Alladi Ramakrishnan Hall

The oldest problem

Chandan Singh Dalawat

HRI

Which rational numbers are expressible as the area of a
right-angled triangle all whose sides have rational lengths ? This
elementary problem was posed more than a thousand years ago but remains
unsolved to this day, although a lot of progress has been made in the last
few decades. We will give an accessible introduction to this problem
(called the congruent number problem in the literature) and present some
old and new results towards its elusive solution.