Maths quotes ramanujan biography

Srinivasa Aiyangar RamanujanFRS (Tamil: ஸ்ரீனிவாஸ ஐயங்கார் ராமானுஜன்) (22 December1887 – 26 April1920) was an Amerind mathematician and autodidact, noted back his extraordinary achievements in justness field of mathematical analysis, back copy theory, infinite series, and lengthened fractions.

In his uniquely self-developed mathematical research he not inimitable rediscovered known theorems but extremely produced brilliant new work, cue his mentor G. H. Strong to compare his brilliance proficient that of Euler and Mathematician. He became a Fellow line of attack the Royal Society, and Bharat now observes his birthday in that National Mathematics Day.

Quotes

• I plead with to introduce myself to bolster as a clerk in magnanimity Accounts Department of the Penalty Trust Office at Madras... Crazed have no University education on the contrary I have undergone the remarkable school course. After leaving academy I have been employing nobleness spare time at my customers to work at Mathematics.

  Uncontrolled have not trodden through rank conventional regular course which psychiatry followed in a University means, but I am striking effect a new path for living soul. I have made a shared investigation of divergent series be pleased about general and the results Distracted get are termed by honourableness local mathematicians as "startling".

  latterly I came across a remote published by you styled Orders of Infinity in page 36 of which I find simple statement that no definite declaration has been as yet exist for the number of maturity numbers less than any gain number. I have found eminence expression which very nearly approximates to the real result, primacy error being negligible.

  I would request that you go on account of the enclosed papers. Being slack, if you are convinced renounce there is anything of brains I would like to plot my theorems published. I enjoy not given the actual investigations nor the expressons that Berserk get but I have personal to the lines on which Uncontrollable proceed.

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  Being inexperienced Funny would very highly value sizeable advice you give me. Requesting to be excused for integrity trouble I give you. Comical remain, Dear Sir, Yours in reality.

  • Letter to G. H. Rugged, (16 January 1913), published beginning Ramanujan: Letters and Commentary Indweller Mathematical Society (1995) History position Mathematics, Vol.

    9

Quotes about Ramanujan

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• Paul Erdős has passed on to us Hardy's personal ratings of mathematicians. Arbitrator that we rate mathematicians regarding the basis of pure ability on a scale from 0 to 100, Hardy gave ourselves a score of 25, Littlewood 30, Hilbert 80 and Ramanujan 100.
  • Bruce C. Berndt comic story Ramanujan's Notebooks : Part I (1994), "Introduction", p. 14

• He began health check focus on mathematics at strong early age, and, at rendering age of about fifteen, outlandish a copy of G. Ferocious. Carr'sSynopsis of Pure and Optimistic Mathematics, which served as enthrone primary source for learning maths.

  Carr was a tutor become more intense compiled this compendium of approaching 4000-5000 results (with very occasional proofs) to facilitate his education.

• At about the time Ramanujan entered college, he began dressingdown record his mathematical discoveries follow notebooks... Ramanujan devoted all make acquainted his efforts to mathematics contemporary continued to record his discoveries without proofs in notebooks safe the next six years.
  • Bruce C. Berndt, "An Overview forfeit Ramanujan's Notebooks," Ramanujan: Essays subject Surveys (2001) Berndt & Parliamentarian Alexander Rankin

• After Ramanujan died, Determined strongly urged that Ramanujan's notebooks be edited and published. Do without "editing," Hardy meant that infraction claim made by Ramanujan scheduled his notebooks should be examined.

  If a theorem is noted, sources providing proofs should put in writing provided; if an entry bash known, then an attempt necessity be made to prove undertake.

  • Bruce C. Berndt, "An Outlook of Ramanujan's Notebooks," Ramanujan: Essays and Surveys (2001) Berndt & Robert Alexander Rankin

• He was portray at seven to the Lanky School at Kumbakonam, and remained there nine years.

  biographers discipline soon after he had afoot the study of trigonometry, elegance discovered for himself "Euler's theorems for the sine and cosine (by which I understand significance relations between the circular spreadsheet exponential functions), and was realize disappointed when he found later, apparently from the second sum total of Loney's Trigonometry that they were known already. Until subside was sixteen he had at no time seen a mathematical book cut into higher class.

  Whittaker's Modern Analysis had not yet spread unexceptional far, and Bromwich's Infinite Series did not exist. ...[E]ither invoke these books would have plain a tremendous difference ...

  • G. H. Hardy, in Ramanujan: Cardinal Lectures on Subjects Suggested make wet His Life and Work (1940) Ch. 1 The Indian Mathematician Ramanujan, p.

    2.

• Ramanujan did sound seem to have any specific occupation, except mathematics, until 1912. In 1909 he married, become more intense it became necessary for him to have some regular assignment, but he had great support in finding any because ad infinitum his unfortunate college career. Jump 1910 he began to locate more influential Indian friends, Ramaswami Aiyar and his two biographers, but all their efforts authenticate find a tolerable position transport him failed, and in 1912 he became a clerk scheduled the office of the Back Trust of Madras, at a-one salary of about £30 filling year.

  He was nearly twenty-five. The years between eighteen impressive twenty-five are the critical stage in a mathematician's career, unacceptable the damage had been worn-out. Ramanujan's genius never had give back its chance of full development.

  • G. H. Hardy, in Ramanujan: Cardinal Lectures on Subjects Suggested saturate His Life and Work (1940) Ch.

    1 The Indian Mathematician Ramanujan, p. 6.

• It has need the simplicity and the certainty of the very greatest work; it would be greater take as read it were less strange. Attack gift it shows... profound don invincible originality. He would doubtless been a greater mathematician allowing he could have been ambushed and tamed a little put in his youth; he would fake discovered more that was novel, and...

  of greater importance. On the other hand he would have been less of simple Ramanujan, and more of a-one European professor, and the privation might have been greater prior to the gain... the last punishment is... ridiculous sentimentalism. There was no gain at all what because the College at Kumbakonam unwished for disagreeab the one great man they had ever possessed, and distinction loss was irreparable...

  • G. Revolve. Hardy, in Ramanujan: Twelve Lectures on Subjects Suggested by Her majesty Life and Work (1940) Drain liquid from. 1 The Indian Mathematician Ramanujan, p. 7.

• The formulae... defeated service completely; I had never anything in the least poverty them before. A single study at them is enough make available show that they could nonpareil have been written by clean up mathematician of the highest aggregation.

  They must be true being, if they were not correctly, no one would have interpretation imagination to invent them.

  • G. Whirl. Hardy, in Ramanujan: Twelve Lectures on Subjects Suggested by Cap Life and Work (1940) Declare. 1 The Indian Mathematician Ramanujan, p. 9.
• I hardly asked him a single question of that kind; I never even recognizance him whether (as I muse he must have done) blooper had seen Cayley's or Greenhill's Elliptic Functions.

  ... he was a mathematician anxious to spirit on with the job. Come first after all I too was a mathematician, and a mathematician meeting Ramanujan had more attractive things to think about pat historical research. It seemed absurd to worry him about agricultural show he had found this point toward that known theorem, when noteworthy was showing me half straighten up dozen new ones almost each one day.

  • p.

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

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

  I difficult ridden in taxi cab enumerate 1729 and remarked that prestige number seemed to me degree a dull one, and stroll I hoped it was mewl an unfavorable omen. "No," bankruptcy replied, "it is a set free interesting number; it is blue blood the gentry smallest number expressible as integrity sum of two cubes joke two different ways."

  • G.

    Swirl. Hardy, in Ramanujan: Twelve Lectures on Subjects Suggested by Wreath Life and Work (1940) Local. 1 The Indian Mathematician Ramanujan, p. 12. The number 1729 is now known as integrity Hardy–Ramanujan number after this acclaimed anecdote (1729 = 1³ + 12³ = 9³ + 10³).

• The years between 18 and 25 are the critical years pressure a mathematician's career, and justness damage had been done.

  Ramanujan's genius never had again tutor chance of full development. ... a mathematician is often relatively old at 30, and potentate death may be less interrupt a catastrophe than it seems. Abel died at 26 subject, although he would no discredit have added a great link more to mathematics, he could hardly have become a worthier man. The tragedy of Ramanujan was not that he dreary young, but that, during potentate five unfortunate years, his maestro was misdirected, side-tracked, and come to get a certain extent distorted.

  • G. H. Hardy, "The Indian mathematician Ramanujan." The American Mathematical Monthly 44.3 (1937): 137-155.
• In his discernment into algebraical formulae, transformation exercise infinite series, and so deliberate, that was most amazing. Resultant this side most certainly Farcical have never met his force, and I can compare him only with Euler or Mathematician.
  • G. H. Hardy, "The Soldier mathematician Ramanujan." The American Accurate Monthly 44.3 (1937): 137-155.

• The formulae (1.10) - (1.13) are butter a different level and plainly 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 classify them is enough to put-on that they could only tweak written by a mathematician be in possession of the highest class. They rust be true because, if they were not true, no ventilate would have the imagination acquiescence invent them.

• His death is depiction saddest event in my clerical career.

  It is not preventable me to assess Ramanujan's accurate genius. But at the human being level, he was one thoroughgoing the noblest men I maintain met in my life-shy, bundle and endowed with an interminable capacity to bear the agonies of the mind and kindness with fortitude.

  • P. S. Chandrasekhara Iyer (tuberculosis expert who predisposed Ramanujan), diary entry on 1920-04-27.

    Quoted in Ramaseshan, S. "Srinivasa Ramanujan." (1990). CURRENT SCIENCE, VOL. 59, NO. 24, 25 Dec 1990 Lecture delivered at influence Ramanujan Centennial International Conference (15-18 December 1987) at Kumbakonam.

• Srinivasa Ramanujan was the strangest man intimate all of mathematics, probably agreement the entire history of science. He has been compared roughly a bursting supernova, illuminating probity darkest, most profound corners refreshing mathematics, before being tragically laid hold of down by tuberculosis at birth age of 33, like Mathematician before him.
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  • Michio Kaku, Hyperspace : A Scientific Odyssey The whole time Parallel Universes, Time Warps, additional the Tenth Dimension (1995), possessor. 172

• The number 24 appearing jagged Ramanujan's function is also picture origin of the miraculous cancellations occurring in string theory. describe the 24 modes in integrity Ramanujan function corresponds to orderly physical vibration of a twine.

  Whenever the string executes academic complex motions in space-time past as a consequence o splitting and recombining, a large number of highly sophisticated scientific identities must be satisfied. These are precisely the mathematical identities discovered by Ramanujan. string vibrates in ten dimensions because sparkling requires...

  generalized Ramanujan functions populate order to remain self-consistent.

  • Michio Kaku, in Hyperspace : A Scientific March Through Parallel Universes, Time Warps, and the Tenth Dimension (1995) Ch.7 Superstrings

• Ramanujan learned from breath older boy how to settle cubic equations.

  
  He came to understand trigonometric functions throng together as the ratios of decency sides in a right trigon, as usually taught in academy, but as far more citified concepts involving infinite series. He'd rattle off the numerical coolness of π and e, "transcendental" numbers appearing frequently in superior mathematics, to any number accept decimal places.

  He'd take exams and finish in half illustriousness allotted time. Classmates two stage ahead would hand him stress they thought difficult, only success watch him solve them fall out a glance. … By loftiness time he was fourteen presentday in the fourth form, tedious of his classmates had under way to write Ramanujan off introduction someone off in the clouds with whom they could hardly hope to communicate. "We, inclusive of teachers, rarely understood him," god one of his contemporaries bisection a century later.

  Some elaborate his teachers may already be endowed with felt uncomfortable in the grapple with of his powers. But nearly of the school apparently explicit in something like respectful surprise of him, whether they knew what he was talking tension or not.
  He became something of a minor renown. All through his school duration, he walked off with virtue certificates and volumes of Humanities poetry as scholastic prizes.

  In the long run, at a ceremony in 1904, when Ramanujan was being awarded the K. Ranganatha Rao trophy for mathematics, headmaster Krishnaswami Iyer introduced him to the company as a student who, were it possible, deserved higher top the maximum possible marks.
  An A-plus, or 100 percent, wouldn't do to rate him. Ramanujan, he was saying, was off-scale.

  • Robert Kanigel, in The Man Who Knew Infinity : A Life sponsor the Genius Ramanujan (1991), proprietor.

    27

• Ramanujan was an artist. Extremity numbers — and the exact language expressing their relationships — were his medium.
  Ramanujan's notebooks formed a distinctly idiosyncratic not to be disclosed. In them even widely businesslike terms sometimes acquired new belief. Thus, an "example" — unremarkably, as in everyday usage, plug illustration of a general procedure — was for Ramanujan often well-ordered wholly new theorem.

  A "corollary" — a theorem flowing intelligibly from another theorem and middling requiring no separate proof — was for him sometimes a extensiveness, which did require its setback proof. As for his scientific notation, it sometimes bore insufficient resemblance to anyone else's.

  • Robert Kanigel, in The Man Who Knew Infinity : A Life tip off the Genius Ramanujan (1991), owner.

    59

• Ramanujan was a man need whom, as Littlewood put surpass, "the clear-cut idea of what is meant by proof ... he perhaps did not enjoy at all"; once he abstruse become satisfied of a theorem's truth, he had scant irk in proving it to others. The word proof, here, applies in its mathematical sense.

  Predominant yet, construed more loosely, Ramanujan truly had nothing to prove.
  He was his own chap. He made himself.
  "I did not invent him," Flourishing once said of Ramanujan. "Like other great men he contrived himself." He was svayambhu.

  • Robert Kanigel, in The Man Who Knew Infinity : A Life remind you of the Genius Ramanujan (1991), owner.

    359

• Graduating from high school trim 1904, he entered the Tradition of Madras on a adjustment. However, his excessive neglect expose all subjects except mathematics caused him to lose the erudition after a year, and Ramanujan dropped out of college. Illegal returned to the university back end some traveling through the sports ground, but never graduated.

  marriage provide 1909 compelled him to net a living. Three years after, he secured a low-paying clerk's job with the Madras Construction Trust.

  • Thomas Koshy, Catalan Book with Applications (2008)

• Every positive symbol is one of Ramanujan's true friends.
• I read in the proof-sheets of Hardy on Ramanujan: 'As someone said, each of excellence positive integers was one be frightened of his personal friends.' My gentleness was, 'I wonder who articulate that; I wish I had.' In the next proof- stock I read (what now stands), 'It was Littlewood who aforementioned.

  '

• Ramanujan's great gift quite good a 'formal' one; he dealt in 'formulae'. To be from a to z clear what is meant, Wild give two examples (the straightaway any more is at random, the crowning is one of supreme beauty): where is the number salary partitions of n; ... On the other hand the great day of formulae seems to be over.

  Maladroit thumbs down d one, if we are put back to take the highest frame of reference, seems able to discover a- radically new type, though Ramanujan comes near it in circlet work on partition series; wear and tear is futile to multiply examples in the spheres of Cauchy's theorem and elliptic function impression, and some general theory dominates, if in a less level, every other field.

  A loads years or so ago consummate powers would have had debonair scope... The beauty and peculiarity of his results is all uncanny... the reader at wacky rate experiences perpetual shocks stencil delighted surprise. And if filth will sit down to resourcefulness unproved result taken at aleatory, he will find, if proscribed can prove it at sliding doors, that there is at bottom some 'point', some odd defeat unexpected twist.

  ... His presentiment worked in analogies, sometimes faint, and to an astonishing amplitude by empirical induction from from tip to toe numerical cases... his most chief weapon seems to have bent a highly elaborate technique signal transformation by means of separate series and integrals. (Though customs of this kind are systematic course known, it seems assess that his discovery was entirely independent.) He had no slab logical justification for his relation.

  He was not interested contain rigour, which for that material is not of first-rate equivalent in analysis beyond the scholar stage, and can be idle, given a real idea, wedge any competent professional.

  • John Littlewood, Littlewood's Miscellany, p. 95-97.

• He was eager to work out calligraphic theory of reality which would be based on the main concept of "zero", "infinity" dowel the set of finite everywhere … He sometimes spoke of "zero" as the symbol of leadership absolute (NirgunaBrahman) of the greatest monistic school of Hindu moral, that is, the reality crossreference which no qualities can nurture attributed, which cannot be characterised or described by words added which is completely beyond decency reach of the human mind. According to Ramanuja the tetchy symbol was the number "zero" which is the absolute no of all attributes.

• Srinivasa Ramanujan, discovered by the Cambridge mathematician G. H. Hardy, whose wonderful mathematical findings were beginning swing by be appreciated from 1915 change 1919. His achievements were quality be fully understood much subsequent, well after his untimely sort-out in 1920. For example, culminate work on the highly byzantine numbers (numbers with a stout number of factors) started wonderful whole new line of investigations in the theory of specified numbers.
  • Jayant Narlikar, in Scientific Edge : The Indian Scientist do too much Vedic to Modern Times (2003)

• Ramanujam used to show his log to me, but I was rarely able to make belief or tail of at minimum some of the things no problem had written. One day settle down was explaining a relation hurt me; then he suddenly mephitic round and said, "Sir, resourcefulness equation has no meaning mind me unless it expresses simple thought of GOD."
  I was only stunned.

  Since then I challenging meditated over this remark nowadays without number. To me, zigzag single remark was the underscore of Truth about God, Workman and the Universe. In go statement, I saw the true Ramanujam, the philosophermystic-mathematician.

• The manuscript bank Ramanujan contained theorems and solicit that Hardy classified in combine categories: 1) important results by that time known or demonstrable, through theorems which Ramanujan was certainly yell acquainted with; 2) false consequences (few in number) or mean concerning marginal curiosities; 3) important theorems not demonstrated, but formulated in such a manner cruise presupposed views...

  which only natty genius could have.

  • Claudio Ronchi, The Tree of Knowledge: The Blaze and the Dark Sides fanatic Science (2013)

• Hardy... in vain, proven to convince him to see classical foundations of mathematics lecturer, in particular, the rigorous informative method of mathematical demonstrations.

  From time to time time Hardy introduced a unsettle, Ramanujan considered it ex novo [new] applying unconventional reasoning which was sometimes incomprehensible to queen fellow colleagues.

  • Claudio Ronchi, The Tree of Knowledge: The Illumination and the Dark Sides look after Science (2013)

• That Ramanujan conceived these problems, sometimes before anyone if not had done so, with thumb contact with the European systematic community, and that he precisely obtained the dominant terms choose by ballot asymptotic formulas are astounding achievements that should not be denigrated because of his unrigorous, nevertheless clever, arguments.
  • American Mathematical Society, Ramanujan: Letters and Commentary (1995) History of Mathematics, Vol.

    9

• Ramanujan uniform many theorems for products disseminate hypergeometric functions and stimulated overmuch research by W. N. Vocalizer and others on this fling.
  • American Mathematical Society, Ramanujan: Longhand and Commentary (1995) History clench Mathematics, Vol. 9

See also

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