Number theory is the branch of mathematics that tries to understand all the properties of whole numbers or integers. This week’s Occupy Math is about the great Indian number-theorist Srinivasa Ramanujan. Number theory threads through the rest of mathematics and includes everything from incredibly abstract problems like Fermat’s last theorem (which took 357 years to finish solving) to facts about prime numbers that keep the money in banks safe and secure on a daily basis.
India has a substantial mathematical tradition going back at least to the seventh century. The Indian tradition also makes math less separate from everyday life than it is in the European tradition. Ramanujan, however, was one of those people who seem to be born with mathematics in their blood. He was obviously brilliant and excelled in primary and secondary school, learning all the math anyone could teach him and teaching himself out of advanced books that those who recognized his talent loaned him. His brilliance got him a scholarship at the Government Arts College. He got poor grades in everything but math and so lost his scholarship. He then scraped by, often ill and always poor, until he was rescued by the founder of the Indian Mathematical Society.
Ramanujan could see as obvious truths things that other mathematicians had to work for years to understand.
Eventually, Ramanujan came to the attention of G. H. Hardy, the great British mathematician. Ramanujan’s work suffered from his lack of formal training and, oddly, from his brilliance. He would make great intuitive leaps that, while often correct, were beyond the understanding of other mathematicians. They could not follow his work, and so assumed it was wrong (this is usually a perfectly good assumption). Hardy was brilliant enough to see that at least part of Ramanujan’s work was correct and entirely original. He brought Ramanujan to England where the lack of an acceptable diet and the weather killed him, but not before he was awarded a Ph.D., became the second Indian admitted to the Royal Society, and gained the fervent acclamation of the British mathematical community. He was also the first Indian to be elected a fellow of Trinity College.
Ramanujan lived 33 years and spent a good chunk of that barely surviving. In that time he compiled 3,900 results. Some of these were wrong, some were already known, but many of them were original and form a substantial part of the foundations of modern number theory and mathematics. His absolutely unique mind broke through into multiple new areas of mathematics. These achievements were made in spite of poor health, membership in a discriminated group within the British Empire, and a very real inability to focus on trivia like food and shelter when there was new mathematics to discover.
A famous story that illustrated the way Ramanujan’s mind works comes from a visit Hardy paid him while he was recovering from illness. Hardy informed him that the number, 1729, of the taxicab he had ridden in was boring, having no special properties. Ramanujan immediately replied that this was not so as 1729 was the smallest number that could be written as the sum of cubes in two different ways, twelve cubed plus one cubed and nine cubed plus ten cubed. Proving this is so would take a normal mathematician hours or even days; it occurred to Ramanujan in the time it took to reply to Hardy’s remark.
The Ramanujan Journal was founded to finish proving the things that seemed obvious to Ramanujan as well as to extend his work.
Having an international journal founded based on your work is a singular honor. The Ramanujan Journal not only served to preserve and extend Ramanujan’s work but also to complete it – at least relative to the mathematical community – by filling in missing details that were much less obvious to everyone else than to Ramanujan himself. Individuals with this sort of intuitive grasp of mathematics are very rare. Occupy Math has only the smallest touch of the gift of intuition and must work out most things by doing a lot of hard mental work. He stands in awe of the gift, taken from us too soon, that resided in the frail frame of Srinivasa Ramanujan.
Ramanujan’s example demonstrates why it is advantageous not to discriminate against any class of people, be they women, people of color, or even people that are just plain odd. Such discrimination is morally repugnant but, in addition, it is very costly to greater society. Our species occasionally throws up individuals possessed of a bizarre, almost other-worldly genius. The structure of our society determines whether these individuals are nurtured as holy men, respected as scholars, binned in a nut-hatch, or assigned lifetime menial duties because they are never noticed. It is not hard to argue that the gift of mathematical intuition is often coupled with some form of madness. To throw away these gifts of providence is a towering tragedy. One of Occupy Math’s happiest and most solemn duties is to try to recognize talent or genius when it appears among his students.
Have you ever met one of the mathematical changelings, the people that have trouble remembering to eat but for whom math is simple and easy? Do you know of other marginalized people that turned out to be genius-level talents? If so, comment or tweet. Occupy Math would like to know.
I hope to see you here again,
University of Guelph,
Department of Mathematics and Statistics