Ramanujan, unschooled Genius
1887 - 1920 India
"An equation means nothing to me unless it expresses a thought of God."
-Bowditch Quoted in F Cajori, The Teaching and History of Mathematics in the United States
Ramanujan worked out the Riemann series, the elliptic integrals, hypergeometric series and functional equations of the zeta function.
Ramanujan independently discovered results of Gauss, Kummer and others on hypergeometric series. Ramanujan's own work on partial sums and products of hypergeometric series have led to major development in the topic.
Perhaps his most famous work was on the number p(n) of partitions of an integer n into summands. MacMahon had produced tables of the value of p(n) for small numbers n, and Ramanujan used this numerical data to conjecture some remarkable properties some of which he proved using elliptic functions. Others were only proved after Ramanujan's death.