1 National Pig Day

7/31/2019 1 National Pig Day

1/20

1National Pig Day

1Peanut Butter Lovers' Day

2Employee Appreciation Dayfirst Friday in March

2National Salesperson Day- first Friday in the month

2Old Stuff Day

3I Want You to be Happy Day

3If Pets Had Thumbs Day

3National Anthem Day

3Peach Blossom Day

4Holy Experiment Day

4Hug a GI Day

5Multiple Personality Day

6Dentist's Day

6National Frozen Food Day

7National Crown Roast of Pork Day

8Be Nasty Day

8International (Working) Women's Day

8National Agriculture Day(date varies)

8Popcorn Lover's Daysecond Thursday

9Panic Day

10Middle Name Pride Day

11Johnny Appleseed Day

11Worship of Tools Day- guys, you can relate
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2/20

12Girl Scouts Day

12Plant a Flower Day

13Ear Muff Day

13Jewel Day

14Learn about Butterflies Day

14National Potato Chip Day

14National Pi Day- Why today? Because today is 3.14, the value of Pi.

15Everything You Think is Wrong Day

15Ides of March

15Incredible Kid Day

15Dumbstruck Day

16Everything You Do is Right Day

16Freedom of Information Day

17National Quilting Day- third Saturday of month

17Submarine Day - the hero sandwich or the boat??

17Saint Patrick's Day

18Goddess of Fertility Day

18Supreme Sacrifice Day

19Poultry Day

20International Earth Day

20Extraterrestrial Abductions Day

20Proposal Day

21Fragrance Day
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3/20

22National Goof Off Day

23National Chip and Dip Day

23Near Miss Day

24National Chocolate Covered Raisin Day

25Pecan Day

25Waffle Day

26Make Up Your Own Holiday Day

27National "Joe" Day

28Something on a Stick Day

29National Mom and Pop Business Owners Day

29Smoke and Mirrors Day

30National Doctor's Day

30I am in Control Day

30Take a Walk in the Park Day

31Bunsen Burner Day

31National Clam on the Half Shell Day
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4/20

Oramavasi Divasam Sandhyakku byMundoor Sethumadhavan

Publisher: Mathrubhumi Books/ DC Books ISBN-13: 9788182646131 ISBN-10: 8182646138

Format: Paperback Language:Malayalam No. of Pages: 112

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Urakkam Nashtappetta Gramam byMundoor Sethumadhavan

Publisher: National Book Stall,Kottayam / DC Books ISBN-13: 9788190664776 ISBN-10: 8190664778 Format: Paperback Language:Malayalam No. of Pages: 104
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5/20

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1942 10-. . .

. 1962-. . , , , , , , .. .

search

"Ramanujan" redirects here. For other uses, seeRamanujan (disambiguation).Srinivasa Ramanujan
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6/20

Born22 December 1887

Erode,Madras Presidency

Died

26 April 1920 (aged 32)

Chetput,Madras,Madras

Presidency

Nationality Indian

Fields Mathematics

Alma mater

Government Arts College

Pachaiyappa's College

University of Cambridge

Academic

advisors

G. H. Hardy

J. E. Littlewood

Known for

LandauRamanujan constant

Mock theta functions

Ramanujan conjecture

Ramanujan prime

RamanujanSoldner constant

Ramanujan theta function

Ramanujan's sum

RogersRamanujan identities

Ramanujan's master theorem

Influences G. H. Hardy

Signature
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Srinivasa RamanujanFRS pronunciation(helpinfo)(Tamil:)(22 December 188726 April 1920) was an Indianmathematicianandautodidactwho, with

almost no formal training inpure mathematics, made extraordinary contributions to

mathematical analysis,number theory,infinite seriesandcontinued fractions. Ramanujan wassaid to be a natural genius by the English mathematicianG.H. Hardy, in the same league as

mathematicians likeEulerandGauss.[1]

Born in a poorBrahminfamily, Ramanujan's introduction to formalmathematicsbegan at age

10. He demonstrated a natural ability, and was given books on advancedtrigonometrywritten by

S. L. Loneythat he mastered by the age of 12; he even discoveredtheoremsof his own, and re-

discoveredEuler's identityindependently.[2]

He demonstrated unusual mathematical skills atschool, winning accolades and awards. By 17, Ramanujan had conducted his own mathematical

research onBernoulli numbersand theEulerMascheroni constant.

Ramanujan received a scholarship to study at Government College inKumbakonam, but lost it

when he failed his non-mathematical coursework. He joined another college to pursue

independent mathematical research, working as a clerk in the Accountant-General's office at theMadrasPort Trust Office to support himself.[3]In 19121913, he sent samples of his theorems to

three academics at theUniversity of Cambridge.G. H. Hardy, recognizing the brilliance of his

work, invited Ramanujan to visit and work with him atCambridge. He became aFellow of theRoyal Societyand a Fellow ofTrinity College, Cambridge. Srinivasa died of illness,

malnutrition, and possibly liver infection in 1920 at the age of 32.

During his short lifetime, Ramanujan independently compiled nearly 3900 results (mostly

identitiesandequations).[4]Most of his claims have now been proven correct, although a smallnumber of these results were actually false and some were already known.

[5]He stated results

that were both original and highly unconventional, such as theRamanujan primeand theRamanujan theta function, and these have inspired a vast amount of further research.[6]However,

the mathematical mainstream has been rather slow in absorbing some of his major discoveries.

TheRamanujan Journal, an international publication, was launched to publish work in all areasof mathematics influenced by his work.[7]

In Dec 2011, in recognition of his contribution to mathematics, the Government of India declaredthat Ramanujan's birthday (22 December) should be celebrated every year asNational

Mathematics Day, and also declared 2012 theNational Mathematical Year.[8][9]

Contents

1 Early life 2 Adulthood in India

o 2.1 Attention from mathematicianso 2.2 Contacting English mathematicians
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3 Life in Englando 3.1 Illness and return to Indiao 3.2 Personality and spiritual life

4 Mathematical achievementso 4.1 The Ramanujan conjectureo 4.2 Ramanujan's notebooks

5 RamanujanHardy number 1729 6 Other mathematicians' views of Ramanujan 7 Recognition 8 In popular culture 9 See also 10 Notes 11 Selected publications by Ramanujan 12 Selected publications about Ramanujan and his work 13 External links

o 13.1 Media linkso 13.2 Biographical linkso 13.3 Other links

Early life

Ramanujan's home on Sarangapani Street, Kumbakonam.

Ramanujan was born on 22 December 1887 inErode,Madras Presidency, at the residence of his

maternal grandparents.[10]

His father, K. Srinivasa Iyengar, worked as a clerk in a sari shop and

hailed from the district ofThanjavur.[11]

His mother, Komalatammal, was ahousewifeand alsosang at a local temple.[12]They lived in Sarangapani Street in a traditional home in the town of

Kumbakonam. The family home is now a museum. When Ramanujan was a year and a half old,
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his mother gave birth to a son named Sadagopan, who died less than three months later. In

December 1889, Ramanujan hadsmallpoxand recovered, unlike thousands in theThanjavurDistrictwho died from the disease that year.[13]He moved with his mother to her parents' house

inKanchipuram, near Madras (nowChennai). In November 1891, and again in 1894, his mother

gave birth, but both children died in infancy.

On 1 October 1892, Ramanujan was enrolled at the local school.[14]

In March 1894, he was

moved to aTelugu mediumschool. After his maternal grandfather lost his job as a court officialin Kanchipuram,[15]Ramanujan and his mother moved back toKumbakonamand he was

enrolled in the Kangayan Primary School.[16]

After his paternal grandfather died, he was sent

back to his maternal grandparents, who were now living in Madras. He did not like school inMadras, and he tried to avoid attending. His family enlisted a local constable to make sure he

attended school. Within six months, Ramanujan was back in Kumbakonam.[16]

Since Ramanujan's father was at work most of the day, his mother took care of him as a child. Hehad a close relationship with her. From her, he learned about tradition andpuranas. He learned to

sing religious songs, to attend pujas at the temple and particular eating habitsall of which arepart ofBrahminculture.[17]

At the Kangayan Primary School, Ramanujan performed well. Justbefore the age of 10, in November 1897, he passed his primary examinations in English, Tamil,

geography and arithmetic. With his scores, he stood first in the district.[18]

That year, Ramanujan

entered Town Higher Secondary School where he encountered formal mathematics for the firsttime.[18]

By age 11, he had exhausted the mathematical knowledge of two college students who werelodgers at his home. He was later lent a book on advanced trigonometry written byS. L.

Loney.[19][20]He completely mastered this book by the age of 13 and discovered sophisticated

theorems on his own. By 14, he was receiving merit certificates and academic awards which

continued throughout his school career and also assisted the school in thelogisticsof assigningits 1200 students (each with their own needs) to its 35-odd teachers.[21]He completed

mathematical exams in half the allotted time, and showed a familiarity with infinite series. In

1903 when he was 16, Ramanujan obtained from a friend a library-loaned copy of a book byG.S. Carr.[22][23]The book was titledA Synopsis of Elementary Results in Pure and AppliedMathematicsand was a collection of 5000 theorems. Ramanujan reportedly studied the contents

of the book in detail.[24]

The book is generally acknowledged as a key element in awakening thegenius of Ramanujan.[24]The next year, he had independently developed and investigated the

Bernoulli numbersand had calculatedEuler's constantup to 15 decimal places.[25]His peers at

the time commented that they "rarely understood him" and "stood in respectful awe" of him.[21]

When he graduated fromTown Higher Secondary Schoolin 1904, Ramanujan was awarded the

K. Ranganatha Rao prize for mathematics by the school's headmaster, Krishnaswami Iyer. Iyer

introduced Ramanujan as an outstanding student who deserved scores higher than the maximumpossible marks.[21]He received a scholarship to study atGovernment Arts College,

Kumbakonam,[26][27]However, Ramanujan was so intent on studying mathematics that he could

not focus on any other subjects and failed most of them, losing his scholarship in the process .[28]

In August 1905, he ran away from home, heading towardsVisakhapatnamand stayed inRajahmundryfor about a month.[29]He later enrolled atPachaiyappa's Collegein Madras. He
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again excelled in mathematics but performed poorly in other subjects such as physiology.

Ramanujan failed hisFine Artsdegree exam in December 1906 and again a year later. Without adegree, he left college and continued to pursue independent research in mathematics. At this

point in his life, he lived in extreme poverty and was often on the brink of starvation.[30]

Adulthood in India

On 14 July 1909, Ramanujan was married to a nine-year old bride, Janaki Ammal.[31]

After themarriage, Ramanujan developed ahydrocele testis, an abnormal swelling of thetunica vaginalis,

an internal membrane in the testicle.[32]The condition could be treated with a routine surgical

operation that would release the blocked fluid in the scrotal sac. His family did not have the

money for the operation, but in January 1910, a doctor volunteered to do the surgery for free.[33]

After his successful surgery, Ramanujan searched for a job. He stayed at friends' houses while he

went door to door around the city ofMadras(now Chennai) looking for a clerical position. Tomake some money, he tutored some students at Presidency College who were preparing for their

F.A. exam.[34]

In late 1910, Ramanujan was sick again, possibly as a result of the surgery earlier in the year. He

feared for his health, and even told his friend, R. Radakrishna Iyer, to "hand these [Ramanujan's

mathematical notebooks] over to Professor Singaravelu Mudaliar [the mathematics professor atPachaiyappa's College] or to the British professor Edward B. Ross, of the Madras Christian

College."[35]After Ramanujan recovered and got back his notebooks from Iyer, he took a

northbound train from Kumbakonam toVillupuram, a coastal city under French control.[36][37]

Attention from mathematicians

He met deputy collectorV. Ramaswamy Aiyer, who had recently founded the IndianMathematical Society.[38]Ramanujan, wishing for a job at the revenue department where

Ramaswamy Aiyer worked, showed him his mathematics notebooks. As Ramaswamy Aiyer later

recalled:

I was struck by the extraordinary mathematical results contained in it [the notebooks]. I had no

mind to smother his genius by an appointment in the lowest rungs of the revenue department.[39]

Ramaswamy Aiyer sent Ramanujan, with letters of introduction, to his mathematician friends in

Madras.[38]

Some of these friends looked at his work and gave him letters of introduction toR.Ramachandra Rao, the district collector forNelloreand the secretary of the Indian Mathematical

Society.[40][41][42]Ramachandra Rao was impressed by Ramanujan's research but doubted that itwas actually his own work. Ramanujan mentioned a correspondence he had with Professor

Saldhana, a notableBombaymathematician, in which Saldhana expressed a lack ofunderstanding for his work but concluded that he was not a phony.[43]Ramanujan's friend, C. V.

Rajagopalachari, persisted with Ramachandra Rao and tried to quell any doubts over

Ramanujan's academic integrity. Rao agreed to give him another chance, and he listened asRamanujan discussedelliptic integrals,hypergeometric series, and his theory ofdivergent series,

which Rao said ultimately "converted" him to a belief in Ramanujan's mathematical brilliance.[43]
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When Rao asked him what he wanted, Ramanujan replied that he needed some work and

financial support. Rao consented and sent him to Madras. He continued his mathematicalresearch with Rao's financial aid taking care of his daily needs. Ramanujan, with the help of

Ramaswamy Aiyer, had his work published in theJournal of Indian Mathematical Society.[44]

One of the first problems he posed in the journal was:

He waited for a solution to be offered in three issues, over six months, but failed to receive any.At the end, Ramanujan supplied the solution to the problem himself. On page 105 of his first

notebook, he formulated an equation that could be used to solve the infinitely nested radicals

problem.

Using this equation, the answer to the question posed in the Journal was simply 3.[45]

Ramanujanwrote his first formal paper for theJournal on the properties ofBernoulli numbers. One property

he discovered was that the denominators (sequenceA027642inOEIS) of the fractions of

Bernoulli numbers were always divisible by six. He also devised a method of calculating Bnbased on previous Bernoulli numbers. One of these methods went as follows:

It will be observed that ifn is even but not equal to zero,

(i)Bn is a fraction and the numerator of in its lowest terms is a prime number,(ii) the denominator ofBn contains each of the factors 2 and 3 once and only once,

(iii) is an integer and consequently is an oddinteger.

In his 17-page paper, "Some Properties of Bernoulli's Numbers", Ramanujan gave three proofs,

two corollaries and three conjectures.[46]Ramanujan's writing initially had many flaws. AsJournal editor M. T. Narayana Iyengar noted:

Mr. Ramanujan's methods were so terse and novel and his presentation so lacking in clearness

and precision, that the ordinary [mathematical reader], unaccustomed to such intellectual

gymnastics, could hardly follow him.[47]

Ramanujan later wrote another paper and also continued to provide problems in the Journal.[48]

In early 1912, he got a temporary job in the MadrasAccountant General's office, with a salary of20 rupees per month. He lasted for only a few weeks.[49]Toward the end of that assignment he

applied for a position under the Chief Accountant of the Madras Port Trust. In a letter dated 9

February 1912, Ramanujan wrote:
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12/20

Sir,

I understand there is a clerkship vacant in your office, and I beg to apply for the same. I havepassed the Matriculation Examination and studied up to the F.A. but was prevented from

pursuing my studies further owing to several untoward circumstances. I have, however, been

devoting all my time to Mathematics and developing the subject. I can say I am quite confident I

can do justice to my work if I am appointed to the post. I therefore beg to request that you will begood enough to confer the appointment on me.[50]

Attached to his application was a recommendation fromE. W. Middlemast, a mathematics

professor at thePresidency College, who wrote that Ramanujan was "a young man of quite

exceptional capacity in Mathematics".[51]

Three weeks after he had applied, on 1 March,Ramanujan learned that he had been accepted as a Class III, Grade IV accounting clerk, making

30 rupees per month.[52]At his office, Ramanujan easily and quickly completed the work he was

given, so he spent his spare time doing mathematical research. Ramanujan's boss,Sir Francis

Spring, and S. Narayana Iyer, a colleague who was also treasurer of the Indian MathematicalSociety, encouraged Ramanujan in his mathematical pursuits.
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13/20

Contacting English mathematicians

On the spring of 1913, Narayana Iyer, Ramachandra Rao andE. W. Middlemasttried to presentRamanujan's work to British mathematicians. One mathematician, M. J. M. Hill ofUniversity

College London, commented that Ramanujan's papers were riddled with holes.[53]

He said that

although Ramanujan had "a taste for mathematics, and some ability", he lacked the educationalbackground and foundation needed to be accepted by mathematicians.[54]Although Hill did not

offer to take Ramanujan on as a student, he did give thorough and serious professional advice on

his work. With the help of friends, Ramanujan drafted letters to leading mathematicians atCambridge University.[55]

The first two professors,H. F. BakerandE. W. Hobson, returned Ramanujan's papers withoutcomment.[56]On 16 January 1913, Ramanujan wrote toG. H. Hardy. Coming from an unknown

mathematician, the nine pages of mathematical wonder made Hardy initially view Ramanujan's

manuscripts as a possible "fraud".[57]

Hardy recognised some of Ramanujan's formulae but others

"seemed scarcely possible to believe".[58]

One of the theorems Hardy found so incredible was

found on the bottom of page three (valid for 0 < a < b + 1/2):

Hardy was also impressed by some of Ramanujan's other work relating to infinite series:

The first result had already been determined by a mathematician named Bauer. The second onewas new to Hardy, and was derived from a class of functions called ahypergeometric series

which had first been researched byLeonhard EulerandCarl Friedrich Gauss. Compared toRamanujan's work onintegrals, Hardy found these results "much more intriguing".[59]After he

saw Ramanujan's theorems on continued fractions on the last page of the manuscripts, Hardy

commented that the "[theorems] defeated me completely; I had never seen anything in the least

like them before".[60]

He figured that Ramanujan's theorems "must be true, because, if they werenot true, no one would have the imagination to invent them".[60]Hardy asked a colleague,J. E.

Littlewood, to take a look at the papers. Littlewood was amazed by the mathematical genius of

Ramanujan. After discussing the papers with Littlewood, Hardy concluded that the letters were"certainly the most remarkable I have received" and commented that Ramanujan was "a

mathematician of the highest quality, a man of altogether exceptional originality and power".[61]

One colleague, E. H. Neville, later commented that "not one [theorem] could have been set in themost advanced mathematical examination in the world".[62]
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14/20

On 8 February 1913, Hardy wrote a letter to Ramanujan, expressing his interest for his work.

Hardy also added that it was "essential that I should see proofs of some of your assertions" .[63]

Before his letter arrived in Madras during the third week of February, Hardy contacted the Indian

Office to plan for Ramanujan's trip to Cambridge. Secretary Arthur Davies of the Advisory

Committee for Indian Students met with Ramanujan to discuss the overseas trip.[64]

In

accordance with his Brahmin upbringing, Ramanujan refused to leave his country to "go to aforeign land".[65]Meanwhile, Ramanujan sent a letter packed with theorems to Hardy, writing, "I

have found a friend in you who views my labour sympathetically."[66]

To supplement Hardy's endorsement, a former mathematical lecturer atTrinity College,

Cambridge,Gilbert Walker, looked at Ramanujan's work and expressed amazement, urging himto spend time at Cambridge.[67]As a result of Walker's endorsement, B. Hanumantha Rao, a

mathematics professor at an engineering college, invited Ramanujan's colleague Narayana Iyer to

a meeting of the Board of Studies in Mathematics to discuss "what we can do for S.

Ramanujan".[68]

The board agreed to grant Ramanujan a research scholarship of 75 rupees permonth for the next two years at theUniversity of Madras.[69]While he was engaged as a research

student, Ramanujan continued to submit papers to theJournal of the Indian MathematicalSociety. In one instance, Narayana Iyer submitted some theorems of Ramanujan on summation

of series to the above mathematical journal adding The following theorem is due to S.Ramanujan, the mathematics student of Madras University. Later in November, BritishProfessor Edward B. Ross ofMadras Christian College, whom Ramanujan had met a few years

before, stormed into his class one day with his eyes glowing, asking his students, Does

Ramanujan know Polish? The reason was that in one paper, Ramanujan had anticipated thework of a Polish mathematician whose paper hadjust arrived by the days mail.

[70]In his

quarterly papers, Ramanujan drew up theorems to make definite integrals more easily solvable.

Working off Giuliano Frullani's 1821 integral theorem, Ramanujan formulated generalisationsthat could be made to evaluate formerly unyielding integrals.[71]

Hardy's correspondence with Ramanujan soured after Ramanujan refused to come to England.

Hardy enlisted a colleague lecturing in Madras, E. H. Neville, to mentor and bring Ramanujan to

England.[72]

Neville asked Ramanujan why he would not go to Cambridge. Ramanujan

apparently had now accepted the proposal; as Neville put it, "Ramanujan needed no convertingand that his parents' opposition had been withdrawn".[62]Apparently, Ramanujan's mother had a

vivid dream in which the family GoddessNamagiricommanded her "to stand no longer between

her son and the fulfilment of his life's purpose".[62]

Life in England
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