gottheUIblues

I think lean can verify it implements its own rules, but not that its own rules are sound (you can't prove a contradiction). If you are just prepared to trust that the rules are sound, then you would be able to trust leans implementation (if you had that Lean proof that it implements its own rules)

I think people on here tend to somewhat fixate on the determinism issue. Even with a deterministic LLM - stabilising the floating point arithmetic, and choosing from the distribution by a fixed method, or just save the random seeds - there is still a kind of a chaotic unpredictability that can exist between its inputs and outputs. However maybe that is a price that needs to be paid to get creativity.

Did any mathematics done by G H Hardy turn out to be quite useful in the end?

Ironically of course the answer is yes.

Yes indeed, it's about the time sound takes to travel 4mm

Bill 8 months at $8.33 and 4 months at $8.34?

The dichotomy is more 'human understood' vs 'not human understood', I think

That was exactly my thought - taking out the problems that PhDs and early stage researchers work on kills the pipeline of developing mathematicians

It's an article written by a guest contributor - not an editorial written as the voice of the newspaper

Is the word "nonautological" autological ?

This is only the "problem solving" side of mathematics. Completely missing the theory builders who have completely reshaped the world of mathematics (and far beyond). AI is a long way from matching original thinkers of the calibre of Euclid, Al-Khwarizmi, Newton, Leibniz, Euler, Galois, Riemann, Cantor, Hilbert, and Grothendieck. Or Turing, Gödel and Von Neumann?

The normal term for the logic that has two truth values, the law of non-contradiction, and the law of the excluded middle is 'Classical Logic' which dates back centuries before George Boole. Non-classical logics which deny one or more of three properties that I've mentioned also exist

Rather COBOL is a living fossil? And today's Fortran is the FORTRAN family with horizontal gene transfer from the Algol lineage of programming languages.

Err? Peano Arithmetic is provably consistent in ZFC, but it is not in itself (if PA is consistent). Therefore if PA is consistent it is not equivalent to ZFC (regardless of whether ZFC is consistent or not)

"Embarrassingly" considered harmful?