Srinivasa Ramanujan (1887 – 1920) had almost no formal education in mathematics yet he turned out to be a genius mathematican. He made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. He made around 3900 discoveries which included previously known theorems as well as new work. Nearly all of them have been proven correct although some were proven false. While still in Madras, India, Ramanujan recorded his results in four notebooks. These results were mostly without proofs for several reasons. Paper was very expensive and hence, Ramanujan would do most of his work and perhaps his proofs on a slate, and then just write the results on paper. It is also probable that he was influenced by the style of G. S. Carr's book "A Synopsis of Elementary Results in Pure and Applied Mathematics", where results were stated without proofs. The results in his three notebooks inspired numerous papers by later mathematicians trying to prove what he had found. The mathematician Godfrey Harold Hardy himself created papers exploring material from Ramanujan's work as did G. N. Watson, B. M. Wilson, and Bruce Berndt. A fourth notebook was rediscovered in 1976 by George Andrews and is called the "lost notebook". Notebooks 1, 2 and 3 were published as a two-volume set in 1957 which was a photocopy edition of the original manuscripts, in Ramujan's own handwriting. In 2011, as part of the celebrations of the 125th anniversary of Ramanujan's birth, the notebooks were republished in a coloured two-volume collector's edition. The "Ramanujan Journal", an international publication, was launched to publish work in all areas of mathematics influenced by his work. Sources: Srinivasa Ramanujan. (n.d.). Retrieved December 29, 2014, from http://en.wikipedia.org/wiki/Srinivasa_Ramanujan
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Stanislaw Ulam (1909 – 1984) was a Polish-American mathematician whose contributions weren't limited to mathematics. He invented nuclear pulse propulsion, solved the problem of how to initiate fusion in the hydrogen bomb and thus proposed the Teller–Ulam design of thermonuclear weapons. He also participated in the Manhattan Project . As for mathematics, he developed a number of mathematical tools in number theory, set theory, ergodic theory, and algebraic topology. He also devised the 'Monte-Carlo method' widely used in solving mathematical problems using statistical sampling
Here are some quotes from his book "Adventures of a Mathematician":
When asked to sum up his work Ulam said: "Originally I worked in set theory and some of these problems are still being worked on intensively. It is too technical to describe: measurable cardinals, measure in set theory, abstract measure. Then in topology had a few results. ... Then I worked a little in ergodic theory. Oxtoby and I solved an old problem and some other problems were solved in other fields later. In general I would say luck plays a part, at least in my case. Also I had luck with tremendously good collaborators in set theory, in group theory, in topology, in mathematical physics, and in other method, which is not a tremendously intellectual achievement but is very useful, a few things like that." Sources: M Feigenbaum, Reflections of the Polish masters - an interview with Stanislaw Ulam and Mark Kac, Wiadom. Mat. 30 (1) (1993), 93-114. Stanislaw Ulam. (n.d.). Retrieved December 29, 2014, from http://en.wikipedia.org/wiki/Stanislaw_Ulam |