Associate 1994-95

Bruce C Berndt


Proving the Claims Made by Ramanujan in His Notebooks

When India's greatest mathematician, Srinivasa Ramanujan, died in 1920 at the age of 32, he left behind three notebooks containing the statements of approximately 3000-4000 theorems without proofs. G. H. Hardy, England's most famous mathematician during the first half of the twentieth century, strongly urged that the notebooks be edited and published. Although two English mathematicians worked on this task for several years, they never completed their work and the enormity of the project prevented others from further attempts. It was not until 1957 that a photostat edition of the notebooks was published, but no editing was undertaken.

In 1976, George Andrews discovered in the library of Trinity College, Cambridge, a sheaf of about 140 pages of mathematics from the last year of Ramanujan's life. This work is now called Ramanujan's "lost notebook." Since then, Andrews has devoted considerable effort to proving over half of the claims made in the lost notebook.

Since May, 1977, Professor Berndt has devoted all of his research efforts to proving all of the hitherto unproven claims made by Ramanujan in his three notebooks. Four volumes containing his proofs and (whenever possible) relevant history and connections to contemporary research have been completed. Almost 200 claims remain to be proved, and his goal is to complete this work during his appointment at the Center for Advanced Study. Moreover, he plans to begin proving the claims made in the lost notebook which are not being examined by Andrews.