Laws of Communication of Thought

Madhu Sudan (Harvard) 

In their far-reaching works, Boole and Shannon took mathematics to places where it had never been before: Inside the mind, formulating the "Laws of Thought" and across our senses via "A Mathematical Theory of Communication". Putting the two ingredients together and adding a healthy mix of the theory of computation gives us the ability, in principle, to analyze any human/intelligent process. Indeed many of the resounding successes in the theory of computing in the past thirty years or so may be described as an effect of this ability. In this talk I will briefly cover some of the highlights of these explorations which capture concepts such as randomness, knowledge, secrecy and privacy. I will then turn to the vehicle that I view as central to preserving Thought as it is Communicated: Proofs! I will explain what proofs are, why they are central and how they (can be designed to) behave in unexpected ways. Some of the talk will even be mathematically grounded.