Colloquium: Can Machines Think Logically?

Abstract

Alan Turing famously proposed a test to determine whether machines can "think." In this talk, Riehl poses a slightly different question: "can machines think logically?" In realms, such as mathematics, where statements are unambiguously true or false, can generative AI be trusted to "reason" its way to the correct answer? While such guarantees are not possible for even the best reasoning models, Riehl will describe a potential architecture that could be trustworthy. The idea is to integrate a generative AI with a trusted software program called a computer proof assistant to check the reasoning of logical arguments. This could have significant implications both for mathematics and for the real world in domains amenable to formal methods.

About the Speaker

Emily Riehl is the Kelly Miller Professor of Mathematics at Johns Hopkins University in Baltimore. Her research interests include higher category theory, abstract homotopy theory, homotopy type theory and computer formalization. She has written several books and expository articles directed at various mathematical audiences, most of which are freely available online. She is also a co-founder of Spectra: the organization for LGBTQ mathematicians.

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