A person, born around 100 years ago and died at the age of 32, has left a mystery of series of around 4000 Theorems behind him. These Theorems are compiled in three notebooks and some rough papers. These copies are now famous as Ramanujan’s frayed notebooks. Mathematicians all over the world are trying to unravel those propositions to apply or deny them. Ramanujan’s close associate disclose that he used to solve equations on a slate and used to write his results in a notebook. He was the born Mathematical genius.
Ramanujan was born in Erode on December 22, 1882 into a Brahmin family. Father was an accountant in a cloth store. From childhood itself it was clear that Ramanujan had a great potential. At the age of 13 only, he brought a book on Loni’s Trigonometry from a college library. He not only studied the same but started making his own equations also. A turning point came in his life when one of his friends showed him a book by GC Carr titled ‘A Synopsis of Elementary Results in Pure and Applied Mathematics’. Otherwise this title itself would have been intimidating for a college student but Ramanujan was delighted. This book inspired his Mathematical instincts. He acquired first position in Mathematics at the 10th level and was awarded with the Subramaniam scholarship. In his first year of graduation itself, he failed twice as he completely neglected other subjects like History, Biology and English. His father was disappointed with his passion for numbers and nothing else. He thought that his son was going crazy and to address this problem he got him married to 8 years old Janaki.
After marriage, Ramanujan started looking for a job. This was essential for him not only for bread and butter but also for buying papers to solve Mathematical equations. Every month he required 2000 papers. As a result he started using bits of papers lying on the roads. Sometimes, he used to write in red ink on the same paper on which he had written in blue ink. He used to present himself in dirty clothes and uncombed hair in various stores and offices and requested for a clerical job. He also presented his torn copies but nobody could make any sense out of it. Lastly, the Director of Madras Port Trust, Francis Spring was impressed with his notebooks. He offered
him a clerical job with Rs 25 per month salary.
Later, some academicians and professors started taking interest in his works and on May 9, 1913, University of Madras offered him scholarship of Rs 75 per month, even though he did not have any formal degree. Many high profile people used to visit his small house to solve Mathematical problems.
Then, Ramanujan wrote a letter to famous professor of Mathematics G H Hardy of Cambridge University and sent him 120 Theorems and Equations. It also included some equations which are known as modular in Mathematics. Perry Dell has recently proved his equation. The same letter included the equation which is known as the Rayman Series, which is core of the ‘Definite Integral Calculus’. He did not know that Mathematician George F Rayman had already come up with the series. The famous Hyper-Geometric series well known in his name was also part of that letter. This letter made Prof Hardy and his friends realise the Mathematical brilliance of Ramanujan. He did his research in the Cambridge University. In 1913, he went to London for 6 years.
On February 28, 1918 he was selected as a member of Royal Society. He was only the second Bharateeya to get this distinction. In the same year in October, he became a member of Trinity College, Cambridge. He was the first Bharatiya to attain this extraordinary recognition. He made significant contribution in ‘Number Theory’ and ‘Algebra of Inequality’. He is equated with Leonard Yull and Carl Gustav Jacob Jacobi in the field of Algebra.
In an article published in Span magazine, James Glick writes that if Ramanujan had not started writing letters to the British Mathematicians then he would have never been recognised. He was 25 years old then. Ramanujan had written many such letters to other Mathematicians. But It was Prof Hardy who not only received a letter from Ramanujan but understood what he wanted to convey.
Ramanujan used to write his letter in a peculiar way as, “I know following things ….I also know….. And I have discovered them in the following way…..”. Hardy has written about Ramanujan that he was such an disorganised Mathematician who knew the Pythagoras theorem but was not aware of congruent triangles. He used to make his calculations on the basis of his mental exercises and without knowing anything about the modern European Maths. It was a pure genius which used to take him to the
truth. Prof Hardy reviewed and tested all the equations written in Ramanujan’s letter.
The eyes of this average heighted person carried unique brightness. Ramanujan was a pure vegetarian and used to cook himself. According to Prof Hardy this habit of his became a reason for his illness. He was highly optimistic person. Then there was no cure for Tuberculosis. He was admitted in a nursing home with the ailment of TB in 1919. He returned to Bharat after being discharged. Despite his physical weakness, his interactions with the numbers continued.
Dr George Andrews of Pennsylvania University is still studying Ramanujan’s lost notebook which is nothing but ‘130 equations written on tattered pieces of paper’. Dr Richard Askey of Wisconsin University says that this work of Ramanujan in his last phase of life is equivalent to the lifetime work of a Mathematician. Askey has been working with Andrews to unravel Ramanujan’s work. Ramanujan remained aloof from Geometry as he was not introduced to the standard Mathematics. Mathematics has received many beautiful and clandestine Equations from Ramanujan. His one equation of calculating π is the easiest way to find the solution which was hitherto unknown.
A Computer scientist used the equation in calculating π . This success enabled to explore the usage of his equations not only in Mathematics but also in other disciplines including Forensic Sciences and Archaeology. Andrews found that Ramanujan has solved many Mathematical Equations which could not be found by many Mathematicians in the last fifty years.
This great Mathematician left this world on April 26, 1920.
Dr Manoj Kumar Patairiya (The writer is Director of
DD Kisan Channel)