[tsunamifury]

Real talk.

AI solving these makes me feel like mathematicians put far more importance on their work than was actually there. Many solutions seems to be tautological games, and games of logic where conjecture puzzles that few work on or care can be solved by AI which doesn’t care what it works on.

It seems to always be some form of this:

Mathematician: “Propose conjecture a and conjecture b can’t be true simultaneously”

AI: “they can”

Everyone: “ok…”

I know this might be unfair or out of ignorance but it genuinely is how this field feels today. Games of games with self importance added in.

Edit: the point I should have made is, should we be using AI to figure out what proofs MATTER now vs games of proofs?

[efficax]

"tautological games".

All proofs are a form of tautology, you have to end up back at the point your theorem proposed. Math is games of logic. That's what it is.

[wongarsu]

Academic math is a bit like basic research. You come up with funny ways to look at numbers or prove weird statements about this thing you came up with and call a "group", and a couple years or decades or centuries later it turns out that this solves real problems in electrical engineering or biology

Or it ends up never becoming useful. But you can't know that in advance

[tsunamifury]

Disagree, basic research, no matter how dull, is an observation of a measured reality. Math Theory are patterns of abstraction that may never be useful at all or representative of reality.

[lioeters]

> may never be useful at all

Nobody is qualified to judge the usefulness of mathematical, scientific, artistic, or any other kind of research that people choose to dedicate their time doing. And the world is better for it.

> or representative of reality

This so-called "reality" you speak of is some arbitrary representation in your head. It's your theory and patterns of abstraction, as you call it. Who knows how far or close you are to "objective" reality, whose existence we can only know through representations and abstractions. Mathematics and logic are some of the best tools we have of getting closer to that truth and understanding. All the sciences and even some of the arts are based on it.

[tsunamifury]

This is nonsense. Its the shared based case we can all test against, the things you think are the abstraction.

So wildly goofy train of thought here.

[card_zero]

I agree that rigorous logic shouldn't be assumed to get us closer to Ultimate Objective Truth than other forms of reasoning. It just gets us whatever peculiar oddments we can discover through rigorous logic, so far, here in our local, parochial patch of reality. Things that seem crucial powerful theories (theorems, whatever) to us here and now may not seem that way in the future, and arriving at them through logic doesn't provide a royal road to the Ultimate.

This means abstract mathematics is rooted in our current cultural concerns. I guess I'm saying that it isn't really useful or really abstract, but I also agree with the other poster that people can and should do what they like.

[fn-mote]

Parent seems to conflate “abstract” with “useless”. This comment addresses the “abstract” part only.

> Math Theory are patterns of abstraction that may never be useful at all or representative of reality.

This is a complete misunderstanding of (good) mathematical research.

The results look abstract, but they are based on concepts that are real and have truth or falsehood.

One example that comes to mind (sorry, technical): is it possible that all maps from a high dimensional sphere to a three dimensional sphere (S^2) might form a group that is not even finitely generated?

This is not just “abstract nonsense”, but understanding any of this takes effort.

[tsunamifury]

Abstraction is useless until its proves use in test against a base case of reality.

its the defition of useless most of the time.

[lyu07282]

“May never be useful“? You make it sound as if there aren't countless examples of those "abstractions" of theory/pure math turning out to be useful in all kinds of fields in the past. This feels like the more general anti-science argument of 90% of science is useless and never produces practical applications, the point people never understand is that nobody knows which 10% it's going to be so you have to do the 100% to get to the 10%.

[dwaltrip]

Look up how pure mathematics connects back to reality in countless unexpected and useful ways, time and time again.

[throw-the-towel]

To borrow a common wisdom about marketing, half of all mathematics is a waste of time, but you can't know which half.

[tsunamifury]

But the issues is you have the ratios wrong. 99% of math theory is useless and maybe 1% has value.

[throw-the-towel]

Maybe so! My point was not about the exact percentages, just the fact that you can't predict which avenues of research will yield practical results.

[jstanley]

We call a proof that is not tautological "wrong".

[chermi]

Very useful games, self-importance or no.

See pattern, conjecture generalization, test generalization. It's almost like empirical math. I like it and I also like mathematicians doing it the old way.

[tsunamifury]

I feel like you should search through the thousands of papers that are generated nonsense math theory and laugh at how you cherry picked 3 things.

[deeznuttynutz]

Don't do that...