information on any indian mathematician's contributions in the field of mathematics
Answers
Shakuntla devi - The most famous female Indian mathematician of all time, Shakuntala Devi, was more commonly known as the human computer. She was so called because of her incredible talent to solve calculations without using any calculator. In Dallas she even competed with a computer to give the cube root of 188138517 faster and she won! She went ahead to compete with UNIVAC the world’s fastest computer to solve the 23rd root of a 201 digit number and she won that too! A woman with outstanding talent and outrageous world records!
What are the mathematical contributions of Ramanujan?
Ramanujan stands upright, inevitably as one of the greatest minds who ever breathed on Earth. With an up surging career in Mathematics. Nothing prevented him to live in the realm of Mathematics, neither the World War nor the racism in England (let alone the the mistreated Tuberculosis). And in this remarkable career as a professional mathematician for approximately 5 years he has contributed no less than 5000 theorems and conjectures half of which remains unproven.I highlight few of his remarkable contributions.
Firstly,
Partition theory.Some mathematics claim it to be one of his greatest contributions to number theory.Partition of a number basically implies the number of ways a number can be expressed explicitly as the sum of positive integers(where the order is independent).He discovered collaboratively with G.H. Hardy, an approximation to the number of ways to partition any integer, and also an infinite series that exactly determines the number of partitions.
In the words of G. H. Hardy, quoted from a Mathematician's Apology, “The problem was a rabbit hole mystery, and the greatest of minds had worked on it all destined to failure. However, one fine day Ramanujan walked into my room with this remarkable infinite series, that exactly determined the number of partitions of a number”
He also independantly discovered few congruences related to Partitions, such as
p(5k+4)≡0(mod5)
And, others...
Secondly,
Highly composite numbers a term that was coined independantly by Ramanujan. Highly composite numbers was his first research paper to be published in a foreign journal.
Highly composite numbers are those positive integers that have more divisors than any smaller positive integer.
Thirdly,
Mock theta functions,
One of the biggest discoveries by Ramanujan, the functions are called Mock theta function because, it is very analogous to the Theta functions.The application of such functions are tremendous not only in abstract mathematics but also in Quantum Mechanics, for studying black holes and new advancements in super string theory.
Lastly,
K3 surfaces.A mathematical treasure that remained Hidden in his notebooks,until it's recent discovery by Prof. Ken Ono. That was independantly discovered forty years after his death.Astoundingly,he had discovered it much before any one was even thinking about it.However,coudn't publish it for his untimely death.
Thus,Ramanujan's contribution to mathematics is as profound as his ingenuity, which can be easily introspected from the above mentioned few discoveries. He was regal in his ways of mathematical contribution but unconditionally humble in his dwellings, that's where his true essence sustains.