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What are the contributions of Srinivasa Ramanujan?

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Srinivasa Ramanujan made great contributions to the field of mathematics, including a collaboration with well-known mathematician H.G. Hardy in developing the formula for the number, p(n), of partitions of a number "n." His discoveries also led to the infinite series for infinity formulation.

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Srinivasa Ramanujan was born in Madras, Tamil Nadu, in 1887 and lived until 1920. He had very little formal training in mathematics, largely teaching himself after taking an interest at the age of 10. He did not do well in college, however, because the only class that he passed was mathematics. Srinivasa was awarded a Bachelor of Science from Cambridge for his work involving highly composite numbers.

When he was 15, he obtained a copy of the second volume of "Synopsis of Elementary Results in Pure and Applied Mathematics" by George Shoobridge. Much of the material in the book was out of date, but nevertheless it spurred Ramanujan to delve into the subject and formulate his own theories.

He studied in Cambridge, England, under Godfrey Hardy, after beginning a correspondence with him by mail. It was in England that he made significant progress in the partition of numbers. Partition of a number is a way of writing a number as a sum of positive integers. For example, 4 can be partitioned as the sum of 3 and 1. He and Hardy solved the problem of partitioning p(n), previously a mystery to mathematicians because while it is possible to partition it recursively, there is no explicit formula for it.

Through his work in Cambridge, Ramanujan earned considerable acclaim for his ideas, which were published in many academic journals throughout Europe.

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