What is a closed form?

Richard E. Crandall, Director, Center for Advanced Computation, Reed College

Reed College, Thursday, October 29, 4:10–5:00, Eliot 314

Abstract: The term closed form is one of those mathematical notions that is commonplace, yet virtually devoid of rigor. And, there is disagreement even on the intuitive side; for example, most everyone would say that π + log 2 is a closed form, but some of us say the Euler constant γ is not closed. The lecturer will try to supply some missing rigor to the closed-form discussion, by defining a ring of hyperclosure H to which many fundamental constants belong. We then say an element of H is closed, and give examples from modern research where the question of closure looms both important and elusive.