Speaker: Jonathan C. Mattingly, James B. Duke Professor of Mathematics at Duke University

October 21, 2019 (Monday), Physics 128, 4:30-5:30pm (Tea at 3pm Physics 101)

Title: A mathematician goes to court: Understanding Gerrymandering

Abstract: This a story of both mathematics informing the law AND legal questions suggesting new mathematical problems. How does one identify and understand gerrymandering? Can we really recognize gerrymandering when we see it? If one party wins over 50% of the vote is it fair that it wins less than 50% of the seats? What do we mean by fair? How can math help illuminate these questions? For me these question began with a Duke Math PRUV undergraduate research program project in 2013, continued through a sequence of iiD Data+ projects, and has lead me to testify twice in two cases. Common Cause v. Rucho went to the US Supreme court and Common Cause v. Lewis resulted, just last month, in the redrawing of the NC State Legislative district maps. The legal discussion has been informed by the mathematical frame work, but the problem of understanding gerrymandering has also prompted the development of a number of new computational algorithms which come with new mathematical questions.

Speaker: Michael Harris, Professor of Mathematics at Columbia University

March 28, 2019 (Thursday), LSRC B101, 4:30-5:30pm (Tea at 3pm Physics 101)

Title: Mechanical Mathematician

Abstract: A mathematical claim is only accepted as valid if it is accompanied by a proof. Ideally, a proof should be a deduction from accepted principles that meets two requirements: on the one hand, it must strictly follow the rules of logical reasoning, but on the other hand, it should clarify why the claim had to be valid in the first place. When these two criteria come into conflict, the first takes priority. Some deductions, however, are so long or complex that they cannot be checked for errors by human beings. The success in designing computer systems to provide mechanical verification of the proofs of some famous theorems has led some mathematicians to suggest that all future proofs be written in computer readable code. A few mathematicians have gone so far as to predict that artificial intelligence will make human mathematicians obsolete. Is mathematics a means to an end that can be achieved as well, or better, by a competent machine as by a human being? If so, what is that end, and why should we trust machines over humans? Or is mathematics rather an end in itself, pursued for its intrinsic human value? If so, what could that value be, and can it ever be shared with machines?