My colleagues in math are now frightened about the (very expensive) mathematical theorem proving ability of these AIs, and many of them really do think that if they can do math, they can do all cognitive tasks. Running a store like this should be so easy! Every single conversation about AI with them has become more frustrating. They are so confused when I still say that the AI companies will die a painful death. When I give my usual points about their expense and their failures in other domains, I am given the usual spiel of "it'll get better in other areas" and "it'll get cheaper".

Unlike them, I have actually been paying attention to this stuff from the beginning. What they think is going on is AI solving math first and shortly getting around to all the other stuff, but what I've seen is that AI labs had already tried all the other stuff first and only managed to win the booby prize of theorem proving, which doesn't pay the bills. And what's the point of spending thousands or millions to output random blobs of Lean that technically compile if there is no one around to bother making sense of them?

One example I gave is when Anthropic vibe coded an entire C compiler from scratch back in February, which turned out to be a pile of shit. I've said that if AI had made similarly rapid progress on software engineering, we would have seen Anthropic continue to put out these demonstrations, and they would have become truly high quality. They would release a compiler more efficient than gcc one week, and a browser better than Chrome the next. (OpenAI's actual attempt at a browser didn't go so well.) And if they could do this, they would actually have a shot of making money!

If they could do this, they would have already. The theorem proving stuff actually works (for certain things, in certain ways, at enormous expense), and look at how OpenAI and Anthropic do not hesitate to snipe mathematicians for results rather than being content as tool vendors. But lately I haven't heard of any software demonstrations. Silence is much louder than noise. More Millennium prize problems bashed with tens of millions in compute costs are not going to change my mind very much.

The counterargument I got was that AI can already one-shot most programming tasks and I shouldn't be cherry-picking the failures. I am far too tired to argue at this point.

Despite all the doomer propaganda that has been swirling around for many years, it's still easier to imagine the end of the world than the end of capitalism.

Signed.

Terry Tao talks about how he used to try to cooperate with the AI industry to achieve a positive outcome, but now he finally sees their true colors. Link

During this event, OpenAI requested an interview concerning my vision of the future of AI and mathematics. I accepted, and spoke with them for perhaps an hour. I had done similar interviews in various venues, and I assumed that, as with these other cases, they would eventually post the entire interview online, which talked about both the possibilities and risks of AI much as I have done in these other interviews. As it turned out, they only used a few snippets of that interview for that infamous advertisement instead. In retrospect, I should have pushed back harder on their decision; but I decided at the time that even a selective release of my commentary would help raise awareness of the potential for AI, and in particular on the possibility of the “best of both worlds”.

Since then, the situation has deterioriated markedly. Many of the people in the industry that shared my views have left or become sidelined, with most major tech companies now increasingly focused on the race to develop extremely powerful, autonomous AI technologies regardless of their actual value to society. The current drama surrounding the Navier-Stokes global regularity problem is the most dramatic and visible instance of this, but there have been multiple other such examples, and much of my commentary in the last few months has been aimed that the increasingly severe divergence between the current objectives of the AI industry, and of mathematics in general.

Much respect to artists for seeing all this coming from the very beginning, and holding the line.

One detail that seems to have not spread around: the announcement was so rushed that when the 165 page output was released, it only included 16 citations, and those citations did not even include the work of Diego Córdoba and Luis Martínez-Zoroa, who introduced the overarching framework for attacking the problem (that Buckmaster-Alpöge and OpenAI used). After the announcement and after these redditors pointed it out, they threw in a few more citations to include them, but come on.

Of course there are people trying to find a silver lining to this by conjuring up the hypothetical scenario where a student only uses the AI to aid in learning the material instead of just doing all the work.

First, any convenience in learning the material just reduces your ability to learn it. The friction involved with learning may seem like an inconvenience to be smoothed away, but it turns out that the friction is how learning happens. It's called engaging with the material. This has been the case with previous technologies: handwriting is better for retaining memory than typing (https://pmc.ncbi.nlm.nih.gov/articles/PMC11943480/), although it seems like AI is on an entire new level. (I guess there is some commentary about the sadly common worldview that life is about avoiding inconveniences. I feel like this mindset draws a lot of people to AI.)

Second, there is a very thin line between "helping" you learn the material and just doing the work for you. The temptation to cut corners is always there, and when you have the Corner Cutting Machine at your disposal, you are kidding yourself if you think you will have perfect discipline. Tools influence behavior.

Glad to see that OpenAI has not changed in their scummy ways. Despite all that has changed in the meantime, they have kept their time-honored tradition of passing off other people's work as their own.

One of OpenAI's math announcements a month ago claimed that their results cost only $2000 worth of tokens, which frustrated me because they were likely sweeping away many inconvenient details and almost certainly misrepresenting their true costs. But people took this as a gotcha. This is the same bullshit as the water usage arguments. We are literally seeing city council members signing motherfucking NDAs about this, and you think that water usage numbers provided by the tech companies themselves are going to sway me?

I am also questioning OpenAI's strategy of strip-mining math for PR, since it seems like advances in math do not actually register that well in the public. From what I remember, the Hugging Face incident got a lot more press than any of the math results.

I decided to take a look at the bitcoin white paper.

Usually, the introduction of a technical paper is fluff and people quickly move on to the technical parts. However, the casual claims made in the first paragraph of this paper have aged extremely poorly, to say the least. In a better world, Bitcoin would have remained as an obscure academic toy, and this introduction would have remained fluff.

While the system works well enough for most transactions, it still suffers from the inherent weaknesses of the trust based model.

What weaknesses are there in the trust based model? Let's find out!

Completely non-reversible transactions are not really possible, since financial institutions cannot avoid mediating disputes. The cost of mediation increases transaction costs, limiting the minimum practical transaction size and cutting off the possibility for small casual transactions, and there is a broader cost in the loss of ability to make non-reversible payments for non-reversible services. With the possibility of reversal, the need for trust spreads. Merchants must be wary of their customers, hassling them for more information than they would otherwise need.

It seems like this guy really loves non-reversible transactions! But as we've seen with the history of crypto, non-reversible transactions sound really good until you fall victim to a crypto scam and there is no way to appeal to the bank to reverse the charges. Reversibility actually increases trust because you no longer need to be absolutely certain that you're dealing with an honest person.

A certain percentage of fraud is accepted as unavoidable.

Almost like that is a problem of human nature. And it's not like cryptocurrency has a spotless record when dealing with fraud! The problem with fraud is not the third party (the bank), but with the second party (the merchant or customer you're dealing with).

The introduction is not long, and most of the paper concerns the technical details of the construction of Bitcoin. By itself, there really is no way to complain about a pile of definitions. But there are still dumb comments that have aged poorly in retrospect.

A block header with no transactions would be about 80 bytes. If we suppose blocks are generated every 10 minutes, 80 bytes * 6 * 24 * 365 = 4.2MB per year. With computer systems typically selling with 2GB of RAM as of 2008, and Moore's Law predicting current growth of 1.2GB per year, storage should not be a problem even if the block headers must be kept in memory.

But why would you want a block header with no transactions? If you wanted to, I don't know, replace the world's financial system, you would need to handle millions of transactions every 10 minutes. How big would the blocks be then? And remember that many copies of the same blockchain would need to be stored (certainly, every miner would need to store a copy). How many thousands or millions of times would that multiply things?

Businesses that receive frequent payments will probably still want to run their own nodes for more independent security and quicker verification.

Turns out it was a bold assumption to think that businesses would just run their own bitcoin miners.

The proof of security (Section 11) is extremely sketchy by modern standards. (They're assuming that all attackers would follow a certain format to attack and not try something different. I get it, proper proofs of security in cryptography are very subtle and difficult.) There is also a page of fluff making random calculations with the Poisson distribution. In any case, the security of Bitcoin requires that the collective computational power of the defenders exceeds the power of any attacker (so the defenders can make new blocks faster).

Bitcoin is very strange as a cryptographic system in that the defender must have more resources than any possible attacker. In most cryptographic systems, the system should be secure even if the attacker has vastly more resources than the defender. Your phone's cryptography should be secure even if some government agency dedicated their supercomputers to try and break it. This means that Bitcoin must waste tons of energy, since that is required to maintain security. Any more energy dumped into it will only increase security and not make the actual transactions faster, which makes Bitcoin horrendously inefficient.

As a purely academic idea in cryptography, it is an interesting curiosity, but the arguments for why it's useful are sketchy. There are other such curiosities that are much more interesting, like homomorphic encryption or secure multiparty computation. It would be a nice line on a CV, but not "incredible".

The true significance of Bitcoin was the terrible libertarian economic argument for it, and the chain of events that would transform it into nothing more than a speculative fashion trend. It has nothing to do with the technical details of Bitcoin. The technical and economic arguments for Bitcoin turned out to be so weak that nowadays, the only real support for Bitcoin is that maybe you can sell it for a higher price to a greater fool.

“California is, I believe, the only state to give health insurance to people who come into the country illegally,” Kauffman said nervously. “I think we probably should not be providing that.”

“So you’d rather everyone just be sick, and get everyone else sick?” another reporter asked.

“That’s not what I’m saying,” said Kauffman.

“Isn’t that effectively what happens?” the reporter countered. “They don’t have access to health care and they just have to get sick, right?”

Kauffman contemplated that one for a moment. “Then they have to just get sick,” he said. “I mean, it’s unfortunate, but I think that it’s sort of impossible to have both liberal immigration laws and generous government benefits.”

Do I need to comment on this one?

It is how professors talk to each other in ... debate halls? What the fuck? Yud really doesn't have any clue how universities work.

I am a PhD student right now so I have a far better idea of how professors talk to each other. The way most professors (in math/CS at least) communicate in a spoken setting is through giving talks at conferences. The cool professors use chalkboards, but most people these days use slides. As it turns out, debates are really fucking stupid for scientific research for so many reasons.

1. Science assumes good faith out of everyone, and debates are needlessly adversarial. This is why everyone just presents and listens to talks.
2. Debates are actually really bad for the kind of deep analysis and thought needed to understand new research. If you want to seriously consider novel ideas, it's not so easy when you're expected to come up with a response in the next few minutes.
3. Debates generally favor people who use good rhetoric and can package their ideas more neatly, not the people who really have more interesting ideas.
4. If you want to justify a scientific claim, you do it with experiments and evidence (or a mathematical proof when applicable). What purpose does a debate serve?

I think Yud's fixation on debates and "winning" reflects what he thinks of intellectualism. For him, it is merely a means to an end. The real goal is to be superior and beat up other people.

Just had a conversation about AI where I sent a link to Eddy Burback's ChatGPT Made Me Delusional video. They clarified that no, it's only smart people who are more productive with AI since they can filter out all the bad outputs, and only dumb people would suffer all the negative effects. I don't know what to fucking say.