I am not sure of the premise. You can have a filter which takes garbage in and outputs the clean data from the garbage, a denoiser. Also your definition of slop is not specific to slop. Any input can be garbage, including this human sourced and thought comment.
One thing about human mathematicians is that they only publish positive results. Professors etc might have file drawers full of "negative results", but the incentives and bandwidth of human mathematicians makes publishing these useful results impossible.
In general though, LLMs do not have the same limitations and incentives as human mathematicians, and the next year's tsunami of change will make this abundantly. clear.
What is a "negative result" in maths? "I tried something and it didn't work" isn't really a result. It's experience maybe. But it's not like science where finding only evidence for the null hypothesis is considered boring. Even unsurprising results are published and even celebrated in mathematics, like Fermat's last theorem.
it might be something explaining that a certain path towards a solution didn't work or provide anything useful. the result itself might not be useful but it could prevent future mathmaticians from going down the same road and wasting effort.
The bandwidth is absolutely there ("we tried this and it didn't work" is totally the stuff of conference discussions).
The incentives are not.
The incentives are skewed towards "a magician never reveals her secrets". The results are presented as if a rabbit got pulled out of a hat, with a maximum ta-da! effect, and little backstory of how the hell did we get there.
Don't get me wrong, these things are discussed, often over beers (you better drink it you want to make a career in the field).
But not published.
The younger mathematicians are trying to change that with the blogging culture. But the professional incentives aren't there. (In corp-speak: can't put blogging on perf). They burn out.
That's why math blogs usually come from either the top dogs in the field, like Terrence Tao, who don't need to care about perf, or people outside academia.
That's one thing that I hope the disruptive/destructive effects of LLMs will force mathematicians to face.
As one of my fellow mathematicians sarcastically wrote¹, we've reached a point where we should become a cult because we're acting like one anyway.
The other possibility is, of course, that the shake-up will take us precisely into that direction.
My point here is that the real problem here is not mathematical; it's a social one: incentives and politics, organizational structures, policies, allocation of jobs and funding.
All of this directly impacts how we do mathematics, who we do it with and teach it to, how we teach and communicate, and, of course, what math we even do and look at.
Given that, I'm neither too worried about humans vs. AI standoff, nor hyped about the Glorious New Future full of AI-assisted discoveries.
AI or not, the organizational issues in the field are still there, as are the incentive structures (including the infamous publish-or-perish).
We are doomed, yes, but by our own hands and committees. And it's up to us, not the AI, to get us out of there.
The little shove from the AI might be just the thing we need.
This is not specific to math. To non-academics, you basically have to rewrite your commit history to make it seem more impressive. You often write the motivation section last. At least math publication culture allows saying "We consider the problem of" and then solve it. In AI/ML academic papers you need much more "story" around why, what the applications are, why aren't you doing something else, defend against lack-of-novelty attacks, defend against "this is just A + B known techniques used together" etc.
Because your institution's PR department and the journal you're publishing in want the publicity of "scientist cures cancer". And you probably wrote "I'm curing cancer" in your grant application, team charter, or whatnot.
I think its a total travesty of our society that people are desired to identify both the problem and the solution
people without solutions are told not to point out the problem
and people with the skillset to bring solutions dont have the skillset to search for problems or apply their seemingly unrelated disciplines to it
so you get a lot of capital and energy thrown at people who purport to be both
If AI can address this too, that would be profoundly impactful. The cross disciplinary work that a single college course is supposed to reveal, finally realized
Yeah, LLMs are great at generating negative results for math-related prompts "We scanned values {a,b,c} from 0-100 and no results" Great..too bad journals will not publish this. But good job, I guess. A negative result is only truly useful if it can be bounded, requiring an actual proof.
> A negative result is only truly useful if it can be bounded, requiring an actual proof.
That's at least true for current journals, since they're supposed to be read by actual humans. I suppose one could imagine a sort of "AI" pure data journal that just "publishes" (in actuality aggregates) any sort of partial result. This body of knowledge would be entirely useless to humans, but could serve as a sort of "computation cache" for these stochastic systems.
A great scientist once said, that the scientific method also includes stating, why what one "found out" could be wrong, and that one might need to retry experiments, whose results one relies upon. I think it was in "Cargo Cult Science" by Feynman.
In a way what they are doing, only publishing positive results is no longer good science.
(Project creator here): Someone actually posted the site without me- I wasn’t planning on launching for a few weeks! If you see any issues, feel free to report them and i’ll get on fixing them right away!
Im taking a lot of inspiration from MathOverflow, where I’ve been a user for several years. I think there is a protocol approach to this project that can be built, but it’s not what I’m building. I’m optimizing more for building in community features, since that is the genre of site I have enjoyed using in the past.
Project creator here- I really did not expect it to get posted on hackernews! A nice surprise for sure though.
Seems like someone found the site and posted without me.
I am still working on the site and was planning on launching in a few weeks. There are some usability issues and some
features on my roadmap I haven’t gotten to yet.
That said- if folks are interested in helping contributing new problems/proofs, hunting bugs, or giving suggestions, we have a discord https://discord.gg/ds23BgPq6
Gist: the seed for the curve has unknown origin. Possible attack: let's say there is an attack possible on 1/10^6 curves. Just loop through a million curves until you find one vulnerable, and publish it into the standard.
When I tried to read Crime and Punishment, I got confused by all the characters. When I tried to look things up online, I got spoilers!
So I created an illustrated reader (using Claude Fable) which updates as you read, so that there are no spoilers buy you can follow along with the story.
I built a small, free site for reading public-domain books (magicbookshelf.org). Today, it has three books:
1. The Brothers Karamazov
2. Crime and Punishment
3. Pride and Prejudice
You don't have to make an account and there are no ads. I just think the classics deserve a nicer home than a wall of plain text.
When I first tried reading Karamazov, it was really difficult for me to keep up with everything.
Karamazov is the book where everyone gets lost in the names. Alexey / Alyosha / Alyoshka, Dmitri / Mitya, Fyodor Pavlovitch, Smerdyakov, two different Ivanovnas. The usual fix is to keep a wiki or a character list open, but those spoil everything that happens later.
So the reader comes with a companion I call the Margin: a guide to the people, places, and ideas in each book that only ever shows what you'd know at your current point.
For example.. Alyosha's entry while you're in chapter 3 and you get who he is by chapter 3, with nothing about his later arc.
A few notes:
The translation is Constance Garnett
There's optional narration if you'd rather listen.
I make and run it on my own, so if you spot a wrong note in the Margin, a typo, or an entry that gives away too much too early, please tell me.
Beyond the sensationalization here’s what Terry had to say -“ In any case, I would indeed say that this is a situation in which the AI-generated paper inadvertently highlighted a tighter connection between two areas of mathematics (in this case, the anatomy of integers and the theory of Markov processes) than had previously been made explicit in the literature (though there were hints and precursors scattered therein which one can see in retrospect). That would be a meaningful contribution to the anatomy of integers that goes well beyond the solution of this particular Erdos problem.”
