gjulianm

> The phase where AI proves Millennium Prize level problems but can't write up a human-like paper explaining the proof strategy may be similarly brief

It's absurd to assume that because LLMs are improving in certain aspects they will improve in everything, specially when the part they are lacking in is not precisely something that would be a strength of their architecture. I mean, models have improved a lot but they are still not good at strictly following instructions consistently (there's a reason why AI labs are worried about safety alignment). They are still mediocre to bad at software design, even the latest models (haven't tested Astra seriously yet). And it's the same reason they are bad at creating mathematical theories: they do not have mental models like we do, it's not even useful for them. Their comprehension is limited to textual context that they need to refresh and reprocess continuously. That's just how LLMs work.

> I find it interesting how many people are incapable of imagining that the tech capability will not be frozen

I find it interesting that after taking this long to, I assume, finally understanding the point the letter was making, you automatically switch to "oh well AI will do that too".

Why is it strange? Are you familiar with how unsupervised proofs are made? It’s basically iterating on Lean code, even if it were able to explain the code to humans it doesn’t mean it can extract actual understanding and structure from it. The papers being outputted by these approaches are nowhere close to being understandable, much less useful.

> If the AI can digest it better, then academic mathematicians will become humanities professors

Cool, then once that happens we can discuss what to do. In the meantime, AI does not digest proofs properly, does not explain them and does not generate any understanding, and it doesn’t look like that’s going to change. Hence the letter and the criticism made to the approach taken by AI labs. It is not that hard to understand.

> I have read the letter.

And you have not understood it.

> they don't want the answer key because prestige reasons

No, that’s not the reason. They don’t want the answer key because the answer key is useless.

> This doesn't consider that many people, like engineers, use math as a tool

Of course it considers it. Many people, like engineers, could not care less about the answers to most problems mathematicians work on. They do care about the tools they develop in the process. I’ve already shown examples of this but I’ll do it again: Galois theory was developed when trying to answer whether there are formulas to solve roots of polynomials of degree 5. Fourier analysis was developed when trying to find an analytical solution to the heat equation. Riemann developed his geometry to explore which Euclidean axioms were actually important. None of the direct answers were as important as how they got to them.

> Again, they want funding, they have to explain why exactly they should get it. And it better be an explanation that still holds water with AI available.

The explanation will be exactly the same. Only it will not be just hard to explain why the problem is important, but also it will be harder to explain that no, just the answer by itself is not useful without the understanding. Just like I am here having a really hard time explaining to someone who doesn’t understand how mathematical research works why “just getting the answer” is not a useful output.

> AI won't just say cancer can be cured without saying how.

It was an example, an analogy to argue that answering a question might not be as important as how it arrives to that question. Hence the “imagine”.

> These people are concerned about internal community dynamics like tenure, chairs, PhDs, grad students, the whole ecosystem, papers, hiring, conferences, journals etc.

You just described most of the parts of the mathematical community.

> But the wider population doesn't care about this and academics don't understand that nobody cares about this outside their bubble.

I don’t care about the logistic system and yet I want my food to be in the market. If the population at large wants to use mathematics they will have to find a way to support a mathematical community. Now, if you don’t want mathematics, again, go argue about that.

> Indeed, now people can do this with AI and it makes mathematicians salty that they will have less prestige.

Except that they can’t. I do not know how many more times we need to explain that “answering questions” is not what mathematics is about. That if that path is followed, then mathematics will suffer as a result and the pace of mathematical development will slow down.

Honestly, I think it would be better for you to really stop attributing the arguments of mathematicians that are by no means anti AI to saltiness or other childish feelings. Try to be more humble and try to find what kind of ideas they might hold for them to argue this letter. Of course, that requires reading the letter and trying to understand it.

But did you read the letter, or are you familiar with the people signing it? Several things tell me you didn’t:

- The useful part of math is the tools, the understanding and the theories. Knowing whether the result is true or not is usually not useful. Imagine an AI that just says “cancer can be cured” but doesn’t say how: that’s what the letter is criticizing.

- Terry Tao is one of the biggest proponents of AI use in math. He’s been for quite some time and he shares a lot on his blog.

Seriously, it seems like you’re arguing about some idea you have in your head and you’re not making the effort to actually understand anything about this letter.

I don’t get the argument you are making. If you want to reduce funding for mathematics research, argue for that. But wanting to make getting funding and coordination and collaboration harder in exchange for nothing other than PR for AI labs does not make sense

There are no similarities whatsoever, other than them having opinions on a new tech that affects their field.

> nothing stops mathematicians from doing both of those things

Actually yes, and they explain that pretty clearly in the letter. These problems have been used as "goals" not because the solutions are necessarily worth it, but because they set a clear direction whose process would probably yield very useful theories, and also more conjectures and problems. If the goals get solved by AI models that do not generate comprehension, then the direction gets less clear, it's harder to collaborate and get funding (think what would be easier, to get funding to try and solve Navier-Stokes or to try and understand an already proven Navier-Stokes?), and we get less open problems to work on.

> I read the article and they are all wrong

I would recommend a bit more humility and trying to better understand why 25 Fields medalists, among them people like Terence Tao (who isn't anti-AI by any means, he's even promoted a registry of AI Lean proofs), are saying this.

> Okay, to elaborate, substantively, their point is that the people using these AI models are not doing it for the love of the game, but for marketing.

No. The point is that AI companies are using the models to solve problems in such a way that the useful part of problem-solving, i.e. the theories and tools developed during the process, is not present. And they are doing that because the companies seem to be motivated not by honest advancement of math but by marketing and publicity.

> they synthesize and solve lots of other problems nobody asked for.

No one asked Fourier to solve series representation of functions when he was studying the heat equation, and yet thanks to that we have Fourier analysis.

> if they want to remain relevant as academics and mathematicians, they need to learn how to replicate the proofs and the steps that alluded humans for decades

The point they are making is that if AI keeps being used as "problem solver" rather than "theory understanding", replicating the proofs and getting the useful parts out of them will be far more difficult.

> Like the mathematicians working on famous problems in private

This is an extremely rare situation that practically never happens. Most mathematical research is done in the open, with partial results being published, conferences where approaches are discussed, collaborations... The Navier-Stokes solution is a great example: the approach that OpenAI ended up using was something that two mathematicians had proposed previously and was being studied and followed by several others, with different sub-paths within the same approach.

In that case a better answer would be "I'm fairly certain it does satisfy it, but in any case I asked Claude to double check for any issues and it didn't find any unsatisfied requirement". That's the information that matters, and it's probably faster anyways.

I try to not use AI to write text that's meant to be read by other people. I might use AI to understand and research beforehand, but the writing is mine. The most important reason is that writing allows me to check whether I actually understand what I am trying to communicate. Too many times I've started writing something and once the ideas need to be put in writing, I notice that there are concepts that I'm missing or that I don't really understand.

Second is that the LLMs are not going to have original input, they're just going to expand what I say. So at that point I might as well just send the prompt or the assorted collection of ideas and others can expand on their own. Seems more honest and efficient as I'm not just pushing a wall of slop.

I don't think you need to tear open busy streets to install fiber. In my area we got fiber (up to 10G now) and they didn't open any trench.

I am not sure how much do I trust an article about Madrid's metro that doesn't mention the fact that one of those expansions (Line 7, in San Fernando de Henares) was done with political instead of technical criteria, ending up in several hundreds losing their homes and a metro line that has to close every once in a while for repairs.

I am also heavily distrusting of the "75 percent of passengers described themselves as ‘very satisfied’". The infrastructure might be ok now, but the frequencies are getting worse (except when the pope visits, in that case they apparently have the money) and in rush hour everything is packed.

Cursor has BYOK support too. I think it also has Bedrock support.

I don’t think it’s false, much less obviously false. On one hand I have my personal experience about it, on the other you can see there’s only a small range in the “I want a conversation” scale where they want it enough to ignore the nonverbal signs that the person doesn’t want to talk but not enough to ignore the verbal ones.

> People forgot how to interact with each other because the forcing function that gets everybody mixed together into the same pot got taken away.

A lot of offices don't force you to interact with each other, much less in meaningful ways.

> And if you don’t take some fairly extreme steps to counter it, you’ll be completely alone and isolated

Are "having more time to meet with friends and family" or "having time to do hobbies with other people" extreme steps?

The people likely to talk to strangers unprompted are also likely to ignore those kind of messages. Anything that can lead to further conversation can be used (like "oh, what's worrying you?") so actually politely nodding and smiling without giving any footing to further conversation works better than being assertive.

I think this mindset is maybe too close to being just "people that don't think like I do are just crazy" and dismissive of people's actual concerns.

Several options on how to burn that amount of money without being specifically looking to tokenmaxx

- Agents that spawn other agents

- Telling agents to go look at the entire codebase or at a lot of documents constantly

- MCP/API use with a lot of noise

- Loops where the agent is running unattended.

I do think it's not really responsible use and a loop where the agent is trying to fix CI for one hour for something that would take you five minutes (for example) is absurd. But people do that.

I explored quite a bit because I was curious to see how it was possible that sauna had these great effects and why no one used it outside of Finland. But to this point I haven’t seen anything that really supports the idea that sauna is such a massive health protector as claimed. It’s probably beneficial, yes, but the real benefits are probably far lower than claimed.

> Bias is different from precision. If both conditions have the same bias, their difference is still unbiased.

Not really, and I wouldn’t assume that when the condition under study can also affect how the measurement is taken.

> If you quantize so much that you have no variance in the measurements, then sure. But watches typically have 1 bpm quantization, which is fine at the scale of variation in HR.

At the scale of variation in HR in general yes, but not if the difference you’re trying to measure is in the range of 3 BPM.

> If you have independent error in measurements and quantization that gives you variance in measurement

That’s a big if. I am not confident we can claim that the errors are independent in this case, using sauna or not can affect how the sensor measures BPM.

The first study shows a 0.37 hazard ratio for frequent sauna use. That’s better than a lot of the HRs reported for physical activity. It’s even better than not smoking. It just doesn’t really fit.

Also, the fact that there are practically no sauna related studies outside of Nordic populations is suspicious too. I bet that with those hazards ratios a lot of people have tried to study the effects more, it’s suspicious there’s practically nothing out there.

> of estimate of mean

But you can't really assume that the estimate of the mean represents the real value. For example, if the sensor is equally likely to show 80 or 81 BPM when the real heartrate is 80.7, the mean estimator will be biased.

> with 100 measurements

Also, wearables aren't taking 100 measurements of the BPM at a given point in time. I think the highest frequency they usually have is 1 second measurement interval. So they don't really have a lot of measurements for each point in time.

> mean estimate standard deviation

That's the standard deviation of the mean of the values. Doesn't imply that the standard deviation of the values themselves will go to zero.

> I don't understand what you mean by that.

That as a rule of thumb, you should not assume that repeating measurements will give you more precision than what the tool can offer. E.g., trying to measure down to milimeters with a ruler that has only 1cm marks will not really work well.

It does, specially if the error bars from multiple measurements show higher precision than what would be expected.

Much of that body of evidence relies on self-reported and self-assigned sauna usage rather than actual randomized trials, and also the papers show massive risk reductions that do not really fit with the country-level data (e.g., if saunas are that good for cardiovascular health and finns use them that much, why do they have similar rates of CV disease as neighboring countries that don't use that much sauna?)

> Effect survives controlling for activity level.

How did you control for activity level? Do you have similar BPM plots for the different situations (sauna+exercise, sauna+no exercise, no sauna + exercise, no sauna + no exercise) for a visual representation?

> minimum nighttime HR drops ~3 bpm (~5%)

What wearables were used? These devices don't usually have enough precision to reliably detect ~3bpm changes. Also, the measurements are sensitive to skin, blood flow changes and temperature. How do you know the difference doesn't come from different sensor behavior after sauna?

Unless the effect they're measuring is that the wearable measures differently in sauna days.

> Feeling good and with lasting energy is pretty much the same as having good health.

I'm referring to feeling like that specifically after the sauna. I also feel great after eating a great steak and yet it's not the same as having good health.

> Yes and there are studies, so do you have anything concrete why they ain't beneficial, besides your personal dislike?

> You lead with "Basically, the sauna studies are probably mostly discovering that "healthier people can stand sauna longer" that implies you did not even read them.

Not that they are not beneficial, but that the benefits are not as large as they are assumed to be. The main reason is that there are no randomized trials and practically no replications outside of nordic countries. Also, if you compare the risk reduction reported by sauna use to other health interventions, you'll quickly see that it doesn't really make that much sense. Depending on the studies, you'll see risk ratios that say that frequent sauna use is as effective (or more) as doing high intensity exercise or smoking cessation.

> (Besides, allmost everyone goes to Sauna in the nordic countries, that implies allmost everyone there is healthy by your logic)

Actually, you have that backwards. If finnish people go so much to the sauna compared to other countries and it's as good as the studies say, why are they not much more healthy than other countries? Prevalence of cardiovascular disease in Finland is pretty similar to other countries. Same with life expectancy. There are two options: either the finns are doing something radically different from other countries that negates the benefits from sauna use; or the risk reduction shown from the studies is not real.

The most likely explanation is that sauna provides similar benefits as any of the other interventions based around mildly stressing your body: somewhat beneficial but nothing magical, with probably an additional, significant placebo effect.

> But if Sauna for you was breathing fire .. one easy solution is to go to a less hot sauna.

Another easy solution is to not go to a sauna and just do anything else that's beneficial to me in that time and not extremely uncomfortable. I already live in Spain, I get more than my fair share of hot uncomfortable environments.

It’s not only that confounder but also the fact that the studies show massive risk reductions that are really surprising. Considering how much finns apparently go to the sauna compared to similar countries and how good the sauna appears to be based on the studies, it’s weird that they have similar health stats at a country level.

There are two separate issues there. One, you feeling good about going to the sauna. If you feel good, that’s nice. But it’s your personal feeling from it. I personally did not have the same opinion about my lungs feeling as I was breathing fire, but to each their own. I’d rather do other nicer things to activate blood flow and feel revived.

The other is the health benefits, and that can only be measured from serious studies and not from how you or me feel about it later.