The thing about these math proofs is that they really add nothing of value. Its a cool tech demonstration on how LLMS can search the trained space, but fundamentally, LLMS haven't "discovered" anything groundbreaking.
For NS equations, they are trying to model something that is discrete (i.e molecules colliding) in a continuous manner. You can easily think of a condition where they fail - imagine a vaccum where there is sufficient space between air molecules, so that collisions aren't always possible. NS won't be able to predict the state of the fluid in every single point in space.
In practice, when you do CFD, no package uses direct differential simulation of NS equations, you usually have simpler approximations that are good enough for the space you are working for. And if you want accuracy, you usually do something like LBM which simulates particle collisions using probability distributions.
I can't wait to tell my pure maths professors that their most of their research adds nothing of value. I mean I am sure most of them would agree to some extent, but like, dude, have some more faith in the utility of pure maths, esp. centuries down the line
I do wonder if perhaps LLMs take credit from some mathematicians working in obscurity in some dark corner of the web, it’s not unheard of for some to be reclusive. Perhaps someone completely unaware that they might have sovled something someone else considers important.
Discussions:
https://news.ycombinator.com/item?id=49613262
https://news.ycombinator.com/item?id=49605915
https://www.youtube.com/watch?v=GddkKIhDE2c
Enumeration of syntax patterns when rules restrict legal syntax patterns can be done without LLMs
The data center cartel that sprang up over the last 20 years is desperate to not have their entire social moat go up in smoke
https://archive.is/vlSuj
The thing about these math proofs is that they really add nothing of value. Its a cool tech demonstration on how LLMS can search the trained space, but fundamentally, LLMS haven't "discovered" anything groundbreaking.
For NS equations, they are trying to model something that is discrete (i.e molecules colliding) in a continuous manner. You can easily think of a condition where they fail - imagine a vaccum where there is sufficient space between air molecules, so that collisions aren't always possible. NS won't be able to predict the state of the fluid in every single point in space.
In practice, when you do CFD, no package uses direct differential simulation of NS equations, you usually have simpler approximations that are good enough for the space you are working for. And if you want accuracy, you usually do something like LBM which simulates particle collisions using probability distributions.
I can't wait to tell my pure maths professors that their most of their research adds nothing of value. I mean I am sure most of them would agree to some extent, but like, dude, have some more faith in the utility of pure maths, esp. centuries down the line
There is value in knowing (as opposed to hypothesizing) whether some interesting claim is true or false.
Actually, just knowing that a claim is true may motivate people to search simpler proofs, as it happened in mathematics in the past.
I do wonder if perhaps LLMs take credit from some mathematicians working in obscurity in some dark corner of the web, it’s not unheard of for some to be reclusive. Perhaps someone completely unaware that they might have sovled something someone else considers important.