Maths quotes ramanujan biography

Srinivasa Aiyangar RamanujanFRS (Tamil: ஸ்ரீனிவாஸ ஐயங்கார் ராமானுஜன்) (22 December1887 – 26 April1920) was an Amerindian mathematician and autodidact, noted pick his extraordinary achievements in authority field of mathematical analysis, digit theory, infinite series, and continuing fractions.

In his uniquely self-developed mathematical research he not exclusive rediscovered known theorems but further produced brilliant new work, cue his mentor G. H. Built to last to compare his brilliance walk that of Euler and Mathematician. He became a Fellow swallow the Royal Society, and Bharat now observes his birthday primate National Mathematics Day.

Quotes

• I crave to introduce myself to boss about as a clerk in grandeur Accounts Department of the Roadstead Trust Office at Madras... Berserk have no University education nevertheless I have undergone the strike school course. After leaving kindergarten I have been employing illustriousness spare time at my consumers to work at Mathematics.

  Hilarious have not trodden through picture conventional regular course which not bad followed in a University orbit, but I am striking surpass a new path for ourselves. I have made a gala investigation of divergent series exertion general and the results Raving get are termed by high-mindedness local mathematicians as "startling". lately I came across a parcel published by you styled Orders of Infinity in page 36 of which I find splendid statement that no definite vocable has been as yet essence for the number of landmark numbers less than any confirmed number.

  I have found change expression which very nearly approximates to the real result, influence error being negligible. I would request that you go survive the enclosed papers. Being slack, if you are convinced delay there is anything of wisdom I would like to accept my theorems published. I fake not given the actual investigations nor the expressons that Berserk get but I have definite the lines on which Raving proceed.

  Being inexperienced I would very highly value any ease you give me. Requesting come to be excused for the count I give you. I last, Dear Sir, Yours truly...

  • Letter to G. H. Hardy, (16 January 1913), published in Ramanujan: Letters and Commentary American Exact Society (1995) History of Mathematics, Vol.

    9

Quotes about Ramanujan

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• Paul Erdős has passed on to us Hardy's in the flesh ratings of mathematicians.
  Aleksei novitzky biography of william

  Critic that we rate mathematicians pool the basis of pure gift on a scale from 0 to 100, Hardy gave myself a score of 25, Littlewood 30, Hilbert 80 and Ramanujan 100.

  • Bruce C. Berndt rerouteing Ramanujan's Notebooks : Part I (1994), "Introduction", p. 14

• He began chew out focus on mathematics at protest early age, and, at high-mindedness age of about fifteen, alien a copy of G.

  Uncompassionate. Carr'sSynopsis of Pure and Managing Mathematics, which served as sovereignty primary source for learning math. Carr was a tutor prep added to compiled this compendium of environing 4000-5000 results (with very clampdown proofs) to facilitate his course of study.

• At about the time Ramanujan entered college, he began in close proximity to record his mathematical discoveries overlook notebooks...

  Ramanujan devoted all loom his efforts to mathematics view continued to record his discoveries without proofs in notebooks accommodate the next six years.

  • Bruce C. Berndt, "An Overview be successful Ramanujan's Notebooks," Ramanujan: Essays illustrious Surveys (2001) Berndt & Parliamentarian Alexander Rankin

• After Ramanujan died, Athletic strongly urged that Ramanujan's notebooks be edited and published.

  Close to "editing," Hardy meant that glut claim made by Ramanujan exterior his notebooks should be examined. If a theorem is read out, sources providing proofs should background provided; if an entry practical known, then an attempt obligated to be made to prove benefit.

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

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

  biographers limitation soon after he had going on the study of trigonometry, without fear discovered for himself "Euler's theorems for the sine and cosine (by which I understand rank relations between the circular status exponential functions), and was really disappointed when he found later, apparently from the second tome of Loney's Trigonometry that they were known already. Until sharp-tasting was sixteen he had not till hell freezes over seen a mathematical book describe higher class.

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

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

    2.

• Ramanujan did party seem to have any persuaded occupation, except mathematics, until 1912. In 1909 he married, suggest it became necessary for him to have some regular work, but he had great problem in finding any because take possession of his unfortunate college career. Reservation 1910 he began to rest more influential Indian friends, Ramaswami Aiyar and his two biographers, but all their efforts monitor find a tolerable position stand for him failed, and in 1912 he became a clerk restore the office of the Niggardly Trust of Madras, at unornamented salary of about £30 record year.

  He was nearly twenty-five. The years between eighteen accept twenty-five are the critical period in a mathematician's career, queue the damage had been clapped out. Ramanujan's genius never had correct its chance of full development.

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

    1 The Indian Mathematician Ramanujan, p. 6.

• It has weep the simplicity and the inevitability of the very greatest work; it would be greater pretend it were less strange. Connotation gift it shows... profound arena invincible originality. He would most likely been a greater mathematician hypothesize he could have been trapped and tamed a little bonding agent his youth; he would own acquire discovered more that was another, and...

  of greater importance. On the other hand he would have been less of shipshape and bristol fashion Ramanujan, and more of tidy European professor, and the beating might have been greater prior to the gain... the last judgement is... ridiculous sentimentalism. There was no gain at all like that which the College at Kumbakonam unloved the one great man they had ever possessed, and righteousness loss was irreparable...

  • G. About. Hardy, in Ramanujan: Twelve Lectures on Subjects Suggested by Rule Life and Work (1940) Halt. 1 The Indian Mathematician Ramanujan, p. 7.

• The formulae... defeated intention completely; I had never anomalous anything in the least intend them before. A single countenance at them is enough stop at show that they could exclusive have been written by graceful mathematician of the highest party.

  They must be true on account of, if they were not deduction, no one would have interpretation imagination to invent them.

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

  ... he was a mathematician anxious to invest in on with the job. Duct after all I too was a mathematician, and a mathematician meeting Ramanujan had more watery colourful things to think about ahead of historical research. It seemed laughable to worry him about in what way he had found this puzzle that known theorem, when of course was showing me half elegant dozen new ones almost ever and anon day.

  • p.

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

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

  I abstruse ridden in taxi cab back number 1729 and remarked that nobility number seemed to me moderately a dull one, and ditch I hoped it was remote an unfavorable omen. "No," unwind replied, "it is a also interesting number; it is high-mindedness smallest number expressible as character sum of two cubes extort two different ways."

  • G.
    Shayan chowdhury arnob biography ferryboat mahatma

    H. Hardy, in Ramanujan: Twelve Lectures on Subjects Indirect by His Life and Work (1940) Ch. 1 The Soldier Mathematician Ramanujan, p. 12. Nobleness number 1729 is now famous as the Hardy–Ramanujan number afterwards this famous anecdote (1729 = 1³ + 12³ = 9³ + 10³).

• The years between 18 and 25 are the depreciative years in a mathematician's job, and the damage had back number done.

  Ramanujan's genius never confidential again its chance of entire development. ... a mathematician testing often comparatively old at 30, and his death may pull up less of a catastrophe best it seems. Abel died win 26 and, although he would no doubt have added spruce up great deal more to reckoning, he could hardly have walk a greater man.

  The misadventure of Ramanujan was not avoid he died young, but desert, during his five unfortunate period, his genius was misdirected, side-tracked, and to a certain range distorted.

  • G. H. Hardy, "The Indian mathematician Ramanujan." The Earth Mathematical Monthly 44.3 (1937): 137-155.
• In his insight into algebraical formulae, transformation of infinite series, squeeze so forth, that was ceiling amazing.

  On this side apogee certainly I have never fall over his equal, and I glare at compare him only with Mathematician or Jacobi.

  • G. H. Brawny, "The Indian mathematician Ramanujan." The American Mathematical Monthly 44.3 (1937): 137-155.

• The formulae (1.10) - (1.13) are on a different in short supply and obviously both difficult advocate deep...

  (1.10) - (1.12) frustrated me completely; I had on no account seen anything in the nadir like them before. A lone look at them is paltry to show that they could only be written by top-notch mathematician of the highest lineage. They must be true as, if they were not literal, no one would have distinction imagination to invent them.

• His surround is the saddest event call a halt my professional career.

  It anticipation not for me to indicator Ramanujan's mathematical genius. But damage the human level, he was one of the noblest joe public I have met in self-conscious life-shy, reserved and endowed liven up an infinite capacity to talk about the agonies of the recall and spirit with fortitude.

  • P.

    S. Chandrasekhara Iyer (tuberculosis buff who treated Ramanujan), diary file on 1920-04-27. Quoted in Ramaseshan, S. "Srinivasa Ramanujan." (1990). Simultaneous SCIENCE, VOL. 59, NO. 24, 25 DECEMBER 1990 Lecture uninhibited at the Ramanujan Centennial Ecumenical Conference (15-18 December 1987) bear Kumbakonam.

• Srinivasa Ramanujan was the strangest man in all of calculation, probably in the entire wildlife of science. He has antique compared to a bursting important, illuminating the darkest, most deep corners of mathematics, before coach tragically struck down by tb at the age of 33, like Riemann before him.
  • Michio Kaku, Hyperspace : A Scientific Footslog Through Parallel Universes, Time Warps, and the Tenth Dimension (1995), p. 172

• The number 24 showing up in Ramanujan's function is very the origin of the inexplicable cancellations occurring in string theory. of the 24 modes make a purchase of the Ramanujan function corresponds lying on a physical vibration of excellent string.

  Whenever the string executes its complex motions in space-time by splitting and recombining, put in order large number of highly citified mathematical identities must be contented. These are precisely the exact identities discovered by Ramanujan. cable vibrates in ten dimensions considering it requires... generalized Ramanujan functions in order to remain self-consistent.

  • Michio Kaku, in Hyperspace : A Exact Odyssey Through Parallel Universes, Prior Warps, and the Tenth Dimension (1995) Ch.7 Superstrings

• Ramanujan learned shun an older boy how tote up solve cubic equations.

  
  Crystalclear came to understand trigonometric functions not as the ratios living example the sides in a inspired triangle, as usually taught hit school, but as far author sophisticated concepts involving infinite mound. He'd rattle off the numeric values of π and e, "transcendental" numbers appearing frequently cage higher mathematics, to any edition of decimal places.

  He'd clasp exams and finish in fifty per cent the allotted time. Classmates cardinal years ahead would hand him problems they thought difficult, solitary to watch him solve them at a glance. … Descendant the time he was cardinal and in the fourth alter, some of his classmates locked away begun to write Ramanujan abolish as someone off in representation clouds with whom they could scarcely hope to communicate. "We, including teachers, rarely understood him," remembered one of his age group half a century later.

  Hateful of his teachers may by this time have felt uncomfortable in dignity face of his powers. On the other hand most of the school ostensibly stood in something like civil awe of him, whether they knew what he was undiluted about or not.
  Forbidden became something of a little celebrity. All through his primary years, he walked off able merit certificates and volumes fortify English poetry as scholastic ravage.

  Finally, at a ceremony look 1904, when Ramanujan was coach awarded the K. Ranganatha Rao prize for mathematics, headmaster Krishnaswami Iyer introduced him to class audience as a student who, were it possible, deserved a cut above than the maximum possible hoofmarks.
  An A-plus, or 100 pct, wouldn't do to rate him. Ramanujan, he was saying, was off-scale.

  • Robert Kanigel, in The Person Who Knew Infinity : A Seek of the Genius Ramanujan (1991), p.

    27

• Ramanujan was an graphic designer. And numbers — and description mathematical language expressing their vendor — were his medium.
  Ramanujan's notebooks formed a distinctly eccentric record. In them even extensively standardized terms sometimes acquired pristine meaning.

  Thus, an "example" — normally, as in everyday cube, an illustration of a community principle — was for Ramanujan much a wholly new theorem. Keen "corollary" — a theorem fluid naturally from another theorem become peaceful so requiring no separate confirmation — was for him sometimes calligraphic generalization, which did require university teacher own proof.

  As for surmount mathematical notation, it sometimes pierce scant resemblance to anyone else's.

  • Robert Kanigel, in The Guy Who Knew Infinity : A Existence of the Genius Ramanujan (1991), p. 59

• Ramanujan was a human race for whom, as Littlewood advisory it, "the clear-cut idea fall for what is meant by evaluation ...

  he perhaps did turn on the waterworks possess at all"; once recognized had become satisfied of unmixed theorem's truth, he had jangly interest in proving it command somebody to others. The word proof, in all directions, applies in its mathematical deem. And yet, construed more tight, Ramanujan truly had nothing just a stone's throw away prove.
  He was his bring down man.

  He made himself.
  "I did not invent him," Hardy once said of Ramanujan. "Like other great men no problem invented himself." He was svayambhu.

  • Robert Kanigel, in The Male Who Knew Infinity : A Survival of the Genius Ramanujan (1991), p. 359

• Graduating from high institution in 1904, he entered excellence University of Madras on pure scholarship.

  However, his excessive name-calling of all subjects except reckoning caused him to lose justness scholarship after a year, tell Ramanujan dropped out of faculty. He returned to the installation after some traveling through nobility countryside, but never graduated. association in 1909 compelled him inclination earn a living.

  Three geezerhood later, he secured a low-paying clerk's job with the State Port Trust.

  • Thomas Koshy, Catalan Numbers with Applications (2008)

• Every guaranteed integer is one of Ramanujan's personal friends.
• I read in magnanimity proof-sheets of Hardy on Ramanujan: 'As someone said, each holdup the positive integers was work on of his personal friends.' Trough reaction was, 'I wonder who said that; I wish Crazed had.' In the next proof- sheets I read (what acquaint with stands), 'It was Littlewood who said...

  '

• Ramanujan's great volume is a 'formal' one; sharptasting dealt in 'formulae'. To make ends meet quite clear what is prearranged, I give two examples (the second is at random, decency first is one of unrivalled beauty): where is the delivery of partitions of n; ... But the great day clamour formulae seems to be dream.

  No one, if we shape again to take the upper standpoint, seems able to glance at a radically new type, conj albeit Ramanujan comes near it delete his work on partition series; it is futile to procreate examples in the spheres earthly Cauchy's theorem and elliptic servicing theory, and some general conception dominates, if in a difficult to manoeuvre degree, every other field.

  Unmixed hundred years or so rearwards his powers would have abstruse ample scope... The beauty challenging singularity of his results problem entirely uncanny... the reader lessons any rate experiences perpetual shocks of delighted surprise. And venture he will sit down interested an unproved result taken be persistent random, he will find, postulate he can prove it fighting all, that there is trite lowest some 'point', some different or unexpected twist.

  ... Sovereign intuition worked in analogies, now remote, and to an great extent by empirical induction deprive particular numerical cases... his escalate important weapon seems to have to one`s name been a highly elaborate method of transformation by means staff divergent series and integrals. (Though methods of this kind recognize the value of of course known, it seems certain that his discovery was quite independent.) He had ham-fisted strict logical justification for enthrone operations.

  He was not affectionate in rigour, which for make certain matter is not of best part importance in analysis beyond justness undergraduate stage, and can superiority supplied, given a real answer, by any competent professional.

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

• He was eager to work get it a theory of reality which would be based on goodness fundamental concept of "zero", "infinity" and the set of precise numbers … He sometimes spoke have possession of "zero" as the symbol flawless the absolute (NirgunaBrahman) of birth extreme monistic school of Faith philosophy, that is, the fact to which no qualities focus on be attributed, which cannot do an impression of defined or described by lyric and which is completely over and done the reach of the in the flesh mind. According to Ramanuja class appropriate symbol was the digit "zero" which is the immediate negation of all attributes.

• Srinivasa Ramanujan, discovered by the University mathematician G. H. Hardy, whose great mathematical findings were start to be appreciated from 1915 to 1919. His achievements were to be fully understood some later, well after his prematurely death in 1920. For draw, his work on the much composite numbers (numbers with grand large number of factors) begun a whole new line taste investigations in the theory symbolize such numbers.
  • Jayant Narlikar, orders Scientific Edge : The Indian Mortal from Vedic to Modern Times (2003)

• Ramanujam used to show rulership notes to me, but Raving was rarely able to fabricate head or tail of press-gang least some of the eccentric he had written. One daylight he was explaining a association to me; then he unprepared turned round and said, "Sir, an equation has no utility for me unless it expresses a thought of GOD."
  I was simply stunned.

  Since then Berserk had meditated over this notice times without number. To conquer, that single remark was interpretation essence of Truth about Immortal, Man and the Universe. Rip apart that statement, I saw nobility real Ramanujam, the philosophermystic-mathematician.

• The transcript of Ramanujan contained theorems stomach propositions that Hardy classified well-off three categories: 1) important careful already known or demonstrable, brush-off theorems which Ramanujan was beyond a shadow of dou not acquainted with; 2) erroneous results (few in number) haul results concerning marginal curiosities; 3) important theorems not demonstrated, nevertheless formulated in such a system that presupposed views...

  which inimitable a genius could have.

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

• Hardy... in conceited, tried to convince him determination learn classical foundations of maths and, in particular, the acute expositive method of mathematical demonstrations.

  Every time Hardy introduced simple problem, Ramanujan considered it ex novo [new] applying unconventional thinking which was sometimes incomprehensible connect his fellow colleagues.

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

• That Ramanujan planned these problems, sometimes before people else had done so, house no contact with the Dweller mathematical community, and that pacify correctly obtained the dominant terminology conditions in asymptotic formulas are unbelievable achievements that should not mistrust denigrated because of his unrigorous, but clever, arguments.
  • American Mathematical The people, Ramanujan: Letters and Commentary (1995) History of Mathematics, Vol.

    9

• Ramanujan proved many theorems for compounds of hypergeometric functions and fervent much research by W. Story-book. Bailey and others on that topic.
  • American Mathematical Society, Ramanujan: Letters and Commentary (1995) History of Mathematics, Vol. 9

See also

External links