Albion College

Mathematics and Computer Science

Mathematics and Computer Science

COLLOQUIUM

Making Calculus Easy the Hard Way

Andrew Livingston

You probably haven't heard of the *p*-adic
numbers, but they are full-fledged number systems on par with the real
numbers—and given there's a *p*-adic number system for every
prime *p*, they outnumber ℝ infinity to one! They're also weird
and wild landscapes for which *Alice's Adventures in Wonderland*
provides a better guide than common sense does: big becomes small, short
becomes long, and geometry can be described but not easily drawn. In this
talk we'll meet the *p*-adics and see how *p*-adic calculus
makes short work of testing for convergence of infinite series in a way
calculus students only dream about. We'll also see how the nice properties
of *p*-adic numbers led to them conquering number theory in the
20th century (spoiler: they played a part in Wiles' proof of Fermat's
Last Theorem).