Ramanujan's Lost Notebook
Bruce C. Berndt, '61
Professor
Department of Mathematics
University of Illinois at Urbana-Champaign
In the spring of 1976, while searching through papers of the late
G. N. Watson at Trinity College, Cambridge, George Andrews found a
sheaf of 138 pages in the handwriting of Srinivasa Ramanujan,
generally regarded as India's greatest mathematician. In view of
the fame of Ramanujan's earlier notebooks, Andrews naturally
called these papers Ramanujan's "lost notebook." This work,
comprising about 650 results with no proofs, arises from the last
year of Ramanujan's life and represents some of his deepest work.
Since many in the audience may not be familiar with Ramanujan, we begin
with a brief biography. Second, we provide a history of the lost
notebook. Third, a general description of the topics found in the lost
notebook will be provided. For some of the topics, in particular,
q-series, theta functions, mock theta functions, continued fractions, partitions,
and infinite series, we offer some details. In the time remaining, the
fourth portion of the lecture will be devoted to a more detailed
discussion of one of the topics prominently addressed in the lost
notebook, namely continued fractions.