In the years following the death of the greatest Indian mathematician, Srinivasa Ramanujan, three notebooks containing unfinished and unpublished work of his were discovered. The contents of the notebooks reflected much of the mathematical style of the man. There are unsupported conjectures, claims and formulas written in an unorganized manner, covering vast areas of mathematics. No other recorded genius is known to have practiced mathematics like Ramanujan. He worked in isolation with only a few old books at his disposal. He was not aware - or apparently concerned - with structured mathematics as it had developed in the western world during the early part of the twentieth century. Indeed, even today, none of those who have studied his remarkable contributions and legacy, can comprehend how he came to have such remarkable insight with so little formal training. It is the search for this insight which motivates much of the work to be supported by this award. The means by which this effort will be carried out is simple to state. One goes through the notebooks statement by statement (there are roughly 3000 results stated without proof), verifying or negating each one, using all the powerful mathematical tools now available. This task has been going on for many years. The first notebook is essentially understood and the second is also nearly complete. As a result of this, over 40 papers and two definitive books have appeared. Work is now progressing on the third which will involve higher order transformations of hypergeometric series and inversion formulas stated by Ramanujan. Some of the deepest work and potentially most difficult challenges will be in the area of asymptotic expansions of infinite series, products and integrals. At some later time attention will have to be given to brief allusions to generalizations in the theory of elliptic functions made by Ramanujan in a 1914 paper. Any progress here is expected to be of considerable interest to physicists.
