[HN Gopher] Formalising modern research mathematics in real time
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Formalising modern research mathematics in real time
Author : mauricioc
Score : 79 points
Date : 2023-11-05 12:25 UTC (2 days ago)
(HTM) web link (xenaproject.wordpress.com)
(TXT) w3m dump (xenaproject.wordpress.com)
| tezthenerd wrote:
| If you want to see this kind of thing done "really in real time"
| check out Terry Tao's recent mathstodon posts where he learns
| Lean while formalizing a paper of his own. Fascinating stuff.
| n4r9 wrote:
| Cool to see the mention of Andrew Thomason! He was my
| supervisor/tutor for several undergrad courses, as well as
| lecturing a couple of the courses I took over the years. He had a
| brilliant Yorkshire accent, and if I remember rightly he enjoyed
| eating Walkers crisps and making good use of Fellows' privilege
| to ride their bike on college grounds. I actually had no idea
| that he had a seminal result on Ramsey numbers, and in the same
| year I was born no less.
| dunham wrote:
| The guy behind the xena project, Kevin Buzzard, recently got a
| grant to formalize Wiles' proof of Fermat's theorem in Lean4:
| https://mathstodon.xyz/@xenaproject/111170563403967905
| V1ndaar wrote:
| > An obvious question when formalising a maths paper is how much
| the proof needed to change to be formalised: in other words
| whether there were any flaws in the paper. This question is
| surprisingly subtle, but a simple summary is that most of the
| mistakes I identified were easily fixable. Importantly all
| mistakes were fixable in a way that preserved the spirit of the
| argument, so the Lean version of the proof can reasonably be said
| to be a translation of the informal proof.
|
| > I like to consider certain such small mistakes "mathematical
| typos". It's fair to call them errors, and just like typos in
| English prose can confuse a non-native speaker, mathematical
| typos can impede meaning for a reader who isn't familiar with
| mathematics. However, with a little experience, it's not hard to
| see what the intended meaning was, and fixing it isn't too bad. A
| mathematical typo certainly doesn't constitute a flaw in the
| proof, and almost all the problems I found fall in this category.
|
| If only we had better ways to distribute fixes to papers. These
| kind of issues happen all the time and unlike in code where
| someone can just come in and provide a fix, these usually remain
| forever in papers. Yes, some publish errata or upload a new
| version to the arxiv, but the majority remain as a form of
| horrendous "exercise for the reader". If I'm an expert in a field
| I may quickly notice such issues, but more often than not I won't
| spend the time required to do so. And hence I probably propagate
| wrong information myself / wonder why my numerical calculations
| don't produce the correct result etc.
|
| It is especially bad when branching out into areas somewhat out
| of your area. The amount of mistakes and utterly wrong
| information I had to deal with just in the last few months thanks
| to papers being sloppy is just sad. So much time wasted. :( (I'm
| a physicist)
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