The Value of Errors in Proofs

 Avi Widgerson | Herbert H. Maass Professor, School of Mathematics, Institute for Advanced Study, Princeton
Genomics in the Age of AI

ABSTRACT:
In the year 2020, a group of theoretical computer scientists posted a paper on the Arxiv with the strange-looking title “MIP* = RE”, impacting and surprising not only complexity theory but also some areas of math and physics. Specifically, it resolved several long standing problems in these areas. As it happens, both acronyms MIP* and RE represent proof systems, of a very different nature. To explain them, we’ll take a meandering journey through the classical and modern definitions of proof. I hope to explain how the methodology of computational complexity theory, especially modeling and classification (both problems and proofs) by algorithmic efficiency, naturally leads to the generation of new such notions and results (and more acronyms, like NP). A special focus will be on notions of proof which allow interaction, randomness, and errors, and their surprising power and magical properties. 

You can find the paper here