20th century

The profession of mathematician became much more important in the twentieth century. Every year, hundreds of new Ph.D.s in mathematics are awarded, and jobs are available both in teaching and industry. Mathematical development has grown at an exponential rate, with too many new developments to even touch on any but a few of the most profound.


In the 1910s, Srinivasa Aiyangar Ramanujan (1887-1920) developed over 3000 theorems, including properties of highly composite numbers, the partition function and its asymptotics, and mock theta functions. He also made major breakthroughs and
discoveries in the areas of gamma functions, modular forms, divergent series, hypergeometric series and prime number theory.
Famous theorems of the past yielded to new and more powerful techniques. Wolfgang Haken and Kenneth Appel used a computer to prove the four color theorem. Andrew Wiles, working alone in his office for years, proved Fermat's last theorem.

Entire new areas of mathematics such as mathematical logic, the mathematics of computers, statistics, and game theory changed the kinds of questions that could be answered by mathematical methods. Bourbaki, a non-existent French mathematician, attempted to bring all of mathematics into a coherent whole.

There were also new investigations of limitations to mathematics. Kurt Gödel proved that in any mathematical system that includes the integers, there are true statements that cannot be proved. Paul Cohen proved the independence of the continuum hypothesis from the standard axioms of set theory.
By the end of the century, mathematics was even finding its way into art, as fractal geometry produced beautiful shapes never seen before.

source:http://en.wikipedia.org/wiki/History_of_mathematics