Ramanujan's personal notes

While he was still in India, Ramanujan recorded the bulk of his results in four notebooks of loose leaf paper. These results were mostly written up without any derivations. This is probably the origin of the perception that Ramanujan was unable to prove his results and simply thought up the final result directly. Mathematician Bruce Berndt, in his review of these notebooks and Ramanujan's work, felt that Ramanujan most certainly was able to make the proofs of most of his results, but chose not to..

This style of working may have been for several reasons. Since paper was very expensive, Ramanujan would do most of his work and perhaps his proofs on slate, and then transfer just the results to paper. Using a slate was common for mathematics students in India at the time. He was also quite likely to have been influenced by the style of one of the books from which he had learned much of his advanced mathematics: G. S. Carr's Synopsis of Pure and Applied Mathematics, used by Carr in his tutoring. It summarised several thousand results, stating them without proofs. Finally, it is possible that Ramanujan considered his workings to be for his personal interest alone; and therefore only recorded the results. The first notebook has 351 pages with 16 somewhat organized chapters and some unorganized material. The second notebook has 256 pages in 21 chapters and 100 unorganized pages, with the third notebook containing 33 unorganized pages. The results in his notebooks inspired numerous papers by later mathematicians trying to prove what he had found. Hardy himself created papers exploring material from Ramanujan's work as did G. N. Watson, B. M. Wilson, and Bruce Berndt. (Berndt, 1998) A fourth notebook, the so-called "lost notebook", was rediscovered in 1976 by George Andrews.

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

Sankalp Unit