Suppose you are a maths researcher and you come across a problem, ... most likely, you will feed it to an AI. There are two possibilities: either the AI solves the problem or it does not.
If it solves the problem, you can ask the AI to explain it you. But if it does not solve it, will you really wager 30 years of your life on the possibility that you might be smarter than the AI?
I keep hearing about people spending their entire career on a single problem. And I think that time has ended. I think in Mathematics will be like chess.
> But if it does not solve it, will you really wager 30 years of your life on the possibility that you might be smarter than the AI?
The "AI" is trained on centuries of human theoretical frameworks and innovations. The "AI" can also work on problems full-time without teaching, admin, or mentoring duties. OpenAI spent millions to race human researchers on Navier Stokes, and that doesn't account for any training costs. How many person-years would that pay for? Since the key ideas were developed by humans just a few years prior, it's not unreasonable to surmise that a comparable level of total effort by humans would also have decent chances of breakthrough, with the additional benefit that the insights uncovered along the way would be immediately digestible and easy to communicate to other mathematicians.
Do you think more people than ever will start doing math, with millions of people solving daily math puzzles on their phone on math.com[1] while commuting ?
I dont get this. What is the difference if you replace "AI" by "Tao"? And people still were doing math.
I get HN is a Software site. But all math posts are invaded by people that think Math=Software. Probably based on the way they were taught maths when they were young.
Why would a theoretical physicist spend 30 years developing a theory that could be made false by a new experiment with a new technology? Was Newton gravitation worth if einstein was going to come later?
We are heading directly into a world where people forget about what values, philosophy, poetry, math, physics, or any other "non economically valuable" things are. And we all know what happened any other times in history when that happened.
Thanks for telling it better than I could have! But if you could expand on your last sentence, what instances in history are you referring to? Dot com boom? Great depression?
I was thinking more about dictatorships that block the entry of outside knowledge into the population for example, because its not useful to their goals (which is a particular shape of what economic value is for them). But you dont have to go that far away, you can just see the difference between democratic cultures that value at different levels those fields. In the end "economic value" is less objective than what it seams.
Math research isn't all or nothing on a single problem. Rather, the problem would serve as inspiration to explore achievable subproblems, weaker problems, related topics, etc. These would be interesting papers by themselves, but if lucky may also lead to progress on the main problem. So this leaves lots of room for using AI as an assistant.
> If it solves the problem, you can ask the AI to explain it you.
Will I get an understandable and verifiable explanation? And, if the system cannot solve the problem, will I get an understandable and verifiable explanation of that? As a researcher I'd think that shared understanding is the point.
> But if it does not solve it, will you really wager 30 years of your life on the possibility that you might be smarter than the AI?
Right now it’s not a terrible bet. If the OpenAI results from the past week are representative then the AI success rate for verified proofs on open math problems is somewhere below 10%. There’s a long way to go before you can assume an AI failure to solve means the problem is unsolvable.
> I keep hearing about people spending their entire career on a single problem. And I think that time has ended. I think in Mathematics will be like chess.
Is the Langlands Program a single problem? Much of it is still ill-defined. How will AI win at newfangled chess when they haven’t got the rules yet?
i cant be more against that idea, AI is a copy machine, it knows what we feed it to it, it can draw conclussions of course that may be apparently new information but it is not, it is merely connecting dots. math researchers, as well as any other high level professional will be doing much more than that, thats why AI is a tool, it can not, by definition, create new things
I suspect most of these projects are started by people who get Claude Code at work, and just want to make sure that they spend all of their tokens before the weekly reset. In that case, cost is not relevant.
The project the blog post is attacking is Artcraft, spearheaded by HN's most vocal AI evangelist zealot. He's stated that he's financing the thing with the revenue from his $3, no $4, no $5M/year AI image generator.
Which is why the salient part of the post is "Unless your intention is just to generate headlines and promote an AI business." Because that's exactly what this is. A cynical scheme to draw attention to his commercial services.
To ask that question suggests you are unfamiliar with the difference between arithmetic (which computers are good at) and pure mathematics (which is like metaprogramming combined with formal methods, and Gödel's incompleteness theorem is worse than the Halting problem)?
Simply put: For the same reason computers have not already solved all problems in mathematics.
More concretely:
Consider the Collatz conjecture. It's a very simple rule to write down:
Take some positive integer: If the number is even, divide it by two; otherwise triple it and add one. With enough repetition, do all positive integers converge to 1?
Trivial to write a program to test numbers starting at 1 and going up. We know it holds up to at least 2.36e21 (according to Wikipedia), but to prove it is true with such a program requires testing all of the infinite set of positive integers.
But you may notice some things about the rules, that they suggest a subset of numbers will trivially always converge to 1, so that you don't need to even test them: any integer 2^n where n is also a positive integer.
You may find other easy wins, or ways to simplify the test, e.g. once you know the numbers up to m will converge to 1, you can terminate your loop early if you test m+1 and it ever has an intermediate value less than or equal to m. You can combine that with applying one of the rules in reverse, and know that all even numbers between m and 2m will on their first move be halved, making them smaller than m, which means you know they'll eventually converge.
But actually proving this is fully general? Nobody knows. You can't just throw arithmetic at the problem directly, you have to figure out patterns that would let you prove that it always holds, no matter what.
Or, you may find many such patterns and directly calculate some number not in any of them, to find one which doesn't converge to 1.
depending on which model one is using, and the error the employee needs to be retrained on, i strongly disagree that you can retrain an llm as easily as you can a person.
particularly most of the commercial models.
again, i’m sure we can all come up with a thousand “hypotheticals”, and tbh, the hypothetical parade is not something i’m interested in having. but i’ll state again, “entirely removing humans” from the situation is silly-tier thinking.
particularly as even the ceos of sota frontier producing models will each and every single one tell you to never trust their model.
“our model is smartest thing in the world…”
…next breath..
“wait, you trusted our model? that was silly of you. always double check it”
If I instruct an employee to prioritize my profit in a way that opens both of us to criminal prosecution, there is a non zero chance of them whistle blowing or even cooperating with the authorities to prosecute me.
> The term is a compound word joining goy, a Hebrew and Yiddish word for a non-Jew or gentile,[4][3] and slop, meaning food waste or refuse of low quality
So you're telling me that a word which has "slop" in its origins is itself the origin of "slop"?
This must be the first case of circular etymology!
There are a couple of other cases. Dog was once (1845, UK) slang for sausage, due to fears of dog meat. Then a hot sausage was a hot dog, and then hot dog was a sausage, and finally just dog was slang for a sausage again, with the sinister implication removed. I also found pepper, from Latin (from Sanskrit?), leading to pep, the thing a pepper does to you, leading back to pepper (a kind of pre-game warm-up in baseball designed to give players pep).
You might object that those are really back-and-forth, but so is the claim being made here about slop. (I kind of doubt the claim though.)
I don't think your examples apply though. The dog example is just dog meaning sausage, sometimes with a temperature quality added (or ignored), but always a sausage with no other connotations.
The pepper one, maybe a little, though according to Etymonline [0] pep is short for pepper, so it's all the same really.
That’s a different word. And it’s a word that came long after “slop.” It only makes sense if you know what “slop” means. I don’t actually understand why you’re linking me to this.
Google drive, icloud drive, anything drive is also file/folders based. Someone that doesn't know about that is a modern-day illiterate. Yeah, I know, there are many of them nowadays.
Are they actually? Google Drive has folders, but there's no concept of things like "which folder is this file in", you can have access to many root folders but not a list of them all, and the most convenient way to find anything is to search.
I don't understand this comment. We use AI for prototyping all the time. We write ERP software. Client wants to know how process XYZ could be automated? Send them a prototype UI (sans the three A's) so they can play around with it. Takes 30 minutes.
If it wanted to: total war using nukes, followed by a nuclear winter. Satellites and drones track and exterminate remaining pockets of anthropic activity.
It doesn't need to have a habitable earth, it just needs atoms.
If it solves the problem, you can ask the AI to explain it you. But if it does not solve it, will you really wager 30 years of your life on the possibility that you might be smarter than the AI?
I keep hearing about people spending their entire career on a single problem. And I think that time has ended. I think in Mathematics will be like chess.
reply