I’m not sure they take themselves 100% seriously… but I don’t know. Still–I think it’s a nice effort to prove things using the weakest possible set of axioms. Plus, constructive arguments do tend to be more satisfying than non-constructive ones. Like the axiom of choice–use it if you need to, but it’s nicer if you don’t.
I listened. The truly noteworthy fact is his claim that it came out of his study of the fine structure constant. Now, the fine structure constant is an observable quantity, related to Planck’s constant and not a mathematical quantity at all. In a different universe it could, as far as anyone knows, have a different value. It seems inconceivable to me that any study of the FSC could bear on the RH.
We had a discussion of proof by contradiction a while back, by the way Professional Mathematicians -- Bias against non-direct proofs? - Factual Questions - Straight Dope Message Board
While I hesitate to do so out of respect, look into his claimed 12-page Feit Thompson proof and paper on 6-spheres before you dedicate too much time.
I started to itemize issues or required points of clarification with this claim but stopped as it felt like I was stepping on puppies.
I’ll leave it to others.
It looks like his purported 12-page proof of Feit-Thompson isn’t available anywhere online, but he has a paper about complex structures on S^6 on the arxiv and another in a book called “Foundations of Mathematics and Physics One Century After Hilbert.” The former is just nonsense. I can only find a preview of the first two pages of the latter, but they’re just elementary, unrelated stuff about Minkowski space, and the entire thing is only four pages long. Oh well.
Sir Michael Atiyah just passed away:
More extensive obituary:
Sorry to hear that. There is a line in the NYT obituary that says his proof of RH did not hold up.
As an aside, I’ve long suspected that the fine-structure constant can, in fact, be mathematically calculated. It’s not like it’d be the first time that a dimensionless constant of fundamental physics has been discovered to be calculable. But at the same time, any claim of a calculation should be treated with skepticism, especially if it doesn’t come from a coherent physical model which makes other testable predictions. I’m not convinced by arguments like “this simple formula produces α to ten decimal places, and that can’t be coincidence!”, because even “simple” formulae generally contain more information than they seem to, and coincidences happen, especially when you have the whole universe of numbers to look for.