The reason LLMs fail at solving mathematical problems is because: 1) they are terrible at arithmetic, 2) they are terrible at algebra, but most importantly, 3) they are terrible at complex reasoning (more specifically they mix up quantifiers and don't really understand the complex logical structure of many arguments) 4) they (current LLMs) cannot backtrack when they find that what they already wrote turned out not to lead to a solution, and it is too expensive to give them the thousands of restarts they'd require to randomly guess their way through the problem if you did give them that facility

Solving grade-school problems might mean progress in 1 and 2, but that is not at all impressive, as there are perfectly good tools out there that solve those problems just fine, and old-style AI researchers have built perfectly good tools for 3. The hard problem to solve is problem 4, and this is something you teach people how to do at a university level.

(I should add that another important problem is what is known as premise selection. I didn't list that because LLMs have actually been shown to manage this ok in about 70% of theorems, which basically matches records set by other machine learning techniques.)

(Real mathematical research also involves what is known as lemma conjecturing. I have never once observed an LLM do it, and I suspect they cannot do so. Basically the parameter set of the LLM dedicated to mathematical reasoning is either large enough to model the entire solution from end to end, or the LLM is likely to completely fail to solve the problem.)

I personally think this entire article is likely complete bunk.

Edit: after reading replies I realise I should have pointed out that humans do not simply backtrack. They learn from failed attempts in ways that LLMs do not seem to. The material they are trained on surely contributes to this problem.

To take Iran as an example: when US sanctions prevent Boeing or Airbus from selling to them, I can understand why Embraer doesn't step in and offer to supply planes, because they are afraid of secondary sanctions affecting their business with the rest of the world.

But tech isn't like aircraft production — building a GitHub, Okta or Auth0 clone is a chunk of work but hardly infeasible — hell, most companies routinely built a partial Auth0 clone in-house until not that long ago. Many still do.

So why don't we see alternatives pop up that don't block Iran? It's a niche, but you get the whole niche to yourself, and Iran is not a small market.

From a legal perspective you would set up somewhere like UAE where they have a good climate for business but regularly do business with Iran, so that part shouldn't be an issue.

Network effects are a factor, but when you're blocked from the popular platform, you have a bigger incentive than usual to consider the less-popular one.

This is being said a lot these days, but I haven't seen any proof of it. I'm not saying that proofs don't exist nor that it's wrong, just that I've been reading it everywhere, and haven't seen evidence. So I'd be happy if someone reading this could point out to some clues