Simons Foundation Lectures are free public colloquia related to basic science and mathematics. These high-level talks are intended for professors, students, postdocs and business professionals, but interested people from the metropolitan area are welcome as well.
Since at least the time when it was understood that the circumference of a circle is pi multiplied by its diameter, the applications of mathematics have raced on far ahead of the foundations of the subject itself. By considering a variety of examples, principally from the 19th century, we will explore the tension between mathematics and its applications, and reasons why it remains a valuable and rewarding occupation to develop the necessary framework for existing and “well understood” theories. If time permits, I will give a short discussion of recent work I have done on the mathematical foundations for diffusion models in population genetics.