traes

You aren't accounting for volume.

This is not my experience. Having an intuitive grasp of e.g. the graphical interpretation of the determinant instantly lets you figure out most of the key determinant properties without having to memorize them. That's the primary thing you get from intuition imo, having a sense of what must be true without having to memorize or prove it.

If you don't find the way he presents e.g. linear algebra intuitive I think our brains must work fundamentally differently.

> AI seems to be very good at getting answers, but not always answers to the correct questions.

I don't think that's an accurate summary of the article you linked. The Lean proof solved the exact problem it was supposed to, it just had minor discrepancies from the writeup of the proof (on the level of saying a theorem requires m+4 derivatives when it actually requires m+5 derivatives). Obviously a problem but not really a bombshell.

An unpleasant part of the AI math revolution is that people's hatred of AI is bringing to bear their hatred of pure mathematics in general. I've always known in the back of my mind that mathematicians were secretly despised and looked down upon by many, but it's a bad feeling to see it become so mainstream.

It's quite amusing that this mistake gets made on every single one of these guest posts when the first words on the page are "This is a guest post by Álvaro Lozano-Robledo" and the first paragraph starts with "I would like to give Terry my heartfelt thanks for giving me the opportunity to contribute a post to his blog." It's pretty clear that everyone is skimming these at best. Maybe he should put the disclaimer in a bigger font or something.

This same thing happened back in the 10 advances in math and CS release a month or two ago. The non sofic group construction relied on false prior literature. They realized this and fixed it in the lean program but didn't modify it in the writeup, so the written proof was both incorrect as stated and did not correspond to the lean proof. I was surprised how little press it got at the time, it seems like a huge risk factor.

My point is it is crazy to make public claims about how important or not important a mathematical result is when you can't spell Riemann. Yes, it technically doesn't matter, but it betrays a damning lack of familiarity with introductory mathematics.

The mathematicians don't make this mistake, I assure you. I doubt there is a math professor on planet earth who would spell Riemann as Reinmann. In fact, I imagine no one who has ever heard the name pronounced would do so.

I just don't understand how it happens. If they had ever taken an intro to real analysis class they would learn to spell his name. If they were just parroting what an AI told them... shouldn't they still just say his name? An individual could just be dyslexic or mistaken but it seems to be a substantial volume. I guess they just don't care enough about it to commit the correct name to memory, only remembering the "pattern" of the name and filling in the spelling via guesswork?

GitHub is a significantly worse place to store important results than Arxiv. Of course, slop does not belong on Arxiv, buy slop should also not get published.

Not to pick on you specifically, but as someone who spends a lot of time unproductively reading AI math discourse it's truly shocking how incapable all the supposed math enthusiasts are of spelling Riemann.

Hmm, I'm not so sure. You may have never had a truly horrible math teacher. I distinctly remember learning matrix multiplication in high school for the first time. We were taught the algorithm without any motivation at all. Not a single picture was drawn, she just did some examples and then passed out a giant worksheet. I didn't learn linear algebra in that class. If Grant Sanderson had taught it I'm sure I would have.

> The insane popularity of channels such as 3Blue1Brown suggests that a lot of people do.

I don't think this is true.

First of all, the fact that watching videos is not a sufficient way to learn math does not mean that videos cannot be an excellent supplement for learning math. 3B1B's linear algebra videos for example are wonderful tools for gaining geometric understanding and motivation behind why things are the way the are in linear algebra, but of course they won't teach you how to invert a matrix. (He even says something to this effect explicitly many times throughout the series, if I recall.) Not everyone who watches those videos is engaging shallowly with math just because they're watching videos about it, there's plenty of value for serious students as well.

Your next argument might be that the sheer number of views indicates an unrealistic volume of serious students. This is true, but it still doesn't indicate that people think watching videos is a good way to learn math; in particular, nothing says they're watching those videos because they're trying to learn math. They're beautiful and interesting and well put together videos, and I'm sure many people enjoy watching them passively fully conscious of the fact that they aren't actually deeply learning math. I don't think there's anything wrong with that!

I'm sure there is a subset of viewers who think they're actually learning math by merely watching videos, but I'm willing to bet it's a relatively small fraction.

This is the single most popular opinion about learning math.

(2023)

I recall reading in the past that the primary reason parser generators aren't used for production compilers is the difficulty of making them produce useful error messages on malformed code. (Of course, the need for fine tuned optimizations also plays a role). Is this still true, or have parser generators caught up in this regard?

Because the shithole countries are poor and rife with violence that is hostile to operating a profitable company? Obviously?

Regarding 1, it's not clear what you want them to actually do. Would you rather they just gave up, rolled over and died instead of at least trying to rescue their field? What is to be gained from considering this?

This is simply blatant misinformation. If you play a game online on lichess and go to the analysis board you can find when your game becomes novel. It will be within 20 turns unless you are intentionally following a known opening. In fact it will likely become unique within 10-15 turns.

> one of the obvious applications of novel mathematical results is in building stronger AI models.

This gets repeated a lot and seems to be one of the primary stated goals of making AI solve math problems, but I still have no idea by what mechanism this is even supposed to happen. I guess they could make some minor improvements to matrix multiplication algorithms or whatever but I don't see what groundbreaking theorem could possibly significantly improve LLMs.

> Also, his opinion of AI has continually changed in the past years, after the capabilities were demonstrated.

Ignoring the other ridiculous parts of your comment, isn't this exactly what you're supposed to do? Update your beliefs according to the newest information available?

This is true, but I'm not sure it matters? I was poking around at the lichess database recently and those elo calibrated bots are remarkably well calibrated, their rating variance sticks out like a sore thumb compared to human players even at similar game volumes. So it should still be a decent predictor of how good a human at that level is, even if the playstyle seems alien.

Yes, it absolutely is what it shows[0]. I have no idea what data you're looking at that suggests otherwise. Worldwide or in the US, as public individuals or as search terms with quotes or without quotes, over any reasonable timespan, they get roughly the same amount of searches.

[0]: https://trends.google.com/explore?geo=US&q=%2Fm%2F047mjr%2C%...

> Now, Tao is a sort of a celebrity of the quarter on HN, but I promise you that outside this forum, almost no one has ever heard of him.

This is an absurd thing to say. Hacker news is not the only place that knows about the most famous mathematician in the world. Glancing at Google Trends he seems to be roughly as famous as Linus Torvalds. Not exactly a household name but by no means obscure.

He was specifically working on the Euler equations, which are the Navier-Stokes equations with the viscosity term removed. This is definitionally a smaller related problem. I'm not sure how you are calling that claim wrong.

Which seems to be entirely true by their own admission! [0] Both the comments about him risking his career and about Levent's authorship seem to have indeed occurred.

> 2) I never ever asked for Levent to be removed from authorship of his own work (as indicated by my text). I was surprised to learn during the call with Tristan that they had only solved Euler and not Navier-Stokes; after learning this we brainstormed possible paths forward. One option we discussed was that Tristan could be the lead author on a rewrite of OpenAI’s Navier-Stokes proof. It is in that context that I said “it would be simpler if Levent was not an Anthropic employee” because I felt it would be inappropriate for an Anthropic employee to author OpenAI’s work. Importantly it was admitted that internal Anthropic models had been used in their proof of Euler blowup; I therefore felt I could not consider Levent to be an independent academic. Another option I wanted to propose (but got cut short) is to offer access to our internal model so that they could try to finish their proof and bridge the gap between Euler and NS. Again I did not know how to navigate giving access to internal OpenAI IP to an Anthropic employee.

> 3) To reiterate it plainly: as my text clearly indicates, and as I said during our call, OpenAI's intention was to do everything possible to celebrate their mathematical achievements and the heroic efforts that they made on Euler. In the call I was immediately met with a litany of slander, including direct threats that if we were to announce Navier-Stokes he would immediately go to the press with a barrage of unfounded accusations. I refuted all these accusations but he replied “there is nothing you can do, I simply do not trust you”. I was confused why one would turn an incredible source for celebration (of their achievements!) into such bickering, which is when I said that I did not understand why one would risk their career [over unfounded accusations]. Genuinely, at that moment, I was trying to care for him and do a last ditch attempt to get a chance to give them all the credits that they deserve. I deeply apologize for this extremely poor choice of words, it is the opposite of what I was trying to convey. (I should say that I retracted them on the spot by the way.)

https://xcancel.com/SebastienBubeck/status/20973794116915163...

I would assume they are calling the snark from Noam Brown and Dan Roberts bullying, not the somewhat bland denial.

Perhaps out of a sense of academic good will, knowing that he got there first?

It seems like the timeline according to OpenAI is that:

1. Buckmaster developed a counterexample to a reduced version of Navier-Stokes with Anthropic employee Levent

2. Rumors start spreading that Anthropic has solved Navier-Stokes

3. OpenAI learns this and starts throwing a ridiculous amount of compute at it, now knowing it's within reach of LLMs

4. Their LLMs (with human assistance) get FARTHER than Buckmaster, using the exact same method.

5. OpenAI reaches out to Buckmaster to negotiate a fair way to publish both results and properly assign credit

Perhaps they simply and honestly feel he is owed credit. I can't help but imagine it at least played some small part. I expect that's what Bubeck is going to claim: https://xcancel.com/SebastienBubeck/status/20972141224714323...

Because OpenAI employees kept leaking that Anthropic had a solution to Navier-Stokes and he wanted to figure out what was going on, since he was working on Navier-Stokes with an Anthropic employee. The rumor has been loudly circling the math community for the past week or so. For a bit of context, here's a timeline from mathematician and AI researcher Elliot Glazer:

https://xcancel.com/ElliotGlazer/status/2096298696438906934#