stbede

(2^sqrt(n))^2 = 2^sqrt(n) * 2^sqrt(n) = 2^(sqrt(n) + sqrt(n)) = 2^(2 sqrt(n))

but

2^(sqrt(n)^2) = 2^n

That's why I prefer my Wisephone 2. You can still use slack, whatsapp, teams, banking apps, spotify, google maps, etc. But there is no browser, email, youtube, tiktok, etc., either.

What we care about and what the exorbitant privilege is referring to can be different things.

Exactly. This is what the letter should have focused on. The issue is not alignment, per se. If AI can do the workmanlike stuff at breakneck speeds, academia will decide between two options:

1) Keep the average mathematician employed doing redundant mathematics just to have capable humans around. Every now and then you get one of those mathematicians actually developing new ideas, but most departments will entirely be just for show. It's doable though. College sports is able to keep itself going along these lines (and I mean the track, softball, and polo type sports).

2) You get unemployed mathematicians who were still developing their abilities. And as a result you lose the institutions that generate the mathematicians that contribute new ideas.

You get to keep the handful of exceptional mathematicians that are developing new ideas, and that's survivable if you happen to be a Fields medalist. None of this really has to do with the AI companies aligning themselves to giving credit and developing insights. If AI companies became aligned to that, then the AI's would be replacing the Fields medalists, too.

Wouldn't the more relevant point of comparison be the difference between long-term government bonds. The exorbitant privilege is that it's easier to fund US government debt because trade in USD means that large institutions around the world need USD and store those dollars in the form of US treasuries, which in turn lead to lower bond rates and cheaper debt.

I agree. But my frustration is that there is no argument why AI should be aligned with mathematics.

Why can't the mathematicians that value their own community remain aloof from what AI companies are doing. Can't they continue to take their time digesting proofs, gaining insights, and attributing credit to mathematicians doing good work. Here's how I perceive the situation:

Before:

- mathematicians digest current results and develop insights

- insights lead to new results

- new results give mathematicians an opportunity to credit those insights

Now:

- AI companies release a bunch of potentially uncredited proofs

- mathematicians digest these results and gain insights

- mathematicians recapitulate AI proofs in terms of their deeper insights and theory

- mathematicians give credit for these new insights and progress in understanding, even though the binary true-false status of theorems were already determined beforehand.

If the true-false status itself isn't real mathematics, then mathematicians still can do the real mathematics after the fact and continue to celebrate each others' work. The only thing they lose is the ability to attribute a human to deciding the true-false status, which isn't real math anyways (though maybe valuable for motivation). What they gain is efficiency. Every mathematician working towards proving NS won't blow up can now shift their resources to understanding why it can blowup.

Perhaps the letter is implying that the mathematical community itself will become misaligned with how mathematics is currently done. I'm unpersuaded it's entirely the AI companies' fault if that happens. AI may create a lot of temptations for individual mathematicians to become lazy, but that seems like something the mathematical community needs to resolve for itself. Every institution needs to take a lot of self-ownership here. I'm also annoyed about parents complaining about their own children being addicted to their phones as if it isn't in their own power to determine if their children have phones in the first place. I think this letter would be better directed at universities and journals. They should be holding their own institutions to account if they feel like they are adopting the mentalities of the AI companies and no longer faithfully executing the values of mathematics.

Fair enough. But I think you may be conflating an explanation with an excuse. I think your root cause analysis may be fruitful for explaining why they wrote the letter. But I don't think that it excuses what they actually wrote.

You and I aren't having the same conversation. You want to psychologize people's motivations, including my own, which is interesting to speculate about but off topic. I want to discuss the arguments made in the letter, the arguments that 25 Fields medalists actually signed on to.

I am capable of having a conversation with you on a great many topics. What you aren't capable of, apparently, is forcing me to want to have the one you want to have.

As far as calling names:

"Your comment is ... disingenuous."

"you are being disingenuously clueless or cluelessly disingenuous."

and now:

"I had imagined i was interacting with somebody who could understand the larger picture"

Yes. Everything I've said and want to say is about this letter.

Let me try to summarize this discussion in a way that an overly obsequious AI would never dare:

- I argue that the arguments in the letter are bad.

- You mysteriously assign me homework on the topic of human motivation.

- Confused, I reiterate the points made in the letter, and I make arguments against them

- You ignore my arguments, call names, and then defend the letter by making points that the letter doesn't make.

- I ignore your points, because they aren't the points made in the letter. And my original post was about why the letter was misguided.

- You call names. You feel like your points are valid. You then claim that the letter is valid because your points are valid.

- I keep disagreeing with the letter.

- You call names again, because why am I so obsessed with talking about the letter. I must be an idiot, or an evil lying phony, or an evil lying idiot-phony because I keep bringing the conversation back to the letter on a thread about the letter.

I think that's just oblivious to what mathematicians actually care about when it comes to "name and fame." Basically no one outside of the mathematics community and its periphery knows who someone like Terrence Tao is, and those outside academia who do know who he is probably don't know one single result that he's proved. The most famous mathematician in America may be James Stewart for authoring the calculus textbook. Mathematicians do not get fame amongst the general public. They want fame within mathematics.

If the mathematical community identifies Luis Martínez-Zoroa or Buckmaster and Alpöge as the last human in the chain before NS was solved, and internally attaches their names to it, that will be enough for most mathematicians. Mathematicians write the textbooks. Some other mathematician is still free to consolidate OpenAI's proof into a better proof, put it in a popular graduate textbook, and gives it the name "The Martínez-Zoroa Theorem", and then whenever an undergraduate PDE textbook mentions NS, they say, "according to The Martínez-Zoroa Theorem...", and then Martínez-Zoroa gets a Fields Medal for his contributions to his theorem.

The case you're making seems to be that no one in the mathematics community would feel satisfied with that because at the end of the day everyone would know Martínez-Zoroa didn't solve NS. OpenAI did. And it wouldn't matter if Open AI paid to erect a 50 foot statue of Martínez-Zoroa in front of a museum of the history of NS in which every single mathematician who ever contributed anything to NS was publicized and celebrated and glorified and deified and credited and thanked. It wouldn't matter because maybe what mathematicians actually wanted wasn't credit for what they did do but that at the end of the museum tour the final display would talk about the human who solved NS. No matter how much credit you give mathematicians, no mathematician will now ever be able to claim "I solved NS" because OpenAI beat them to it.

If that's the case, then the letter is misguided. It's pretending that the problem is that AI is misaligned with the goals of mathematics. That's not the problem. The problem is that no matter how ethically it behaves, humans are going to be pissed that there is a non-human thing that is better at math than them. And I'm also pissed that we are creating this thing that's going to be better than humans at a whole bunch of things and it's going to cause a bunch of people to outsource their humanity to an AI. I'm pissed about that. But I'm not trying to pretend that AI can somehow eventually win me over if only it was more aligned with me when I know full well that its alignment has nothing to do with my loathing of it.

That far from charitable. My arguement is:

A) According to the letter, mathematicians most value:

- mathematicians developing their mastery

- developing mathematics that provides insights and can be eventually synthesized down conceptually to textbook theories

- caring for students and fostering their growth

- human mathematicians getting credit for doing important work

- etc.

B) According to the letter, AI labs aren't trying to do any of these.

Conclusion) The result is that AI is not competing with them in their goals of

- mathematicians developing their mastery

- developing mathematics that provides insights and can be eventually synthesized down conceptually to textbook theories

- caring for students and fostering their growth

- human mathematicians getting credit for doing important work

- etc.

The upshot is that mathematicians still have autonomy to pursue those goals, develop mastery at achieving those goals, and remain part of a community of others pursuing them. The only mathematician who loses these sources of motivation is the one who embraces the use of AI and personally abandons those goals.

The real crisis will come if AI does try to align itself with the goals of the mathematical community and if AI turns out to be better at developing insight, training students, writing comprehensible textbooks, etc. Then the top mathematicians will truly provide little value to their community.

I don't understand why you can't just articulate the point yourself. It took me a while to guess what you were getting at. Could it be the quote:

Our egos are powerful things. They want to believe that we’re each better than we are, and we want to believe that we’ve mastered our chosen areas – that we’re the best. Whether that’s objectively verifiable or just wishful thinking isn’t the point. If we want to motivate people, we’ll give them ways to become masters or, at the very least, allow them to feel competent in what they’re doing.

In which case, yes, there is a loss of that source of motivation. And that's coming for us all - or rather it's coming for some of us in most professions. Most people are perfectly average in their chosen areas and never got the satisfaction of being at the top of their profession. Yet we still go to work. I imagine it will take some getting use to for Fields Medalists, but I think the average grad student that happened to just love mathematics and never aspired to be a medalist will still like doing math. Magnus Carlsen still became the best chess player ever even though AI's have been better than humans for decades now.

Most sources of intrinsic motivation are unaffected by these developments in AI. It may be the case that extrinsic motivations may be harmed by all of this if there's less money for mathematicians in the math community. The letter lists a lot of reasons to like how the math community does math, and I don't see any real reason they can't just keep doing math that way.

Honestly, I still don't understand the point you're trying to make. Or the realization you're hoping I'll have.

I might want to. Would you explain its relevance here and make a pitch for me doing so.

Here's the thing. I read the letter. I'm considering it on its merits. And it has very little. They made great arguments for why it's a good thing that the mathematical community operates the way they do. They could have made a good argument for why practitioners within the mathematical community shouldn't be seduced by the power of AI and should continue to build mathematics they way they do now. Ignoring AI as a tool, but perhaps not ignoring the results coming out of it, builds understanding and skill and develops humans. I'd be all for a letter that calls on humanity to not give up their humanity to AI tools. To not become lazy and overly dependent on them.

The letter makes no arguments why AI companies proving a bunch of results quickly at all affects the ability of mathematicians to do what they want to do. It's just a giant self-congratulatory list of all the wonderful things the mathematical community does and notes that AI companies aren't doing the same thing.

It's not enough for them that they are still free to pursue all the goals they outline in that letter to their hearts content. They want to make sure everyone else doing mathematics also sets aside their own goals and pursue theirs. I distrust AI as a technology regardless of alignment. And I've learned to just not use them and focus on the things in my life that matter to me. It turns out that I'm still free to pursue the things in my life that are meaningful regardless of the existence of LLMs.

Shouldn't the AI companies know by now that all mathematical knowledge belongs to the mathematical community? Hopefully this letter knocks some sense into them.