points by leonidasrup 4 days ago | 0 comments
Even Peter Scholz is not always sure of correctness of extremely complicated mathematical statements and welcomes computer assistance in verification of his results.
See the Liquid tensor experiment:
https://xenaproject.wordpress.com/2020/12/05/liquid-tensor-e...
https://www.ma.imperial.ac.uk/~buzzard/xena/pdfs/liquid_tens...
" I spent much of 2019 obsessed with the proof of this theorem, almost getting crazy over it. In the end, we were able to get an argument pinned down on paper, but I think nobody else has dared to look at the details of this, and so I still have some small lingering doubts. "
In a sense, mathematics is not very different from software engineering.
More precisely: Curry–Howard correspondence
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon...
[–] niemandhier 4 days ago
[–] hardbass 3 days ago
Are they publishing cryptographic proof they never used AI? They should request the AI companies that their IP addresses, etc blacklisted and hard banned from AI services and present some kind of verifiable cryptographic proof they submitted to such a ban.
[–] datsci_est_2015 3 days ago
Or, maybe, they assume their peers within the organization are operating in good faith because they're not drawn from morally bankrupt communities like Silicon Valley.
[–] hardbass 3 days ago
How would you know? Its easy to also accidentally use AI. They are mathematicians, they know mathematics demands proofs. If they pledge they shall not use AI, they should provide cryptographic proof otherwise the statement is considered untrue.
[–] hardbass 3 days ago
How is silicon valley morally bankrupt?
[–] datsci_est_2015 2 days ago
Because they're the only community that requests cryptographic proof that their peers are acting in good faith. (:
[–] bongofizzbuzz 4 days ago
Just like small numbers appear in almost all places in mathematics. Small numbers are limited. Sometimes these may appear as coincidences. Similarly small elegant explanations are limited in numbers. As mathematical universe expands, only way to explain these additional results will be to have complex explanations.
[–] adrianN 3 days ago
That is true in theory, in practice the space of proofs that fit in thirty pages or so is so vast that I find it unlikely that we’ll exhaust it for the foreseeable future.
“ 1. Members commit to not working with commercial AI companies by providing technical labor, mathematical knowledge, consultation, or publicity.
2. Members commit to not publishing mathematical texts (including papers, reviews, referee reports, lecture notes, teaching materials, and books) generated by AI models. Members only publish their own writing, as opposed to outputs of AI tools. We affirm that mathematical writing should have human authorship. “
https://www.ahmath.org/members