Controversy over OpenAI's Maths Breakthrough
scientificamerican.com
scientificamerican.com
> Leven and Tristan worked over several months on one of the Millenium Prize Problems with various AIs to reach final interesting results. OpenAI apparently heard about it in the last days and prompted their latest models to work on the direction Leven and Tristan found fruitful. They then tried to push for controlling communication of the result and dropping Leven from authorship with some very bad taste social pressure.
(1) https://x.com/Thom_Wolf/status/2097215782484607029
(2) https://mastodon.social/@tristanbuckmaster/11723341370570119...
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
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.
Same with NS equations. Who cares if you can find a singularity.
And if you want an example of something novel that is worth pursuing - Its highly likely that the modern transformer architecture is sub optimal, you probably don't need to do full matrix multiplies in the transformers. There potentially could be a higher level mathematical formulation of minimal math operations that are needed without having to do trial and error - especially because all of the math involves linear combination passed through smooth activation functions.
But coincidentally, there hasn't been any research in terms of point LLMS to self optimize in this way, because there isn't enough human math literature on the LLMs to train on.
like say if god lets me find a single counter example to P=NP and thus disproving it — I think we can learn tons about complexity theory from this counter example by studying it. we should not have the hubris of assuming “oh a single counterexample is generally useless” — why, how. this is the same hubris imo that produced like “number theory is useless” until it is not
P vs NP is a more fundamental problem that if proven, will have insane consequences, perhaps more than anything else out there. For starters, you would be insantly able to design an an actuall all knowing AGI.
The NS equations are far,far,far less meaningful. Like I mentioned earlier, if you actually want accurate CFD, you dont even use them.
> The NS equations are far,far,far less meaningful. Like I mentioned earlier, if you actually want accurate CFD, you dont even use them.
Sure. Consider this: in algorithm research often the most optimal algorithm in big-O is not the one used IRL; examples are numerous: matrix multiplication, LCA data structures, many variants of shortest paths.
An academic can work two years on faster-in-theory matrix multiplication that no one expects to be used in practice (in our currently imaginable univese). Do you consider that less meaningful than working on faster matmul kernels?
On the flip side if P=NP, that means that instead of dedicating compute to running branching simulations, An AGI can dedicate compute to just solving directly the actions it needs to do for any given outcome. This is a shortcut to reality, which means that reality in itself is compressible.