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…
facepalm yet pure mathematics has been instrumental in all scientific progress in modern human history including LLMs, very short sighted view
You're stating it's not a problem- but I'm giving you a reason why it is. This is serendipitously mirrored by a recent post from Terence Tao on Mastodon (https://mathstodon.xyz/@tao/117207856734787448) In most cases in…
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…
the Ramanujan one has some relatively high powered mathematical explanation https://en.wikipedia.org/wiki/Heegner_number
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…
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…
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…
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) ->…
This is fairly obscure but the problem he highlights can be overcome easily by localising at the saturation of S_f, for D(f)=D(g) if and only if the saturations are equal, and localising at saturation is an isomorphism
Stacks, like EGA before it, is a wonderful reference but a terrible textbook. I think even the authors would agree with this! Fortunately there are many other books from which to learn algebraic geometry, after which…
Modern Algebraic Geometry is indeed highly abstract, but generally the conjuring of obscure objects is with a specific goal in mind, for example - consolidation of many types of results into a `simple' theoretical…
They’re all very relevant, but I try not to expect the same from OSS projects as from a VC pitch deck. After all this is work given freely.
That’s rather solipsistic
I’m generally positive on rewriting openssl in rust, but agree the comparisons aren’t completely scientific or necessarily more important than correctness. First you should compare performance using the same…
one issue with OOP in practice that I've seen is the entanglement of the domain representation (member variables of a class) and the varied operations on that data (methods). Classic OOP encourages you to manipulate…
The difficulty with learning 'modern' algebraic geometry is not only is it very dense and general, but that means the original motivation can become lost. So I think understanding Weil conjectures are key for modern…
Writing a type checker is conceptually much more specialised than just a scripting language. Certainly I have no idea how to write one!
Can anyone suggest a good embedded language with static or at least optional typing ? I feel this is a gap in the market for embedded languages.
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…
facepalm yet pure mathematics has been instrumental in all scientific progress in modern human history including LLMs, very short sighted view
You're stating it's not a problem- but I'm giving you a reason why it is. This is serendipitously mirrored by a recent post from Terence Tao on Mastodon (https://mathstodon.xyz/@tao/117207856734787448) In most cases in…
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…
the Ramanujan one has some relatively high powered mathematical explanation https://en.wikipedia.org/wiki/Heegner_number
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…
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…
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…
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) ->…
This is fairly obscure but the problem he highlights can be overcome easily by localising at the saturation of S_f, for D(f)=D(g) if and only if the saturations are equal, and localising at saturation is an isomorphism
Stacks, like EGA before it, is a wonderful reference but a terrible textbook. I think even the authors would agree with this! Fortunately there are many other books from which to learn algebraic geometry, after which…
Modern Algebraic Geometry is indeed highly abstract, but generally the conjuring of obscure objects is with a specific goal in mind, for example - consolidation of many types of results into a `simple' theoretical…
They’re all very relevant, but I try not to expect the same from OSS projects as from a VC pitch deck. After all this is work given freely.
That’s rather solipsistic
I’m generally positive on rewriting openssl in rust, but agree the comparisons aren’t completely scientific or necessarily more important than correctness. First you should compare performance using the same…
one issue with OOP in practice that I've seen is the entanglement of the domain representation (member variables of a class) and the varied operations on that data (methods). Classic OOP encourages you to manipulate…
The difficulty with learning 'modern' algebraic geometry is not only is it very dense and general, but that means the original motivation can become lost. So I think understanding Weil conjectures are key for modern…
Writing a type checker is conceptually much more specialised than just a scripting language. Certainly I have no idea how to write one!
Can anyone suggest a good embedded language with static or at least optional typing ? I feel this is a gap in the market for embedded languages.