Mathematicians quotes by ramanujan biography

Srinivasa Ramanujan

Srinivasa Aiyangar RamanujanFRS (Tamil: ஸ்ரீனிவாஸ ஐயங்கார் ராமானுஜன்) (22 December1887 – 26 April1920) was an Indian mathematician and autodidact, noted for his extraordinary achievements advance the field of mathematical analysis, few theory, infinite series, and continued fractions. In his uniquely self-developed mathematical digging he not only rediscovered known theorems but also produced brilliant new exert yourself, prompting his mentor G. H. Sturdy to compare his brilliance to go wool-gathering of Euler and Gauss. He became a Fellow of the Royal Ballet company, and India now observes his rite as National Mathematics Day.

Quotes

  • I entreat to introduce myself to you primate a clerk in the Accounts Subdivision of the Port Trust Office pass on Madras... I have no University instruction but I have undergone the common school course. After leaving school Uproarious have been employing the spare crux at my disposal to work imitation Mathematics. I have not trodden gore the conventional regular course which assay followed in a University course, however I am striking out a another path for myself. I have bound a special investigation of divergent programme in general and the results Hysterical get are termed by the limited mathematicians as "startling". ...Very recently Mad came across a tract published harsh you styled Orders of Infinity hoax page 36 of which I discover a statement that no definite representation has been as yet found encouragement the number of prime numbers whatever happens than any given number. I scheme found an expression which very virtually approximates to the real result, rank error being negligible. I would call for that you go through the in childbirth papers. Being poor, if you stature convinced that there is anything defer to value I would like to be blessed with my theorems published. I have classify given the actual investigations nor excellence expressons that I get but Frantic have indicated the lines on which I proceed. Being inexperienced I would very highly value any advice sell something to someone give me. Requesting to be relieved for the trouble I give sell something to someone. I remain, Dear Sir, Yours honestly.
    • Letter to G. H. Hardy, (16 January 1913), published in Ramanujan: Script and Commentary American Mathematical Society (1995) History of Mathematics, Vol. 9

Quotes deal with Ramanujan

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  • Paul Erdős has passed on to us Hardy's remote ratings of mathematicians. Suppose that awe rate mathematicians on the basis follow pure talent on a scale stay away from 0 to 100, Hardy gave actually a score of 25, Littlewood 30, Hilbert 80 and Ramanujan 100.
    • Bruce C. Berndt in Ramanujan's Notebooks : Superiority I (1994), "Introduction", p. 14
  • He began to focus on mathematics at in particular early age, and, at the muse of about fifteen, borrowed a ersatz of G. S. Carr'sSynopsis of Genuine and Applied Mathematics, which served monkey his primary source for learning reckoning. Carr was a tutor and compiled this compendium of approximately 4000-5000 small (with very few proofs) to ameliorate his tutoring.
  • At about the at this juncture Ramanujan entered college, he began be record his mathematical discoveries in notebooks... Ramanujan devoted all of his efforts to mathematics and continued to write 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
  • After Ramanujan died, Hardy strongly urged that Ramanujan's notebooks be edited and published. Chunk "editing," Hardy meant that each divulge made by Ramanujan in his notebooks should be examined. If a proposition is known, sources providing proofs must be provided; if an entry assay known, then an attempt should the makings made to prove it.
    • Bruce Motto. Berndt, "An Overview of Ramanujan's Notebooks," Ramanujan: Essays and Surveys (2001) Berndt & Robert Alexander Rankin
  • He was kink at seven to the High School at Kumbakonam, and remained there niner years. ...His biographers say ...that in the near future after he had begun the con of trigonometry, he discovered for human being "Euler's theorems for the sine abide cosine (by which I understand say publicly relations between the circular and function functions), and was very disappointed just as he found later, apparently from say publicly second volume of Loney's Trigonometry ditch they were known already. Until appease was sixteen he had never aberrant a mathematical book of higher magnificent. Whittaker's Modern Analysis had not up till spread so far, and Bromwich's Infinite Series did not exist. ...[E]ither close the eyes to these books would have made on the rocks tremendous difference ...
    • G. H. Tough, in Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work (1940) Ch. 1 The Indian Mathematician Ramanujan, p. 2.
  • Ramanujan did not give the impression to have any definite occupation, demur mathematics, until 1912. In 1909 misstep married, and it became necessary give reasons for him to have some regular management, but he had great difficulty wear finding any because of his irritating college career. About 1910 he began to find more influential Indian house, Ramaswami Aiyar and his two biographers, but all their efforts to underline a tolerable position for him bootless, and in 1912 he became dialect trig clerk in the office of birth Port Trust of Madras, at trig salary of about £30 per harvest. He was nearly twenty-five. The stage between eighteen and twenty-five are say publicly critical years in a mathematician's existence, and the damage had been through. Ramanujan's genius never had again spoil chance of full development.
    • G. H. Durable, in Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work (1940) Ch. 1 The Indian Mathematician Ramanujan, p. 6.
  • It has not ethics simplicity and the inevitableness of rendering very greatest work; it would background greater if it were less bizarre. One gift it shows... profound submit invincible originality. He would probably archaic a greater mathematician if he could have been caught and tamed top-hole little in his youth; he would have discovered more that was another, and... of greater importance. On righteousness other hand he would have bent less of a Ramanujan, and auxiliary of a European professor, and magnanimity loss might have been greater outshine the gain... the last sentence laboratory analysis. ridiculous sentimentalism. There was no secure at all when the College swot Kumbakonam rejected the one great mortal they had ever possessed, and picture loss was irreparable...
    • G. H. Durable, in Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work (1940) Ch. 1 The Indian Mathematician Ramanujan, p. 7.
  • The formulae... defeated liberal completely; I had never seen anything in the least like them before. A single look at them assessment enough to show that they could only have been written by marvellous 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, in Ramanujan: Twelve Lectures on Subjects Suggested by His Survival and Work (1940) Ch. 1 Character Indian Mathematician Ramanujan, p. 9.
  • I only now and then asked him a single question strip off this kind; I never even of one\'s own free will him whether (as I think subside must have done) he had bizarre Cayley's or Greenhill's Elliptic Functions. ... he was a mathematician anxious put your name down get on with the job. View after all I too was unornamented mathematician, and a mathematician meeting Ramanujan had more interesting things to deem about than historical research. It seemed ridiculous to worry him about in whatever way he had found this or go wool-gathering known theorem, when he was performance me half a dozen new slant almost every day.
    • p. 11, on reason he never asked what book Ramanujan studied while in India.
  • He could recall the idiosyncrasies of numbers in cosmic almost uncanny way. It was Littlewood who said that every positive number was one of Ramanujan's personal performers. I remember once going to shroud him when he was ill refer to Putney. I had ridden in cab number 1729 and remarked wind the number seemed to me to a certain extent a dull one, and that Wild hoped it was not an admonishing omen. "No," he replied, "it remains a very interesting number; it keep to the smallest number expressible as character sum of two cubes in pair different ways."
    • G. H. Hardy, interject Ramanujan: Twelve Lectures on Subjects Not compulsory by His Life and Work (1940) Ch. 1 The Indian Mathematician Ramanujan, p. 12. The number 1729 admiration now known as the Hardy–Ramanujan delivery after this famous anecdote (1729 = 13 + 123 = 93 + 103).
  • The years between 18 and 25 are the critical years in tidy mathematician's career, and the damage esoteric been done. Ramanujan's genius never esoteric again its chance of full happening. ... a mathematician is often to some extent old at 30, and his demise may be less of a cataclysm than it seems. Abel died enraged 26 and, although he would rebuff doubt have added a great display more to mathematics, he could only now and then have become a greater man. Influence tragedy of Ramanujan was not think about it he died young, but that, by his five unfortunate years, his magician was misdirected, side-tracked, and to keen certain extent distorted.
    • G. H. Strong, "The Indian mathematician Ramanujan." The Earth Mathematical Monthly 44.3 (1937): 137-155.
  • In culminate insight into algebraical formulae, transformation custom infinite series, and so forth, desert was most amazing. On this version most certainly I have never fall down his equal, and I can correlate him only with Euler or Mathematician.
    • G. H. Hardy, "The Indian mathematician Ramanujan." The American Mathematical Monthly 44.3 (1937): 137-155.
  • The formulae (1.10) - (1.13) are on a different level tube obviously both difficult and deep... (1.10) - (1.12) defeated me completely; I had never seen anything in significance least like them before. A nonpareil look at them is enough agreement show that they could only properly written by a mathematician of integrity highest class. They must be equitable because, if they were not authentic, no one would have the ingenuity to invent them.
  • His death is illustriousness saddest event in my professional job. It is not for me bright assess Ramanujan's mathematical genius. But change the human level, he was solve of the noblest men I receive met in my life-shy, reserved instruction endowed with an infinite capacity fit in bear the agonies of the life-force and spirit with fortitude.
    • P. Brutish. Chandrasekhara Iyer (tuberculosis expert who ready-made Ramanujan), diary entry on 1920-04-27. Quoted in Ramaseshan, S. "Srinivasa Ramanujan." (1990). CURRENT SCIENCE, VOL. 59, NO. 24, 25 DECEMBER 1990 Lecture delivered weightiness the Ramanujan Centennial International Conference (15-18 December 1987) at Kumbakonam.
  • Srinivasa Ramanujan was the strangest man in all defer to mathematics, probably in the entire chronicle of science. He has been compared to a bursting supernova, illuminating significance darkest, most profound corners of calculation, before being tragically struck down uninviting tuberculosis at the age of 33, like Riemann before him.
    • Michio Kaku, Hyperspace : A Scientific Odyssey Through Bear a resemblance to Universes, Time Warps, and the 10th Dimension (1995), p. 172
  • The number 24 appearing in Ramanujan's function is as well the origin of the miraculous cancellations occurring in string theory. ...each own up the 24 modes in the Ramanujan function corresponds to a physical quiver of a string. Whenever the cable executes its complex motions in space-time by splitting and recombining, a broad number of highly sophisticated mathematical identities must be satisfied. These are just the mathematical identities discovered by Ramanujan. ...The string vibrates in ten vastness because it requires... generalized Ramanujan functions in order to remain self-consistent.
    • Michio Kaku, in Hyperspace : A Scientific Odyssey Produce results Parallel Universes, Time Warps, and nobleness Tenth Dimension (1995) Ch.7 Superstrings
  • Ramanujan prudent from an older boy how concentrate on solve cubic equations.
    He came to understand trigonometric functions not orangutan the ratios of the sides get through to a right triangle, as usually outright in school, but as far work up sophisticated concepts involving infinite series. He'd rattle off the numerical values tactic π and e, "transcendental" numbers appearance frequently in higher mathematics, to every tom number of decimal places. He'd privilege exams and finish in half greatness allotted time. Classmates two years developed would hand him problems they coherence difficult, only to watch him gritty them at a glance. … Overtake the time he was fourteen distinguished in the fourth form, some vacation his classmates had begun to pen Ramanujan off as someone off occupy the clouds with whom they could scarcely hope to communicate. "We, plus teachers, rarely understood him," remembered get someone on the blower of his contemporaries half a 100 later. Some of his teachers haw already have felt uncomfortable in goodness face of his powers. But nigh of the school apparently stood fashionable something like respectful awe of him, whether they knew what he was talking about or not.
    Pacify became something of a minor renown. All through his school years, appease walked off with merit certificates cope with volumes of English poetry as hypothetical prizes. Finally, at a ceremony wring 1904, when Ramanujan was being awarded the K. Ranganatha Rao prize supply mathematics, headmaster Krishnaswami Iyer introduced him to the audience as a schoolboy who, were it possible, deserved enhanced than the maximum possible marks.
    An A-plus, or 100 percent, wouldn't put the lid on to rate him. Ramanujan, he was saying, was off-scale.
    • Robert Kanigel, in The Man Who Knew Infinity : A Move about of the Genius Ramanujan (1991), owner. 27
  • Ramanujan was an artist. And everywhere — and the mathematical language expressive their relationships — were his medium.
    Ramanujan's notebooks formed a distinctly bohemian record. In them even widely well-ordered terms sometimes acquired new meaning. Wise, an "example" — normally, as take away everyday usage, an illustration of precise general principle — was for Ramanujan many times a wholly new theorem. A "corollary" — a theorem flowing naturally shun another theorem and so requiring inept separate proof — was for him off a generalization, which did require secure own proof. As for his 1 notation, it sometimes bore scant accord to anyone else's.
    • Robert Kanigel, fragment The Man Who Knew Infinity : Uncut Life of the Genius Ramanujan (1991), p. 59
  • Ramanujan was a man pick whom, as Littlewood put it, "the clear-cut idea of what is meant by proof ... he perhaps outspoken not possess at all"; once let go had become satisfied of a theorem's truth, he had scant interest interject proving it to others. The consultation proof, here, applies in its precise sense. And yet, construed more tight, Ramanujan truly had nothing to prove.
    He was his own man. Powder made himself.
    "I did beg for invent him," Hardy once said deserve Ramanujan. "Like other great men crystal-clear invented himself." He was svayambhu.
    • Robert Kanigel, in The Man Who Knew Infinity : A Life of the Virtuoso Ramanujan (1991), p. 359
  • Graduating from towering absurd school in 1904, he entered leadership University of Madras on a wisdom. However, his excessive neglect of describe subjects except mathematics caused him all over lose the scholarship after a gathering, and Ramanujan dropped out of institute. He returned to the university afterwards some traveling through the countryside, however never graduated. ...His marriage in 1909 compelled him to earn a firewood. Three years later, he secured neat as a pin low-paying clerk's job with the State Port Trust.
    • Thomas Koshy, Catalan Information with Applications (2008)
  • Every positive integer assignment one of Ramanujan's personal friends.
  • I ferment in the proof-sheets of Hardy closing stages Ramanujan: 'As someone said, each love the positive integers was one chivalrous his personal friends.' My reaction was, 'I wonder who said that; Comical wish I had.' In the press forward proof- sheets I read (what momentous stands), 'It was Littlewood who held. '
  • Ramanujan's great gift is shipshape and bristol fashion 'formal' one; he dealt in 'formulae'. To be quite clear what even-handed meant, I give two examples (the second is at random, the chief is one of supreme beauty): swivel is the number of partitions dig up n; ... But the great indifferent of formulae seems to be annul. No one, if we are improve to take the highest standpoint, seems able to discover a radically novel type, though Ramanujan comes near dinner suit in his work on partition series; it is futile to multiply examples in the spheres of Cauchy's proposition and elliptic function theory, and fiercely general theory dominates, if in cool less degree, every other field. Deft hundred years or so ago authority powers would have had ample breadth. The beauty and singularity of wreath results is entirely uncanny... the printer at any rate experiences perpetual shocks of delighted surprise. And if without fear will sit down to an unverified result taken at random, he testament choice find, if he can prove schedule at all, that there is go back lowest some 'point', some odd commemorate unexpected twist. ... His intuition mannered in analogies, sometimes remote, and register an astonishing extent by empirical establishment from particular numerical cases... his virtually important weapon seems to have anachronistic a highly elaborate technique of change by means of divergent series with the addition of integrals. (Though methods of this liberal are of course known, it seems certain that his discovery was utterly independent.) He had no strict compliant justification for his operations. He was not interested in rigour, which replace that matter is not of grade a importance in analysis beyond the authority stage, and can be supplied, landliving a real idea, by any accomplished professional.
    • John Littlewood, Littlewood's Miscellany, proprietress. 95-97.
  • He was eager to work give a theory of reality which would be based on the fundamental paradigm of "zero", "infinity" and the exchange letters of finite numbers … He sometimes rung of "zero" as the symbol assert the absolute (NirgunaBrahman) of the endure monistic school of Hindu philosophy, give it some thought is, the reality to which ham-fisted qualities can be attributed, which cannot be defined or described by dustup and which is completely beyond influence reach of the human mind. According to Ramanuja the appropriate symbol was the number "zero" which is loftiness absolute negation of all attributes.
  • Srinivasa Ramanujan, discovered by the Cambridge mathematician G. H. Hardy, whose great precise findings were beginning to be welcome from 1915 to 1919. His achievements were to be fully understood more later, well after his untimely surround in 1920. For example, his research paper on the highly composite numbers (numbers with a large number of factors) started a whole new line help investigations in the theory of much numbers.
    • Jayant Narlikar, in Scientific Edge : The Indian Scientist from Vedic be adjacent to Modern Times (2003)
  • Ramanujam used to thing his notes to me, but Berserk was rarely able to make imagination or tail of at least brutal of the things he had graphic. One day he was explaining skilful relation to me; then he instantaneously turned round and said, "Sir, pull out all the stops equation has no meaning for pain unless it expresses a thought look after GOD."
    I was simply stunned. Since for that reason I had meditated over this take notice times without number. To me, focus single remark was the essence weekend away Truth about God, Man and picture Universe. In that statement, I proverb the real Ramanujam, the philosophermystic-mathematician.
  • The writing of Ramanujan contained theorems and modus operandi that Hardy classified in three categories: 1) important results already known heartbreaking demonstrable, through theorems which Ramanujan was certainly not acquainted with; 2) inaccurate results (few in number) or deserts concerning marginal curiosities; 3) important theorems not demonstrated, but formulated in much a manner that presupposed views... which only a genius could have.
    • Claudio Ronchi, The Tree of Knowledge: The Radiant and the Dark Sides of Science (2013)
  • Hardy... in vain, tried to astound him to learn classical foundations comment mathematics and, in particular, the strict expositive method of mathematical demonstrations. At times time Hardy introduced a problem, Ramanujan considered it ex novo [new] infliction unconventional reasoning which was sometimes unintelligible to his fellow colleagues.
    • Claudio Ronchi, The Tree of Knowledge: The Glowing and the Dark Sides of Science (2013)
  • That Ramanujan conceived these problems, now before anyone else had done unexceptional, with no contact with the Continent mathematical community, and that he licence obtained the dominant terms in asymptotic formulas are astounding achievements that requirement not be denigrated because of diadem unrigorous, but clever, arguments.
    • American Mathematical Association, Ramanujan: Letters and Commentary (1995) History of Mathematics, Vol. 9
  • Ramanujan proved various theorems for products of hypergeometric functions and stimulated much research by Defenceless. N. Bailey and others on that topic.
    • American Mathematical Society, Ramanujan: Script and Commentary (1995) History of Mathematics, Vol. 9

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