LTT: Simon DeDeo - Alien ProofsSimon DeDeo (Carnegie Mellon University, Indiana University, Bloomington, Santa Fe Institute)
1117 Cathedral of Learning - 11th Floor
University of Pittsburgh, 4200 Fifth Avenue
Pittsburgh 15260
United States
This event is available both online and in-person
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The Center for Philosophy of Science at the University of Pittsburgh invites you to join us for our Lunch Time Talk. Attend in person at 1117 Cathedral of Learning or visit our live stream on YouTube at https://www.youtube.com/channel/UCrRp47ZMXD7NXO3a9Gyh2sg.
Lunch Time Talk - Simon DeDeo
Carnegie Mellon University & the Santa Fe Institute https://proofsandreasons.io
Friday April 10th @ Noon
Join us in person in room 1117 on the 11th floor of the Cathedral of Learning.
Title: Alien Proofs
Abstract:
It is now possible to write verifiably-correct proofs of sophisticated mathematical theorems in computer programming languages such as Lean. Coupled with recent developments in Generative Artificial Intelligence, this means we are now able to explore, for the first time, the space of mathematical proofs in ways that go beyond human intuition, capacity, and patience, and to answer, in new ways and through empirical study, questions that were previously the realm of science fiction and philosophical speculation: how do humans carve the space of mathematics? What regions do we leave unexplored and what lies beyond our ken? How do our cognitive limitations constrain us or, conversely, lead us to explanatory and fertile ground? I will present the first results from the Proofs and Reasons Project, a multidisciplinary collaboration between philosophers, cognitive scientists, mathematicians, and computer scientists. I will present the first statistical studies of artificially-generated proofs, constructed with, and without, human guidance; our first results on so-called "ablation" studies that demonstrate the existence of what we refer to as generative constraints; and the first results that probe the often misaligned preferences of humans and machines in cyborg proofs. These results challenge basic orthodoxies in the philosophy of mathematics, and provide new problems for philosophers of science, mathematics, and AI.
Joint work with Zephyr Fan, Bálint Gyevnár, and Eamon Duede, supported by Grant 63750 from the John Templeton Foundation.
This talk will be available online: Zoom: https://pitt.zoom.us/j/97095624890 and
YouTube: https://www.youtube.com/channel/UCrRp47ZMXD7NXO3a9Gyh2sg
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