Ramanujan (Print Only)

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Srinivasa Aiangar Ramanujan

Born: 22 Dec 1887 in Erode, Tamil Nadu state, India

Died: 26 April 1920 in Kumbakonam, Tamil Nadu state, India

Srinivasa Ramanujan was one of India's greatest mathematical geniuses. He made substantial contributions to

the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series.

Ramanujan was born in his grandmother's house in Erode, a small village about 400 km southwest of Madras

When Ramanujan was a year old his mother took him to the town of Kumbakonam, about 160 km nearer

Madras. His father worked in Kumbakonam as a clerk in a cloth merchant's shop. In December 1889 he

contracted smallpox.

When he was nearly five years old, Ramanujan entered the primary school in Kumbakonam although he would

attend several different primary schools before entering the Town High School in Kumbakonam in January 1898At the Town High School, Ramanujan was to do well in all his school subjects and showed himself an able all

round scholar. In 1900 he began to work on his own on mathematics summing geometric and arithmetic series.

Ramanujan was shown how to solve cubic equations in 1902 and he went on to find his own method to solve the

quartic. The following year, not knowing that the quintic could not be solved by radicals, he tried (and of course

failed) to solve the quintic.

It was in the Town High School that Ramanujan came across a mathematics book by G S Carr called Snopsis

of elementar results in pure mathematics. This book, with its very concise style, allowed Ramanujan to teach

himself mathematics, but the style of the book was to have a rather unfortunate effect on the way Ramanujan was

later to write down mathematics since it provided the only model that he had of written mathematical arguments.

The book contained theorems, formulae and short proofs. It also contained an index to papers on pure

mathematics which had been published in the European Journals of Learned Societies during the first half of the

19th century. The book, published in 1856, was of course well out of date by the time Ramanujan used it.

By 1904 Ramanujan had begun to undertake deep research. He investigated the series (1/n) and calculated

Euler's constant to 15 decimal places. He began to study the Bernoulli numbers, although this was entirely his

own independent discovery.

Ramanujan, on the strength of his good school work, was given a scholarship to the Government College in

Kumbakonam which he entered in 1904. However the following year his scholarship was not renewed because

Ramanujan devoted more and more of his time to mathematics and neglected his other subjects. Without money

he was soon in difficulties and, without telling his parents, he ran away to the town of Vizagapatnam about 650

km north of Madras. He continued his mathematical work, however, and at this time he worked on

hypergeometric series and investigated relations between integrals and series. He was to discover later that he

had been studying elliptic functions.

In 1906 Ramanujan went to Madras where he entered Pachaiyappa's College. His aim was to pass the First


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O R 1

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H. H H 12 N 1912 R' 1911

B .

H R'

. T R B' Theo of infinie eie

R . R E W H H F B

. I J 1913 R G H H 1910

Ode of infini. I R' H [10]:-

I hae had no niei edcaion b I hae ndegone he odina chool coe. Afe

leaing chool I hae been emploing he pae ime a m dipoal o ok a mahemaic.

I hae no odden hogh he conenional egla coe hich i folloed in a nieicoe, b I am iking o a ne pah fo melf. I hae made a pecial ineigaion of

diegen eie in geneal and he el I ge ae emed b he local mahemaician a

'aling'.

H, L, R

. O 8 F R [3], :-

I a eceedingl ineeed b o lee and b he heoem hich o ae. Yo ill

hoee ndeand ha, befoe I can jdge popel of he ale of ha o hae done, i

i eenial ha I hold ee poof of ome of o aeion. Yo el eem o me o fallino oghl hee clae:

(1) hee ae a nmbe of el ha ae alead knon, o eail dedcible fom knon

heoem;

(2) hee ae el hich, o fa a I kno, ae ne and ineeing, b ineeing ahe

fom hei cioi and appaen difficl han hei impoance;

(3) hee ae el hich appea o be ne and impoan...

R H' [8]:-

I hae fond a fiend in o ho ie m labo mpaheicall. ... I am alead a half aing man. To peee m bain I an food and hi i m fi conideaion. An

mpaheic lee fom o ill be helpfl o me hee o ge a cholahip eihe fom he

niei of fom he goenmen.

I U M R M 1913 , 1914,

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Wha a o be done in he a of eaching him moden mahemaic? The limiaion of hi

knoledge ee a aling a i pofndi.

L R . H ([31]):-

... ha i a eemel difficl becae ee ime ome mae, hich i a hogh ha

Ramanjan needed o kno, a menioned, Ramanjan' epone a an aalanche of

oiginal idea hich made i almo impoible fo Lileood o pei in hi oiginal

inenion.

T L H C R

E E, R M 1915

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E, I,

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P.D. 1920). H J 1914

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E.

R 1917 . H

S . I F 1918 H ( [3]):-

Ba Sha fond o, ha ohe doco did no kno, ha he had ndegone an opeaion

abo fo ea ago. Hi o heo a ha hi had eall been fo he emoal of a

malignan goh, ongl diagnoed. In ie of he fac ha Ramanjan i no oe han

i monh ago, he ha no abandoned hi heo - he ohe doco nee gae i an ppo. Tbecle ha been he poiionall acceped heo, apa fom hi, ince he

oiginal idea of gaic lce a gien p. ... Like all Indian he i faaliic, and i i eibl

had o ge him o ake cae of himelf.

O 18 F 1918 R C P S

, ,

R S L. H , H

MM, G, L, B, H, B, L, N, Y, W, F

W. H R S 2 M 1918, 10


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. G N W, M P P M B 1918 1951 14

T R 30

R' . H W R

, 1914 R' I .

T I P O 75

.

Article b:J J O'CE F R

June 1998


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