qnleigh

I wouldn't have guessed foot either, and I'm a human.*

*In case there's any doubt, there are three r's in strawberry.

If your life's work were to get outsourced to AI and you lost your job/the opportunity to do it, I doubt you would make this argument.

I would rather live in a world where mathematicians get the opportunity to do math with AI, rather than AI companies doing the most important mathematical work and leaving them behind. I hope this for all professions that people want to do.

I see two separate arguments in favor of this logic:

1. Academic mathematics has traditionally been meritocratic, and this is a good thing. If you work hard and demonstrate results, then you will be given further opportunities to do math research and the resources to do it. We are concerned that AI will reward money and access to frontier models instead.

2. There is a general concern that AI could lead to massive accumulations of wealth (see concerns of massive job displacement). AI companies claim that they want to raise standards of living and benefit humanity, which means that they will need to share their resources and wealth in some way. If they effectively destroy the mathematical community be racing ahead and taking all the major results for themselves, that does not bode well for the rest of us. It seems like a great opportunity to show the world how AI will benefit humanity rather than replace it.

Wait I have been wondering about this. How do banks make sure that a cyberattack couldn't change the numbers in people's bank accounts? How do you know that they're safeguards are sufficient?

Many of us concluded independently that bioweapons were a serious risk of widely-available AI. Like I remember what I was doing when this occurred to me and who I talked to about it first.

I've seen this sentiment in many discussion here lately, that anyone concerned about these kinds of risks is blindly falling for marketing hype and not thinking for themselves. Please give people the benefit of the doubt and engage with what they are saying. Because if you don't think that bioweapons/nerve agents are a serious concern, I would sleep better if you could convince me if this!

Yes, lots and lots of stuff. For all we know, space may extend infinitely in all directions.

I'm imagining someone who actually did have a deadbeat father growing up then seeing messaging on social media about deadbeat men. Probably their social media feeds create a vicious cycle that only solidifies their distrust of men. It is just showing them things that they saw to be true since they were young children.

This is one of the original papers that described the concept of holography, which is a central concept in quantum gravity research. It's a neat paper because although the subject matter is highly technical, the author describes the basic idea largely using undergraduate physics and without a lot of fancy math.

Posting since there was some interest in a related Quanta article here recently https://news.ycombinator.com/item?id=49845998

Susskind's original paper is shockingly readable. It doesn't use a lot of fancy math or derivations to justify holography. Mostly it uses basic concepts from undergraduate physics to show how the idea of holography is consistent and makes sense, despite it seeming incredibly counterintuitive at first glance.

For instance, figure 3 shows how you can't hide a black hole behind another black hole, which has implications for how a 3D universe can be completely encoded in a 2D region.

https://arxiv.org/html/hep-th/9409089v2

Oh this is a super-important question, and I wish I'd gotten the following advice much earlier than I did:

1. First read the abstract and conclusion

2. Then flip through the figures and their captions, and try to understand them as best as you can (though this doesn't work for all papers)

3. Make a deliberate decision about whether it's worth it to dive into the details and read the full text.

LLMs are incredibly useful for parsing dense literature, but I think it's better to ask specific questions about the paper, jargon, equations etc. rather than to have it summarize the paper for you. Summaries are often shallow or even misleading, and they rob you of the opportunity to engage actively with the paper.

To me he crossed a line by asking the woman to turn around and then crouching down to film her butt. That is a really creepy thing to do and a lot of women would find that threatening. Ask a female friend how they would feel if you find that surprising.

OpenAI put together an advisory panel to provide guidance on how to release their results. Where do you see bullying?

The composition of the panel might give us some clues as to the nature of OpenAI's unreleased results. Some of Ed Witten's work is quite closely related to the Yang Mills existence and mass gap problem, which is one of the remaining Millennium problems. I went through the list of panel members and asked an LLM to associate each member of the panel with one or two millennium problems. Here is the resulting count:

Hodge conjecture: 5 Birch and Swinnerton-Dyer Conjecture: 3 Navier-Stokes: 2 P vs NP: 1 Yang-Mills existence and mass gap: 2

So this gives a bit of further evidence that they made progress on the Hodge and Birch and Swinnerton-Dyer conjectures. Maybe also Yang-Mills.

Notably absent is the Reimann hypothesis.

You realize this is a guest post, right? Terrence Tao didn't write it. He's been using his blog to facilitate discussions about math's future.

I'm frustrated by articles like this that categorically dismiss the risks of AI in security. If you don't trust OpenAI's and Anthropic's motives, that's fine, you probably shouldn't. But don't tell me that there's nothing to be worried about; we need an alternative proposal.

So let's stop talking past each other and engage with the arguments on both "sides." For example, let's discuss how to ensure competition and availability of open-source models in the long-run while giving the world time to prepare for the immediate security risks of agent swarms.

It's possible that they didn't notice.

Waitwaitwait multiple millennium problems? What was the other one???

Increasing a bound on the fraction of Reimann zeros on the critical line doesn't count; even Anthropic says they don't think this line of work will lead to a solution.

> OpenAI / Anthropic models have largely stopped advancing

I'm shocked anyone could conclude this. This year it became common for people to entirely delegate coding to AI (I know many competent programmers/researchers who do this now). Progress in math has just been insane. An internal model at OAI just resolved one of the most celebrated open problems in mathematics. If anything, progress has accelerated.

That was interesting. Highlights for me:

> The Chorleywood bread process allows the use of lower-protein wheats and reduces processing time,[5] the system being able to produce a loaf of bread from flour to sliced and packaged form in about three and a half hours. This is achieved through the addition of vitamin C, fat, yeast, and intense mechanical working by high-speed mixers, not feasible in a small-scale kitchen.

> The process significantly reduced fermentation time and allowed greater use of non-imported wheat, which helped reduce the price of bread.[4] According to a representative of the British Federation of Bakers, "UK bread is around the cheapest in the world."[5]

As of 2011, 80% of bread made in the United Kingdom used the process, which has also spread to other countries such as Australia, South Africa, South America, Turkey and France.

He doesn't seem to be after the prize himself. In this statement he credits the approach of another two researchers:

> I believe Luis Mart´ınez-Zoroa deserves a Fields Medal.

> It was also said that if OpenAI posted after us, they would say that we deserved the Clay Prize, and that we were the “closest humans to the problem”. I declined both offers. I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.”

I'm not even sure what to say to this, but I think this should be widely known if it is indeed what happened.

I wonder what he's feeling about this. Formalizing Fermat's last theorem was a huge undertaking, and has been a big part of his career for some time. Now the announcement has been made, and even if there is more work that he wants to do, he has in some ways been scooped by an LLM.

Fortunately he is a very well-established mathematician, so career-wise he will likely be fine. But if an early-career mathematician gets scooped this badly it could be career-ending.

> "Lena" presents a lush, capitalist ideal where you are a business, and all of the humanity of your workforce is abstracted away behind an API. Your people, your "employees" or "contractors" or "partners" or whatever you want to call them, cease to be perceptible to you as human. Your workers have no power whatsoever, and you no longer have to think about giving them pensions, healthcare, parental leave, vacation, weekends, evenings, lunch breaks, bathroom breaks... This is extremely realistic. This is already real. In particular, this is the gig economy. For example, if you consider how Uber works: in practical terms, the Uber drivers work for an algorithm, and the algorithm works for the executives who run Uber. There is a kind of airtight bulkhead separating the human drivers from the humans who control the algorithm. The management layer sends the drivers instructions electronically, impersonally, at immense scale, and the drivers respond using a narrow collection of APIs. This bulkhead is intentionally designed to make it impossible for these two sets of humans to actually talk to one another

Some of you might have read the short story Lena by qntm [0], which is about brain uploading and the effective enslavement of the uploaded once their humanity is hidden behind an API. That story is actually about the gig economy [1].

Of course having a dishonest Uber driver is annoying, but I think that has nothing on getting suspended or fired by an automated system.

[1] https://qntm.org/mmacevedo

[1] https://qntm.org/uploading

This is no excuse. Prioritizing new features so far above reliability is exactly what makes most Microsoft products infuriating to use.

Learning is an unproductive use of your time??? No one knows how LLMs will change things, but that sounds like terrible advice.

> Another one is having the LLM quiz you on your topics of interest

This is a great idea. I'm going to try it.

Well everyone needs some downtime, and then I think it's important to acknowledge that there is a range of quality within the category of "educational entertainment." You can learn a lot of interesting things from 3BlueOneBrown and Veritasium, even though neither compares to working through a textbook.

100% agree. They are not good teachers. Nevertheless I've been using LLMs more and more to learn complex topics, but my learning is always anchored in something else:

- Getting through textbooks and lecture notes. LLMs have gotten very good at answering basic questions on quite advanced material (e.g. representation theory and quantum field theory). By asking a very specific question or even giving the LLM a screenshot, I can get unstuck a lot faster.

- Learning e.g. new python packages. Instead of hunting for examples on Stack Exchange, now I ask an LLM to write a minimal working example and then build off of that. By writing most of the remaining code myself and only using the LLM to answer questions, I've been able to learn new packages significantly faster.

In both cases, the LLM isn't providing the curriculum or guiding what I learn. The textbooks, papers and coding tasks are. But now I can pick these things up much more efficiently.