I can fire up a Linux terminal with WezTerm and WSL2 at any point. It's customized and beautiful and totally fine. I have Codex running in one right now. I can listen to Dolby Atmos music through Apple Music or fire up a game with zero compatibility issues and full RTX support. It's just versatile like nothing else. I pair it with a gigantic 48" LG OLED TV as my monitor.

The only thing that might tempt me away from this is a fully loaded Mac Studio with 512GB of unified memory. That would be a real capability gap from my current machine. But I've contemplated wiping Windows and installing Omarchy, and I just can't figure out really what I'd gain, but what I'd lose is quite clear.

To really quantify how exotic, it's conjectured that curves with rank 2 or greater have an asymptotic density of zero. That doesn't mean they don't or can't exist, but it does mean they become vanishingly rare, so finding even individual examples of high-rank curves has been absurdly hard.

Anyway, if we put the AGI framing aside, I think the main point you're making is that AI mathematics hasn't yet demonstrated the ability to theory-build in the way that the great human mathematicians have (Grothendieck, Scholze, etc.). And I'd agree with you on that. Where we disagree, I suppose, is I think that capability is coming -- I don't see anything that would prevent its development.

False. You very plainly did. You simply used the term “junk” instead.

> That's baseless speculation.

It might be speculation (as is much of what you’re writing), but it’s not baseless. Obviously, it’s quite easy to direct AI agents, a single one of which can pivot across all of mathematics, unlike all human mathematicians.

> All indications so far are that LLMs produce proofs far longer and far more complicated than humans are capable of, such that only machines can check the proofs for validity.

I’m unaware of any clear evidence of this. Hence, it appears to be baseless speculation.

> Digesting them into a human-readable interpretation of the results is an open problem.

I’m unaware of any clear evidence of this. Hence, it appears to be baseless speculation. Moreover, and more importantly, to my knowledge there hasn’t been any meaningful result in AI mathematics so far that has posed any kind of blocking issue on understanding it yet.

What it comes down to is that there are different types of high performance. Some people are good at just executing tasks given by their manager. Some people are good at being generative, thinking across boundaries, acting autonomously, creating value without direction, etc. A term like "superstar" will get disproportionately applied to someone really good at the latter and rarely someone really good at the former, because the potential impact of the former is typically strictly capped, while the latter is uncapped.

Moreover, the disdain you have for low-value output in mathematics is not unique to you. Talented mathematicians don't like it either. Your mistake is assuming that AI will cause math to be dominated by low-value outputs. In fact, the opposite is likely the case: the marginal value of proofs will fall so low that the bar for meaningful research will become dramatically higher, not lower. I expect the goals of research mathematics to become extremely ambitious relative to the past, organized around substantial and enormous goals, not mass-generated slop as you're imagining.

Of course, yes, there will still be lots of slop, just like GitHub is full of AI coding slop, LinkedIn is full of slop, etc. But that's a generalized issue of the AI era, not unique to math.

And that's an issue why? It would seem to me that producing that also produced the mathematics that revolutionized the world repeatedly for centuries. I would go further and claim that, if you want the mathematics that revolutionizes the world, there's no way to get it without advancing mathematics as a field broadly. Those are not two separate activities, and thinking that they are is indeed a misconception.

> This idea of trying to "prove all the math" with AI makes as much sense to me as using chess engines to try to "solve chess."

You're right: "prove all the math" does not make sense on any level, and nobody serious would phrase any of this in that way. I certainly didn't.

Let me make up an example of where I could imagine this going. Something we essentially cannot do right now is predict coarse-grained phenomena from systems that involve millions or trillions or more of interacting components. Over hundreds/thousands of years of experiment and theory we've derived laws that essentially do this in a few special cases, but we have no systematic theoretical way of doing it in general, and frankly I think it's beyond human ability. Whatever deep patterns or structures exist for doing this in a general way I think are simply out of reach for us.

Imagine if humans couldn't understand multivariable calculus, but we had access to an AI system that developed it, it initially seemed useless, then another AI system found a predictive model of electromagnetism using it.

Why does this tend to be the case, even when some of the smartest people in the world have historically predicted incorrectly that certain branches of math would forever be useless (e.g., number theory)? I can only offer my own theory on that, but my guess is that mathematics is simply a predictive framework based on pattern compression. A more powerful pattern compression framework accelerates every single field that relies on pattern recognition or prediction of the unknown based on patterns.

This is an extraction from that of the actual theorem statement (39 lines): https://github.com/openai/ten-proofs/blob/94bc0feb6a9ff12c7d...

SF and the Bay Area are constantly shuffling through and recombining ideas. What generated money relatively easily in 2010 would've started becoming low value in 2018, rapidly approaching an asymptote of relative uselessness today. 2018 is about the point where you needed to be pivoting to AI if you really wanted to remain part of the city's "upper class", where money feels like it doesn't matter because it's abundant and automatic. 2010 was the era of mobile apps.

I'm perfectly fine being the minority for now. You say that as if you think I'd have a problem with that. That does absolutely nothing to sway my thinking, which is based on my own principles, not a popularity contest at a single moment in time. You are dramatically underestimating my personal comfort maintaining an unpopular perspective for an extended period of time (years) based on fundamentals.

> Anyone with a $300 headset can stream games to it

No thanks. This is, of course, technically possible, but the quality is so astoundingly low compared to the Vision Pro that, for me, it would be a waste of time. You're welcome to do this if you so please with your time.

Besides that, I actually disagree that the Vision Pro is not good for gaming. It's not good for traditional VR gaming, but using apps like Portal it's phenomenal for, e.g., playing existing PS5 games on a massive virtual screen, which in many ways I actually enjoy more than VR gaming, which is far too limited in comparison.

First, the same kind of issue exists with any kind of testing. We all know that having unit tests and integration tests doesn't mean the software is correct and bug-free. Yet we still often believe it's worth investing in writing and maintaining a test suite. Formal methods is an additional level of assurance that I suspect we'd generally find worth it for critical software if it were easy enough to implement, even if it's not perfect.

Second, because formal verification has been so hard, nobody has really bothered making a serious attempt at solving the spec problem before (at least not to my knowledge). We've spent decades building frameworks that make writing tests really easy. We really have not come close to investing the same kind of effort into building frameworks and tools to make writing formal specs easy. I can imagine a world where we have sophisticated tools that help us create specs, plus real-time verification infrastructure that automatically reverifies code against the spec on each PR.

Third, and perhaps most importantly, there are many industries where this is actually low-hanging fruit: aerospace, medical devices, etc., actually already have formal specs that are verified manually by human engineers to satisfy certification requirements. I believe that's a more natural starting point vs. trying to scale formal methods for all software in general.

There's a kernel of a good idea in what you just wrote: open infrastructure can be part of a nation's sovereign technology stack. That's true, and Linux is indeed an example of it. But that has little to do with anything I claimed.

Linux is fundamentally not relevant because investing more in it does not confer exponentially increasing geopolitical leverage to a single nation uniquely above all others. Next-generation frontier AI, however, appears to have that property: if possessed by one nation, that sovereign production capability appears so far to confer exponentially increasing international leverage.