SRINIVASA RAMANUJAN: A man with an infinite sense of numbers

Srinivasa ramanujan (1887-1920) was born on 22nd Dec 1887, Thursday Kumbakonam city, Erode District at Tamilnadu. Mother’s name was Komlattamal and father’s name was Srinivas Iyengar. He learnt bhajan, Ramayana and mahabharata stories from his parents. Srinivasa Ramanujan was an Indian mathematician who lived during the British Rule in India. He made great contributions in such areas as number theory, continued fractions, and infinite series, despite not having any formal education in math.

 Ramanujan’s primary education was started on 1st Oct 1892 and day was Vijayadhashami. One day in maths class, teacher taught if you distribute 8 bananas into 8 children, each will get 1 banana. It means if you divide any number by same number then result comes out be 1.

Ramanujan :- What if we divide 0 from 0.

Teacher :- Obviously 1.

Ramanujan :- It’s not 1 sir, it’s undefined actually. If there is no banana and nobody then how it is possible to distribution of banana.

Teacher was baffled.

During school time, he had solved college level Mathematics. His estimated IQ was 185. Srinivasa was in such poverty that he often sustained on minimal foods and did not even have enough money to obtain paper for his studies. As a result, he used slates for his mathematics and cleaned them with his elbow, leading to bruises and marks. A child prodigy by age 11, he had exhausted the mathematical knowledge of two college students who were lodgers at his home. He was later lent a book written by S. L. Loney on advanced trigonometry. He mastered this by the age of 13 while discovering sophisticated theorems on his own. By 14, he received merit certificates and academic awards that continued throughout his school career, and he assisted the school in the logistics of assigning its 1,200 students (each with differing needs) to its approximately 35 teachers.

At the age of 15, Srinivasa Ramanujan obtained a copy of Synopsis on Elementary Results in Pure and Applied Mathematics, which contained 5,000 theorems, but had either brief proofs or did not have any. C Ramanujan then took to solving each of the theorems, eventually succeeding. Ramanujan had obtained a scholarship for the University of Madras, but he ended up losing it because he neglected his studies in other subjects in favor of mathematics.

On 14 July 1909, Ramanujan married Janaki ammal (1899 – 1994). After the marriage, Ramanujan developed a hydrocele testis. The condition could be treated with a routine surgical operation that would release the blocked fluid in the scrotal sac, but his family could not afford the operation. In January 1910, a doctor volunteered to do the surgery at no cost. After his successful surgery, Ramanujan searched for a job. He stayed at a friend’s house while he went from door to door around Madras looking for a clerical position. To make money, he tutored students at Presidency College who were preparing for their F.A. exam. In 1913, he sent a letter of 11 pages with 120 theorems to Cambridge University Professor G.H.Hardy. He invited him to England. Overcoming his religious objections, Ramanujan traveled to England in 1914, where Hardy tutored him and collaborated with him in some research.

some of his integration work

With the help of Hardy within 1 year he published 9 research papers. Just because of his research papers he got degree of B.A. and he was elected as Fellow of Royal Society. He was the youngest Indian to receive this honor.

Ramanujan’s knowledge of mathematics (most of which he had worked out for himself) was startling. Although he was almost completely unaware of modern developments in mathematics, his mastery of continued fractions was unequaled by any living mathematician. He worked out the Riemann series, the elliptic integrals, hyper geometric series, the functional equations of the zeta function, and his own theory of divergent series. On the other hand, he knew nothing of doubly periodic functions, the classical theory of quadratic forms, or Cauchy’s theorem, and he had only the most nebulous idea of what constitutes a mathematical proof. Though brilliant, many of his theorems on the theory of prime numbers were wrong.

In England Ramanujan made further advances, especially in the partition of numbers (the number of ways that a positive integer can be expressed as the sum of positive integers,for instance, (4 can be expressed as 4, 3 + 1, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1). His papers were published in English and European journals, and in 1918 he was elected to the Royal Society of London. In 1917 Ramanujan had contracted tuberculosis, but his condition improved sufficiently for him to return to India in 1919. 

Once a interesting incident took place. Ramanujan was ill and admitted at hospital. Prof. Hardy came to visited him. Then midst conversation Hardy said, i came from the cab and number of that cab was 1729.

“It is a very interesting number, it is the smallest number expressible as the sum of two cubes in two different ways.”
He found a special property, and even tested that it was the smallest number with such a property, all in a few seconds.

1729 = (10)3 + (9)3 = (12)3 + (1)3.

After that this kind of numbers were known as Ramanujan Numbers. 1729 is smallest Ramanujan number.

After contracting tuberculosis, eventhough the mathematician recovered enough in 1919 to return to India, but died the following year, without much recognition. However, the mathematics community recognized him as a genius without peer.The genius mathematician left as his legacy three notebooks and a huge bundle of pages, which contained unpublished result which were being verified by mathematicians many years after his death.

Remembering Ramanujan and his contributions on his birth ...

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