Instead of imitating human mathematicians and presenting long series of definitions and theorems, I think AI should do as 3blue1brown says – “If you encounter a mathematician at a conference, and ask them how their proof works, then they will almost always give you a clearer insight than what’s in the paper”
That is, the papers are written “backwards” from definitions. But the real explanation is how you got there. What thing tipped you off that a certain definition or theorem would be useful in solving the problem, the angle of attack
In other words, we should use AI to do better than the state of the art in as many dimensions as we can, not just perpetuate the same habits
Anthropic’s repository contains a one-paragraph hint about the construction that is allegedly enough for Claude Opus 5.5 high to disprove ETH, I am not fluent in the terminology but it does have the shape of explaining the core idea well to a specialist! So maybe they are doing a step in the right direction there.
“If you encounter a mathematician at a conference, and ask them how their proof works, then they will almost always give you a clearer insight than what’s in the paper”
Adding to this, the valuable insight – the thing you can actually use in thinking – is the compressed form of the knowledge. You’re more likely to get that in a short in-person conversation. The author’s hand is almost forced. “Ah, yes, I basically just realized I could transform the problem using X, and then theorem Y would apply, and I could convert back and conclude Z” or whatever the case may be. The essence of an insight must end up being short like that, because we can’t “think” on the scale of 20 dense pages of equations. The elaboration is an expansion of the insight, rather than the other way around.
You can in fact take the paper and have a great conversation with the AI or have it create your own visualizations and explanations. Particularly with Opus 5.5 it’s a great experience.
Sure, I do that for learning things in my own domain, for things I want to build
But for a general reader, it’s more efficient and interesting for a few people to produce explanations at different levels, rather than having everyone burn approximately the same tokens with AI
In other words, what people are saying is that now that proofs themselves are more plentiful, explaining proofs becomes relatively more important. So my suggestion is around the “explain” part :-)
I don’t think the paper itself is useful for a lobste.rs audience, other than the meta-knowledge that an AI produced it, trained on some unknown data, with some unknown humans prompting it
Instead of imitating human mathematicians and presenting long series of definitions and theorems, I think AI should do as 3blue1brown says – “If you encounter a mathematician at a conference, and ask them how their proof works, then they will almost always give you a clearer insight than what’s in the paper”
That is, the papers are written “backwards” from definitions. But the real explanation is how you got there. What thing tipped you off that a certain definition or theorem would be useful in solving the problem, the angle of attack
In other words, we should use AI to do better than the state of the art in as many dimensions as we can, not just perpetuate the same habits
score 4 · canonical
Anthropic’s repository contains a one-paragraph hint about the construction that is allegedly enough for Claude Opus 5.5 high to disprove ETH, I am not fluent in the terminology but it does have the shape of explaining the core idea well to a specialist! So maybe they are doing a step in the right direction there.
score 1 · canonical
Adding to this, the valuable insight – the thing you can actually use in thinking – is the compressed form of the knowledge. You’re more likely to get that in a short in-person conversation. The author’s hand is almost forced. “Ah, yes, I basically just realized I could transform the problem using X, and then theorem Y would apply, and I could convert back and conclude Z” or whatever the case may be. The essence of an insight must end up being short like that, because we can’t “think” on the scale of 20 dense pages of equations. The elaboration is an expansion of the insight, rather than the other way around.
score 1 · canonical
You can in fact take the paper and have a great conversation with the AI or have it create your own visualizations and explanations. Particularly with Opus 5.5 it’s a great experience.
score 1 · canonical
Sure, I do that for learning things in my own domain, for things I want to build
But for a general reader, it’s more efficient and interesting for a few people to produce explanations at different levels, rather than having everyone burn approximately the same tokens with AI
In other words, what people are saying is that now that proofs themselves are more plentiful, explaining proofs becomes relatively more important. So my suggestion is around the “explain” part :-)
I don’t think the paper itself is useful for a lobste.rs audience, other than the meta-knowledge that an AI produced it, trained on some unknown data, with some unknown humans prompting it
score 1 · canonical