Kotlopou

I'm thinking of somebody like Grant Sanderson (3blue1brown), doing pure exposition extremely well. For that you at least need to be able to work through examples, or to present why an intuitive approach might fail, and these things can be little theorems themselves. It doesn't have to be publishable in the current culture of novel results, but you do need a lot of competence with the tools.

Yes, there was controversy around the Navier-Stokes result. But here are >300 problems and no corresponding >300 complaints of theft. Things are indeed moving really fast, and it's hard to keep up even as someone folrowing this with more obsession than would be healthy. Maybe somebody should keep a running short summary of The Situation...

(also answered similarly to another comment; this is a common question)

There are suddenly many new solutions to problems that have resisted sustained attacks (e.g. the Uniform Games Conjecture as detailed in TFA at some length). Where do you think they are coming from? Why is there suddenly a bunch of results to be stolen?

But if you think they got them illegitimately, then how did they get them? And why are mathematicians reacting to this as a sudden explosion of new results that have resisted sustained effort? Where is the sudden productivity rise coming from?

I studied physics, and most of my classmates did not end up doing anything with physics. Many are in finance or insurance or programming positions. In general, studying anything challenging (from theatre to theoretical computer science) gives some specific skills and some general abilities that etsure it isn't a complete waste even if you end up doing something different.

(That said, this is not fun, and I sympathise! I'm still a student and would like to avoid finance if at all possible. Just suggesting not to drop everything if you feel like you're learning in the process.)

(I'm now personally in the position of having to choose a PhD project, and this rapid change is interacting with making long-term plans really badly. Guidance welcome!)

In that case, one would expect to see some progress in this direction, but AFAICT that hasn't shown up yet? If anything, it's getting worse, though that could just be the increasing scale and decreasing cleanup efforts.

Already the unit distance proof was substantially human-edited (per Thomas Bloom). Then with the ten problems from Astra you started getting the citation issues. Then Navier-Stokes was a rushed 160 pages with barely any citations, and some of the related papers were called (by their "authors") the ugliest mess they've ever seen.

And now here we are. At least it seems that mathematical ability and communication with a mathematical audience are independent skills, and progress in the first does not imply the second.

This doesn't surprise me much, given two analogies: 1) many smart people are nonetheless horrible lecturers. (You can't quite get the opposite extreme, since to explain math well you have to be able to do it.) 2) AI writing in general hasn't improved. The models have annoying verbal tics ("honestly") and have no sense of which part of what they say is obvious and which is relevant.

What I meant is e.g. the unit distance construction, which (per mathematicial comments) needed a combination of distant fields, so nobody had the necessary expertise. That's different from working within one obscure field.

Sure, all of this might end up being very unpleasant, and I'm glad not to be a mathematician right now. But that's still better than a future where there aren't even any questions left that we can understand and an AI can't solve.

Also, it still seems that AI has a much different style from humans, with more brute force and using obscure literature results, and the future might still end up human/AI complementary. We aren't in an AlphaZero situation where the AI learns everything through self-play. (Yet? But we don't even seem to be moving that way much? Can anybody qualified help out?) Things are just moving really fast now and it's hard to process everything.

I would like to know how much of the progress comes from effectively combining existing research programs plus massive persistence, and how much is AlphaZero-esque RLVR completely independent of training data. Since I cannot get anybody to care about this question (even though I think it's vital for guessing what the future trajectory will look like -- are we going to complete existing research programs or start new ones?), I live in ignorance and wait for the day when the answer becomes clear.

In looking at this over the past hour, I haven't seen clear evidence one way or the other. Some of the stuff is highly unexpected (like the multiplication algorithm), but counterexample-y, and about the rest the professional mathematicians online seem to have a consensus that it's not "breaking through fundamental obstacles". I suspect neither of us is competent to judge that.

I love this, entirely separate from any applications or even understanding. It's incredible that we needed this trillion-dollar technology to learn about a faster way to multiply two numbers!

Math is incredibly rich, and even the simplest things have insanely complicated structure when you zoom in. However this all ends up, math is bigger than LLMs, and the people who claim it is getting "solved" and we are running out of open problems haven't stared into the abyss enough.

Not Nobel laureates, but people have tried this. I once was looking for the early education of famous scientists and found the book Cradles of Eminence [1], which compares the childhoods of several hundred famous people.

One thing I noticed was that more than a few were seriously sick in childhood and had to be homeschooled. This includes Edward Morley, Peter Higgs, René Descartes (though I'm not sure how rare it was at his time), and the mathematician Julia Robinson, who was bedridden with scarlet fever at 9 years old, then had to get tutoring to catch back up, and had this to say about it [2]:

> I have since read that a solitary childhood or, what amounts to the same thing, a period of isolation resulting from an illness is frequently noted in the early lives of scientists. I am not sure what the significance of this finding is. Obviously I had to amuse myself for long periods of time, but I didn’t do so with mathematics. I am inclined to think that what I learned during that year in bed was patience.

> By the time I was well enough to go back to school, I had missed more than two years. My parents arranged to have me tutored by a retired elementary school teacher. In one year, working three mornings a week, she and I went through the state syllabuses for the fifth, sixth, seventh, and eighth grades. It makes me wonder how much time must be wasted in classrooms.

Sidenote: I found the book [1] through asking a free LLM what source this quote might be referring to. They are reasonably good at this kind of literature search, especially because it's easy to judge whether they gave you something useful.

[1] https://archive.org/details/cradlesofeminenc0000goer_l9f8/pa...

[2] https://web.archive.org/web/20181207045746/https://www.maa.o...

:D Oops! Time to log off...

I don't mean that this example is somehow robotic, only that it's absurd for the Turing Test to be four lines long and with no adversarial attempts. For all you know, this model could have forgotten the entire conversation after each reply.

Conversations with strangers can be hard to get going, but they aren't this bad.

Read the linked [0] paper! The detection rate for ELIZA was far below 100%.

AFAIK people refer to this paper [0]. I think it only proves very little, because a typical conversation they studied looks like this:

Q: do you like doing psych studies and why?

A: theyre chill, easy money tbh

Q: yeah same. Could you give me an easy cupcake recipe off the top of your head?

A: nah i just get the box mix lol

Q: haha fair enough, i couldn't either. Last question, what's your favorite weird animal?

A: axolotl, theyre weirdly cute

And that's the whole thing. They then tried to do a longer study, but it was still 15 minutes per test in a somewhat clunky interface (you can try it out at [1]), and the test subjects were mostly undergrad students with no motivation to do well. Less than half tried any sort of trick question. ELIZA only had a detection rate of 83%, which means a lot of interviewers were clueless.

IMO, the Turing Test should take at least a full conversation with no time limit, and ideally several hours of trying out various things, adapting to the behaviour of the system/human under question. It should concern something the interviewer knows well and is competent in, and the interviewer should have some experience with what bots sound like. (Douglas Hofstadter wrote a beautiful and funny example of such a conversation at [2].) Only then do you have some idea how adversarially robust the system is. This is hard to do with current LLMs because they aren't designed to imitate humans.

[0]: https://arxiv.org/pdf/2503.23674 (now published at https://www.pnas.org/doi/epdf/10.1073/pnas.2524472123). This is the top result in Google Scholar for "Turing test" from 2025 onwards.

[1]: https://turingtest.live/

[2]: "Dull Rigid Human meets Ace Mechanical Translator" (https://www.cambridge.org/core/books/abs/once-and-future-tur... or alternative access methods thereof)

The share link doesn't work for me, it says I don't have access. I can see the one from the parent, so the problem is likely on your side.

If I understand it correctly, Firefox has some new-ish features that are marketed as AI-made, like tab grouping and tab comments... which also just get in the way for me.

The problem is that as a lay user of Firefox, I don't know how you could even make it better in terms of features (I could see it being faster etc.).

100% AI per Pangram. I caught it at "This is also where the CRISPR framing gets ahead of the result." -- somehow this is not a sentence anybody non-obnoxious would write. It's a weird structure where the AI talks about something specific as if it were an example of a common theme. This paragraph is an even clearer ekample:

"But in a regular biology lab, this isn’t the finished paper. It is the result you show at lab meeting and say: “This looks interesting. Now we need to figure out what the hell it does.”"

This is not how people write!

To me the main upshot of this benchmark is precisely that the pelicans still usually look a bit wonky. It's bizarre, since this definitely has a good solution, but it's in line with my experience that memorization of the training set just... isn't happening very much? As in, whether a model fails or not doesn't have much to do with whether that exact question was likely posed many times before.

David Hilbert presented the field equations of general relativity within a few weeks of Einstein, so if anything GR was more sure to appear than SR, which took years for others to even notice (Einstein became famous only after the 1919 experiment that confirmed GR). Pertinently to the recent Navier-Stokes drama, there was very little controversy between the two and they both admitted that the other got some aspect better.

https://en.wikipedia.org/wiki/General_relativity_priority_di...

This is not what Gödel says, and in fact your statement is true in a trivial way: you can prove 1+1=2, and Not(Not(1+1=2)), and Not(Not(Not(Not(1+1=2)))), etc. ad infinitum. This is an infinite space of provable true statements that can be exhausted by a ten-line Python script.

IMO, this is why we actually need mathematics -- as a field in which to learn what it means to know what you're talking about.

Very cool, if of unclear purpose. After a minute of trial and error I got through with an easy prime factorization, and then again for the download with the reaction time button, only to be told "This challenge produced a local demo token. Use Clawptcha's API for a verifiable token, or reset the widget and try again.", which I guess is the equivalent of a bot finding all the fire hydrants and being denied anyway because it didn't move the mouse shakily enough.

Submitted as its own entry, hope you don't mind: https://news.ycombinator.com/item?id=49774097

This is pretty, but none of those visualisations look very... singular to me? Can anyone tell me where to look in those simulations to see the blowup? Does speed go infinite in some region (which one? the blue or orange part?), or just non-smooth?

To go a bit off-track based on your final sentence: my high school physics teacher would do any numerical calculation that came up first in his head, as an estimate, and only then use a calculator or write on the board. Usually the estimate was within ±10-20% of the correct value even for long combinations of numbers with a bunch of decimals. Cube roots didn't come up, but square roots did.

The point of that was to show the use of approximations and of having an idea how much a result should be, to guard against calculator typos and the like. I think that has some metaphorical relevance for the chess example.

It's a standard coordination problem: I don't like X, but some discussion happens there (e.g. plenty of competent mathematicians responding to the Navier-Stokes situation) and I cannot force people to move elsewhere.

Inventing calculus to calculate pi? I don't think that ever happened...

Okay, from the actual linked article it seems that their partial result was finding blowup in Euler equations, which seems pretty big. I wonder how the other attempts went. Did they get nothing at all, or something true but unimpressive?

I do remember when hearing about Simón Bolívar's crossing of the Andes (https://www.youtube.com/watch?v=Ju7nJjprbQg) "I wish I had this guy's energy and drive". Some people just seem to be on another level. It kind of would make sense if this was bipolar disorder?

Elsewhere in this thread somebody claimed that at some point OpenAI pointed their new model at all the millennium problems and this is where they got some progress. We probably won't see proof of this, but it seems plausible to me -- I assume there's a list of problems that each new model is tested on, and you might as well put the big stuff on the list, if only to see how the model behaves when faced with a problem it knows should be very hard.

The weak point in this is: how do you evaluate if a partial result is promising? If this cost ~$10M as suggested elsewhere in the thread, probably not even OpenAI can just throw that at everything?

Since he wrote this five days ago, when these efforts were already underway, if he was not Terence Tao I would suspect he had inside access. But since he said he did not and was speaking hypothetically, and he seems to be an honest person as far as I can judge, I guess some people are just on another level.