vitriol83

But Mochizuki didn't actually prove anything, whereas the labs have already done so.

The pessimistic scenario is the AI labs will continuously hoover up new developments in mathematics and gazump everyone in their respective fields. It's clear they have no desire to participate in any silly academic niceties, like properly assigning credit or expository work for normal humans. What incentive then do humans have to do this work ?

Generally the mood amongst research mathematicians is pretty dire, and I don't really blame them.

To be clear I think AI is super useful for mathematical research, the problem is the methods of the big labs are massively disincentivising mathematicians from engaging in research, and other associated tasks like giving seminar, teaching writing books etc. These arguably have much more value than finding an obscure counter example to Navier-Stokes.

facepalm yet pure mathematics has been instrumental in all scientific progress in modern human history including LLMs, very short sighted view

yes society has let the trillion dollar company down

i find this and other efforts from anthropic somewhat antisocial. technically they have achieved their goal, but in a way which does not benefit mathematics or humanity. Kevin Buzzards headline goal was to formalise FLT, but i’m sure the real aim was to create a formalised library of mathematics which is comprehensible to humans. By solving these famous problems by brute force, they are disincentivising the important work of making it digestible for everyone else, and so in my view this work in particular has negative societal value.

majority of parents are in favour of such a ban, otherwise they wouldn't do it

if social media companies hadn't made social media a total cesspit of disinformation, child grooming and algorithmic manipulation then the outcome might have been different

mathlib and lean are currently too cumbersome for many researchers to use in say algebraic geometry, but maybe more suitable for combinatorics where it has been applied recently.

this has templeOS vibes

Formalised proofs and Lean in particular are still too cumbersome for the ``working'' mathematician to use it day-to-day for research-level math. But clearly there is some interest on where it may take us in future.

this seems to be the way. make great technical improvement in a way that's nothing to do with AI. the only way to make executives happy is to then tenuously link it to AI usage.

In my field which involves large legacy codebases in C++ and complex numerical algorithms implemented by PhDs. LLMs have their place but improvements in productivity are not that great because current LLMs simply make too many mistakes in this context and mistakes are usually very costly.

Everyone `in the know' appreciates this, but equally in the current environment has to play along with the AI hype machine.

It is depressing, but the true value of the current wave of LLMs in coding will become more clear over time. I think it's going to take some serious advances in architecture to make the coding assistant reliable, rather than simply scaling what we have now.

are there any tools to convert large latex documents to typst ? it looks a huge improvement, but the migration path is the only thing that's stopping me.

In places where there is not much time for code refactoring, the following is helpful:

Imagine an idealised future state of the codebase, which everyone buys into, and make sure any new feature is going in that direction.

Refactoring existing code can be death by a thousand cuts- having a parallel new codebase which is incrementally adopted can be more efficient and quicker to market.

So many times it’s necessary to ‘identify’ two more objects which are isomorphic, and the ‘canonical’ is supposed to justify why this doesn’t cause a problem.

The reason it is necessary here is that the mapping D(f) -> A_f is a priori multi valued, and we need it to be single valued.

However it’s fairly easy to make a definition which is trivially single valued , so I don’t think it’s a very instructive example of the phenomenon.

Probably more pertinent is an n-fold tensor product with different bracket ordering