Society***19**, p. lvii

- John Littlewood, as recalled in G. H. Hardy (1921), "Obituary Notices: Srinivasa Ramanujan",

- Srinivasa Ramanujan, discovered by the Cambridge mathematician G. H. Hardy, whose great mathematical findings were beginning to be appreciated from 1915 to 1919. His achievements were to be fully understood much later, well after his untimely death in 1920. For example, his work on the highly composite numbers (numbers with a large number of factors) started a whole new line of investigations in the theory of such numbers.
- Jayant Narlikar, in
*Scientific Edge : The Indian Scientist from Vedic to Modern Times*(2003)

- Jayant Narlikar, in

- The manuscript of Ramanujan contained theorems and propositions that Hardy classified in three categories: 1) important results already known or demonstrable, through theorems which Ramanujan was certainly not acquainted with; 2) false results (few in number) or results concerning marginal curiosities; 3) important theorems not demonstrated, but formulated in such a manner that presupposed views... which only a genius could have.
- Claudio Ronchi,
*The Tree of Knowledge: The Bright and the Dark Sides of Science*(2013)

- Claudio Ronchi,

- Hardy... in vain, tried to convince him to learn classical foundations of mathematics and, in particular, the rigorous expositive method of mathematical demonstrations. Every time Hardy introduced a problem, Ramanujan considered it
*ex novo*[new] applying unconventional reasoning which was sometimes incomprehensible to his fellow colleagues.- Claudio Ronchi,
*The Tree of Knowledge: The Bright and the Dark Sides of Science*(2013)

- Claudio Ronchi,

- The great advances in mathematics have not been made by logic but by creative imagination. The title of mathematician can scarcely be denied to Ramanajan who hardly gave any proofs of the many theorems which he enumerated.
- George Frederick James Temple, 100 Years of Mathematics: a Personal Viewpoint (1981)

**That Ramanujan conceived these problems, sometimes before anyone else had done so, with no contact with the European mathematical community**, and that he correctly obtained the dominant terms in asymptotic formulas**are astounding achievements**that should not be denigrated because of his unrigorous, but clever, arguments.- American Mathematical Society,
*Ramanujan: Letters and Commentary*(1995)*History of Mathematics*, Vol.9

- American Mathematical Society,

- Ramanujan proved many theorems for products of hypergeometric functions and stimulated much research by W. N. Bailey and others on this topic.
- American Mathematical Society,
*Ramanujan: Letters and Commentary*(1995)*History of Mathematics*, Vol.9

- American Mathematical Society,

## External links[edit]

- Srinivasa Aiyangar Ramanujan, The MacTutor History of Mathematics Archive