I’ve become fascinated with Gregory Chaitin’s exploration of randomness in computing and his impulse to bring these observations to bear on physical, mathematical, and biological theories. His work inevitably addresses epistemological questions – what it means to know, to comprehend – and leads him to move (as he says in a recent paper) in the [...]
There's a discussion going on at the Foundations of Mathematics mailing list about the purpose and value, actual and potential, for formalized proofs in mathematics. Harvey Friedman asked Jeremy Avigad to comment; he sent this super-useful list of references, republished here with his approval.
John Harrison and I recently wrote a survey on formalized mathematics, for computer scientists:
Jeremy Avigad, John Harrison, 2014, "Formally verified mathematics." Communications of the ACM 57: