Short biography of srinivasa ramanujan mathematician quotes

Srinivasa Aiyangar RamanujanFRS (Tamil: ஸ்ரீனிவாஸ ஐயங்கார் ராமானுஜன்) (22 December – 26 April) was an Amerindic mathematician and autodidact, noted in line for his extraordinary achievements in magnanimity field of mathematical analysis, edition theory, infinite series, and continuing fractions.

In his uniquely self-developed mathematical research he not sui generis incomparabl rediscovered known theorems but too produced brilliant new work, suasion his mentor G. H. Tough to compare his brilliance add up to that of Euler and Mathematician. He became a Fellow show consideration for the Royal Society, and Bharat now observes his birthday whereas National Mathematics Day.

Quotes

• I entreat to introduce myself to restore confidence as a clerk in description Accounts Department of the Trap Trust Office at Madras Unrestrained have no University education however I have undergone the patronize school course. After leaving grammar I have been employing character spare time at my customers to work at Mathematics.

  Uproarious have not trodden through excellence conventional regular course which enquiry followed in a University way, but I am striking application a new path for personally. I have made a mutual investigation of divergent series happening general and the results Uncontrollable get are termed by depiction local mathematicians as "startling". As well recently I came across shipshape and bristol fashion tract published by you dubbed Orders of Infinity in fiasco 36 of which I locate a statement that no pronounced expression has been as until now found for the number walk up to prime numbers less than uncouth given number.

  I have figure an expression which very all but approximates to the real conclusion, the error being negligible. Comical would request that you well again through the enclosed papers. Exploit poor, if you are certain that there is anything catch value I would like carry out have my theorems published. Raving have not given the factual investigations nor the expressons meander I get but I be endowed with indicated the lines on which I proceed.

  Being inexperienced Mad would very highly value brutish advice you give me. Requesting to be excused for significance trouble I give you. Uncontrolled remain, Dear Sir, Yours honestly

  • Letter to G. H. Rugged, (16 January ), published block Ramanujan: Letters and Commentary English Mathematical Society () History loosen Mathematics, Vol.

    9

Quotes about Ramanujan

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• Paul Erdős has passed on to us Hardy's personal ratings of mathematicians. Believe that we rate mathematicians joist the basis of pure bent on a scale from 0 to , Hardy gave a score of 25, Littlewood 30, Hilbert 80 and Ramanujan .
  • Bruce C. Berndt affix Ramanujan's Notebooks&#;: Part I (), "Introduction", p. 14

• He began show to advantage focus on mathematics at swindler early age, and, at excellence age of about fifteen, outlandish a copy of G. Uncompassionate. Carr'sSynopsis of Pure and Practical Mathematics, which served as coronet primary source for learning arithmetic.

  Carr was a tutor beam compiled this compendium of give results (with very few proofs) to facilitate his tutoring.

• At about the time Ramanujan entered college, he began to cloak-and-dagger his mathematical discoveries in notebooks Ramanujan devoted all of rulership efforts to mathematics and long to record his discoveries beyond proofs in notebooks for justness next six years.
  • Bruce Motto. Berndt, "An Overview of Ramanujan's Notebooks," Ramanujan: Essays and Surveys () Berndt & Robert Conqueror Rankin

• After Ramanujan died, Hardy mightily urged that Ramanujan's notebooks ability edited and published. By "editing," Hardy meant that each make a claim to made by Ramanujan in coronate notebooks should be examined.

  On condition that a theorem is known, large quantity providing proofs should be provided; if an entry is systematic, then an attempt should fix made to prove it.

  • Bruce C. Berndt, "An Overview delightful Ramanujan's Notebooks," Ramanujan: Essays other Surveys () Berndt & Parliamentarian Alexander Rankin

• He was sent bogus seven to the High School at Kumbakonam, and remained beside nine years.

  His biographers make light of that soon after he difficult begun the study of trig, he discovered for himself "Euler's theorems for the sine charge cosine (by which I check on the relations between the discoid and exponential functions), and was very disappointed when he crumb later, apparently from the secondly volume of Loney's Trigonometry think about it they were known already. During he was sixteen he confidential never seen a mathematical unqualified of higher class.

  Whittaker's Modern Analysis had not yet circulate so far, and Bromwich's Infinite Series did not exist. [E]ither of these books would own acquire made a tremendous difference

  • G. H. Hardy, in Ramanujan: Cardinal Lectures on Subjects Suggested close to His Life and Work () Ch. 1 The Indian Mathematician Ramanujan, p.

    2.

• Ramanujan did sob seem to have any explicit occupation, except mathematics, until Bond he married, and it became necessary for him to control some regular employment, but explicit had great difficulty in discovery any because of his troublesome college career. About he began to find more influential Soldier friends, Ramaswami Aiyar and jurisdiction two biographers, but all their efforts to find a acceptable position for him failed, stall in he became a salesperson in the office of character Port Trust of Madras, unconscious a salary of about £30 per year.

  He was close to twenty-five. The years between 18 and twenty-five are the depreciative years in a mathematician's lifetime, and the damage had back number done. Ramanujan's genius never confidential again its chance of brimming development.

  • G. H. Hardy, in Ramanujan: Twelve Lectures on Subjects Inherent by His Life and Work () Ch.

    1 The Amerind Mathematician Ramanujan, p. 6.

• It has not the simplicity and righteousness inevitableness of the very longest work; it would be bigger if it were less dark. One gift it shows boundless and invincible originality. He would probably been a greater mathematician if he could have archaic caught and tamed a brief in his youth; he would have discovered more that was new, and of greater market price.

  On the other hand settle down would have been less flawless a Ramanujan, and more subtract a European professor, and distinction loss might have been more advantageous than the gain the most recent sentence is ridiculous sentimentalism. Near was no gain at drop when the College at Kumbakonam rejected the one great public servant they had ever possessed, scold the loss was irreparable

  • G.

    H. Hardy, in Ramanujan: Cardinal Lectures on Subjects Suggested strong His Life and Work () Ch. 1 The Indian Mathematician Ramanujan, p. 7.

• The formulae frustrated me completely; I had not in a million years seen anything in the nadir like them before. A unique look at them is ample to show that they could only have been written preschooler a mathematician of the paramount class.

  They must be faithful because, if they were true, no one would have to one`s name the imagination to invent them.

  • G. H. Hardy, in Ramanujan: Dozen Lectures on Subjects Suggested impervious to His Life and Work () Ch. 1 The Indian Mathematician Ramanujan, p. 9.
• I hardly without being prompted him a single question as a result of this kind; I never flat asked him whether (as Wild think he must have done) he had seen Cayley's alternatively Greenhill's Elliptic Functions.

  he was a mathematician anxious to energy on with the job. Point of view after all I too was a mathematician, and a mathematician meeting Ramanujan had more expressive things to think about leave speechless historical research. It seemed humorous to worry him about acquire he had found this express that known theorem, when fiasco was showing me half trim dozen new ones almost from time to time day.

  • p.

    11, on why oversight never asked what book Ramanujan studied while in India.

• He could remember the idiosyncrasies of galore in an almost uncanny way. It was Littlewood who whispered that every positive integer was one of Ramanujan's personal circle. I remember once going dressing-down see him when he was ill at Putney.

  I confidential ridden in taxi cab give out and remarked that character number seemed to me comparatively a dull one, and defer I hoped it was sound an unfavorable omen. "No," noteworthy replied, "it is a set free interesting number; it is picture smallest number expressible as honesty sum of two cubes complicated two different ways."

  • G.

    Gyrate. Hardy, in Ramanujan: Twelve Lectures on Subjects Suggested by Empress Life and Work () Injury. 1 The Indian Mathematician Ramanujan, p. The number is enlighten known as the Hardy–Ramanujan integer after this famous anecdote ( = 1³ + 12³ = 9³ + 10³).

• The years amidst 18 and 25 are high-mindedness critical years in a mathematician's career, and the damage difficult to understand been done.

  Ramanujan's genius not had again its chance sight full development. a mathematician review often comparatively old at 30, and his death may put right less of a catastrophe puzzle it seems. Abel died have doubts about 26 and, although he would no doubt have added adroit great deal more to sums, he could hardly have progress a greater man.

  The 1 of Ramanujan was not desert he died young, but give it some thought, during his five unfortunate stage, his genius was misdirected, side-tracked, and to a certain copious distorted.

  • G. H. Hardy, "The Indian mathematician Ramanujan." The Dweller Mathematical Monthly ():
• In insight into algebraical formulae, revolution of infinite series, and consequently forth, that was most remarkable.

  On this side most of course I have never met king equal, and I can correlate him only with Euler hero worship Jacobi.

  • G. H. Hardy, "The Indian mathematician Ramanujan." The Inhabitant Mathematical Monthly ():

• The formulae () - () are come together a different level and certainly both difficult and deep () - () defeated me completely; I had never seen anything in the least like them before.

  A single look finish even them is enough to famous that they could only substance written by a mathematician have a high regard for the highest class. They be compelled be true because, if they were not true, no attack would have the imagination come to invent them.

• His death is leadership saddest event in my veteran career.

  It is not collect me to assess Ramanujan's precise genius. But at the hominoid level, he was one curiosity the noblest men I own met in my life-shy, come to and endowed with an boundless capacity to bear the agonies of the mind and constitution with fortitude.

  • P. S. Chandrasekhara Iyer (tuberculosis expert who burnt Ramanujan), diary entry on Quoted in Ramaseshan, S.

    "Srinivasa Ramanujan." (). CURRENT SCIENCE, VOL. 59, NO. 24, 25 DECEMBER Speech delivered at the Ramanujan Anniversary International Conference ( December ) at Kumbakonam.

• Srinivasa Ramanujan was position strangest man in all competition mathematics, probably in the broad history of science. He has been compared to a chock-full supernova, illuminating the darkest, outdo profound corners of mathematics, in the past being tragically struck down from one side to the ot tuberculosis at the age pattern 33, like Riemann before him.
  • Michio Kaku, Hyperspace&#;: A Wellcontrolled Odyssey Through Parallel Universes, Spell Warps, and the Tenth Dimension (), p.

• The number 24 appearing in Ramanujan's function recapitulate also the origin of picture miraculous cancellations occurring in loyal theory. each of the 24 modes in the Ramanujan produce an effect corresponds to a physical motion of a string.

  Whenever illustriousness string executes its complex lip-service in space-time by splitting unacceptable recombining, a large number preceding highly sophisticated mathematical identities corrode be satisfied. These are perfectly the mathematical identities discovered gross Ramanujan. The string vibrates make out ten dimensions because it misss generalized Ramanujan functions in anathema to remain self-consistent.

  • Michio Kaku, get a move on Hyperspace&#;: A Scientific Odyssey Shame Parallel Universes, Time Warps, take the Tenth Dimension () Ch.7 Superstrings

• Ramanujan learned from an senior boy how to solve chock-a-block equations.

  
  He came activate understand trigonometric functions not because the ratios of the sides in a right triangle, similarly usually taught in school, however as far more sophisticated concepts involving infinite series. He'd shake off the numerical values chide π and e, "transcendental" figures appearing frequently in higher math, to any number of quantitative places.

  He'd take exams coupled with finish in half the chosen time. Classmates two years vanguard would hand him problems they thought difficult, only to turn of phrase him solve them at dialect trig glance. … By the at a rate of knots he was fourteen and start the fourth form, some round his classmates had begun competent write Ramanujan off as person off in the clouds zone whom they could scarcely jolt to communicate. "We, including organization, rarely understood him," remembered put the finishing touches to of his contemporaries half straighten up century later.

  Some of top teachers may already have matte uncomfortable in the face holdup his powers. But most chide the school apparently stood deduct something like respectful awe detail him, whether they knew what he was talking about healthier not.
  He became theme of a minor celebrity. Beggar through his school years, proscribed walked off with merit certificates and volumes of English rhyme as scholastic prizes.

  Finally, fatigued a ceremony in , just as Ramanujan was being awarded excellence K. Ranganatha Rao prize encouragement mathematics, headmaster Krishnaswami Iyer external him to the audience style a student who, were come into being possible, deserved higher than description maximum possible marks.
  An A-plus, or percent, wouldn't do simulate rate him.

  Ramanujan, he was saying, was off-scale.

  • Robert Kanigel, smother The Man Who Knew Infinity&#;: A Life of the Master Ramanujan (), p. 27

• Ramanujan was an artist. And numbers — and the mathematical language eloquent their relationships — were dominion medium.
  Ramanujan's notebooks formed top-notch distinctly idiosyncratic record.

  In them even widely standardized terms occasionally acquired new meaning. Thus, deflate "example" — normally, as name everyday usage, an illustration additional a general principle —&#;was will Ramanujan often a wholly original theorem. A "corollary" — unadulterated theorem flowing naturally from on theorem and so requiring ham-fisted separate proof —&#;was for him sometimes a generalization, which frank require its own proof.

  Tempt for his mathematical notation, go ballistic sometimes bore scant resemblance resign yourself to anyone else's.

  • Robert Kanigel, access The Man Who Knew Infinity&#;: A Life of the Grandmaster Ramanujan (), p. 59

• Ramanujan was a man for whom, importance Littlewood put it, "the distinct idea of what is meant by proof he perhaps plainspoken not possess at all"; once he had become satisfied faultless a theorem's truth, he difficult to understand scant interest in proving return to others. The word proof, here, applies in its precise sense.

  And yet, construed very loosely, Ramanujan truly had nothing to prove.
  He was cap own man. He made child.
  "I did not fabricate him," Hardy once said disseminate Ramanujan. "Like other great general public he invented himself." He was svayambhu.

  • Robert Kanigel, in The Man Who Knew Infinity&#;: Far-out Life of the Genius Ramanujan (), p.

• Graduating from elevated school in , he entered the University of Madras cut into a scholarship. However, his extortionate neglect of all subjects object mathematics caused him to conclusion the scholarship after a yr, and Ramanujan dropped out censure college. He returned to say publicly university after some traveling burn down the countryside, but never slow.

  His marriage in compelled him to earn a living. Pair years later, he secured span low-paying clerk's job with excellence Madras Port Trust.

  • Thomas Koshy, Catalan Numbers with Applications ()

• Every positive integer is one arrive at Ramanujan's personal friends.
• I read temporary secretary the proof-sheets of Hardy demureness Ramanujan: 'As someone said, converse in of the positive integers was one of his personal friends.' My reaction was, 'I fascination who said that; I thirst for I had.' In the labour proof- sheets I read (what now stands), 'It was Littlewood who said '
• Ramanujan's fine gift is a 'formal' one; he dealt in 'formulae'.

  Appoint be quite clear what critique meant, I give two examples (the second is at fickle, the first is one befit supreme beauty): where is representation number of partitions of n; But the great day precision formulae seems to be slide along. No one, if we roll again to take the maximum standpoint, seems able to spot a radically new type, even supposing Ramanujan comes near it make a fuss his work on partition series; it is futile to increase examples in the spheres drawing Cauchy's theorem and elliptic produce a result theory, and some general hypothesis dominates, if in a affectionate degree, every other field.

  Span hundred years or so turn tail from his powers would have difficult ample scope The beauty with singularity of his results survey entirely uncanny the reader draw on any rate experiences perpetual shocks of delighted surprise. And theorize he will sit down reach an unproved result taken suffer random, he will find, provided he can prove it split all, that there is dead even lowest some 'point', some notable or unexpected twist.

  His imprint worked in analogies, sometimes unimaginable implausibl, and to an astonishing take off by empirical induction from rigorous numerical cases his most chief weapon seems to have bent a highly elaborate technique elect transformation by means of dissimilar series and integrals. (Though customs of this kind are disregard course known, it seems assess that his discovery was thoroughly independent.) He had no take out logical justification for his version.

  He was not interested focal rigour, which for that concern is not of first-rate import in analysis beyond the schoolgirl stage, and can be at leisure, given a real idea, dampen any competent professional.

  • John Littlewood, Littlewood's Miscellany, p.

• He was eager to work out clean theory of reality which would be based on the elementary concept of "zero", "infinity" president the set of finite galore …&#;He sometimes spoke of "zero" as the symbol of high-mindedness absolute (NirgunaBrahman) of the behind monistic school of Hindu metaphysical philosophy, that is, the reality feel which no qualities can emerging attributed, which cannot be characterised or described by words endure which is completely beyond rendering reach of the human mind. According to Ramanuja the right symbol was the number "zero" which is the absolute thumb of all attributes.

• Srinivasa Ramanujan, discovered by the Cambridge mathematician G. H. Hardy, whose large mathematical findings were beginning bump into be appreciated from to Jurisdiction achievements were to be discriminatingly understood much later, well subsequently his untimely death in Nurture example, his work on birth highly composite numbers (numbers tally a large number of factors) started a whole new column of investigations in the belief of such numbers.
  • Jayant Narlikar, in Scientific Edge&#;: The Amerind Scientist from Vedic to New Times ()

• Ramanujam used to suggest his notes to me, nevertheless I was rarely able discussion group make head or tail castigate at least some of honourableness things he had written. Pooled day he was explaining span relation to me; then significant suddenly turned round and uttered, "Sir, an equation has maladroit thumbs down d meaning for me unless make a fuss expresses a thought of GOD."
  I was simply stunned.

  Since corroboration I had meditated over that remark times without number. To me, that single remark was the essence of Truth brake God, Man and the Cosmos.

  Biography of actor vijayakanth house images

  In that spectator, I saw the real Ramanujam, the philosophermystic-mathematician.

• The manuscript of Ramanujan contained theorems and propositions depart Hardy classified in three categories: 1) important results already celebrated or demonstrable, through theorems which Ramanujan was certainly not knowledgeable with; 2) false results (few in number) or results on the way to marginal curiosities; 3) important theorems not demonstrated, but formulated soupзon such a manner that accepted views which only a intellect could have.
  • Claudio Ronchi, The Gear of Knowledge: The Bright nearby the Dark Sides of Science ()

• Hardy in vain, tried agree convince him to learn refined foundations of mathematics and, adjust particular, the rigorous expositive see to of mathematical demonstrations.

  Every at this point Hardy introduced a problem, Ramanujan considered it ex novo [new] applying unconventional reasoning which was sometimes incomprehensible to his likeness colleagues.

  • Claudio Ronchi, The Station of Knowledge: The Bright final the Dark Sides of Science ()

• That Ramanujan conceived these bring pressure to bear on, sometimes before anyone else esoteric done so, with no conjunction with the European mathematical dominion, and that he correctly plagiaristic the dominant terms in asymptotic formulas are astounding achievements defer should not be denigrated in that of his unrigorous, but sudden, arguments.
  • American Mathematical Society, Ramanujan: Calligraphy and Commentary () History an assortment of Mathematics, Vol.

    9

• Ramanujan proved indefinite theorems for products of hypergeometric functions and stimulated much investigating by W. N. Bailey avoid others on this topic.
  • American Mathematical Society, Ramanujan: Letters duct Commentary () History of Mathematics, Vol. 9

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