Professor Jamie Tappenden, "Styles of Mathematical Explanation. Why do Elliptic Functions Have Two Periods?"

March 27, 2015
All Day
347 University Hall

Abstract: Recent years have seen a growth in the topic of explanation as a phenomenon within mathematics. There appear to be both differences and similarities in the patterns characteristic of mathematical explanations of mathematical events and causal explanations of physical events, but more study is needed to ascertain precisely what the differences are. This talk will present a historical case study illustrating that, among other things, mathematical explanations can exhibit the same interest-relativity and context-dependence that are found in explanations of physical events. The example is the explanation of a particular fact about a class of functions called elliptic functions, that exhibit a property called double periodicity. (This way of describing the case involves seeing the elliptic functions in a nineteenth-century way; today double periodicity is part of the definition of “elliptic function”.) Two ways to address the fact – one using techniques characteristic of Bernard Riemann and another in the style of Weierstrass reveal strikingly different mathematical virtues. The explanations are both “good ones”, but for incommensurable reasons.

 Professor Tappenden is from the University of Michigan.

 

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