Srinivasa Ramanujan developed results in number theory, including the study of highly composite numbers: positive integers having more divisors than every smaller positive integer.[ref]
His analysis connects record values of the divisor function with prime factorization. Prime exponents must be arranged in nonincreasing order as the primes increase: swapping an inverted pair would produce a smaller integer with the same divisor count, contradicting the record property. For example, has six positive divisors. The subject turns irregular arithmetic data into a constrained optimization problem.[ref]
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The cool think about Ramanujan is how British mathematicians heard about him and then just went crazy that someone they had never heard of before had come up with so many novel results. It is as if God had come down from the clouds and handed them those results. Without proof. But in that field of research, the statements are not easy to come up with, so much so that G. H. Hardy commented that:
they must be true, because, if they were not true, no one would have the imagination to invent them
Srinivasa Ramanujan was an Indian mathematician who made significant contributions to mathematical analysis, number theory, infinite series, and continued fractions. Born on December 22, 1887, in Erode, India, he displayed extraordinary mathematical talent from a young age, despite having very little formal training in the subject. Ramanujan's work is known for its depth and originality, and he developed many results that were groundbreaking at the time.