Noson S. Yanofsky's talk "Self-Referential Paradoxes"

Noson S. Yanofsky 
professor of Computer and Information Science
Brooklyn College and The Graduate Center, CUNY
 

"Self-Referential Paradoxes"

Abstract

Over the past 150 years, some of the most profound and influential theorems in mathematics and computer science have emerged from self-referential paradoxes. These theorems deal with systems that exhibit self-reference, challenging our understanding of fundamental concepts. This presentation will explore:

1. Georg Cantor's Theorem: Demonstrating the existence of different levels of infinity.
2. Bertrand Russell's Paradox: Exposing inconsistencies in naive set theory.
3. Kurt Gödel's Incompleteness Theorems: Revealing inherent limitations in formal systems and the notion of mathematical proof.
4. Alan Turing's Halting Problem: Proving the existence of unsolvable computational problems.

Remarkably, these diverse theorems, along with several others, can be understood as manifestations of a single, elegant theorem from basic category theory. This presentation will elucidate this theorem and demonstrate its various instances.

Note: No prior knowledge of category theory is required for this talk.