I think that would only follow if the rest of the world’s purchasing power also grows at the same rate (unlikely), or if you were to cease all international trade (uhh…).

> An AI-generated solution always provides ... proof that there is a solution

This is only true in the most trivial sense. A solution is a solution, sure... but how do you know it's a solution, and not an incoherent jumble of words? A human has to review and vouch for it.

Just because the AI gives you an arxiv-worthy PDF, or a Lean proof which compiles, doesn't mean it proves what the AI says it does. The AI could give you the same PDF/Lean code and says it proves the opposite, how would anyone know the difference?

You can't advance human understanding unless you produce things that humans can understand.

Not an expert by any means but the assumption here as I understand it is that the arxiv worthy PDF would not be acceptable or meaningful for impossible to understand proofs. And the lean proof would be meaningless unless the specific expression being proven is human understandable as the direct translation of the question the human is asking in formal form. So proving the negation is not a thing but if you make a subtle mistake in translating the statement you want to prove then obviously the QI is going to be proving the wrong thing. And otherwise you're relying on the correctness of lean as a system and on identifying/preventing if the proof is adversarially exploiting bugs in lean to falsely prove things.

> Just because the AI gives you an arxiv-worthy PDF, or a Lean proof which compiles, doesn't mean it proves what the AI says it does. The AI could give you the same PDF/Lean code and says it proves the opposite, how would anyone know the difference?

> You can't advance human understanding unless you produce things that humans can understand.

And you can't advance human understating unless you maintain that understanding.

I can see a version of the junior software engineer problem here: AI wrecks the problems that could train and motivate the next generation mathematicians, so students abandon the field because there's no place for them. The senior mathematicians who can review/vouch/prompt for AI output like Tao retire and die. Then there's no more math that anyone can understand and no more open problems for it to solve.

And that's probably happening already. I've read articles about AI performing the journeyman work that mathematicians cut their teeth on, rendering years of work obsolete, and derailing the careers that work was meant to start.

That was exactly my thought - taking out the problems that PhDs and early stage researchers work on kills the pipeline of developing mathematicians

That's why the solution should be presented in a verifiable formal language, such as Lean. Which is the case with the Navier-Stokes problem.

I might be wrong, but making an assumption that you could learn to read the mathematical output of the AI long before you could write a solution yourself. But hey, what do I know, I'm not a mathemagition.

What does "mathematical output of the AI" even mean? A proof? Intermediate tokens?

It's a Lean program that proves the theorem.

This is already a thing? Just replace “robots” with “machines”.

And yet I see videos all the time of Indians running contraptions straight out of the steam age in their shacks to make plastic straws or sandals. Or just doing it by hand. Better machines to do these tasks already exist, but are obviously too expensive for them to afford. Why would these hypothetical robots be any more affordable or disruptive to Indian workers in particular?

If anything I think American blue collars would be the ones to worry about.

Yes, can confirm. Labor is extremely cheap in India, which makes any automation too expensive. The offering would have to be drastically cheaper. Small to medium businesses don't usually buy machines/software unless absolutely necessary, because they can simply throw more people at it for a fraction of the cost.

> It’s very easy to send an AI agent on an open-ended bug hunt, and if it wastes a bunch of time and effort and finds nothing, no big deal.

No big deal? It’s not like it’s free… tokens cost money.

Often rounds to free compared to human costs.

When talking about LLM tokens the cost is almost always being implicitly compared to very expensive human developer time.

Sort of. For me it’s more like seeing out of a third eye (while also seeing out of your real eyes). Like how if you put your finger right in front of your face, you can see two images of it at once. With concentration I can ignore what my real eyes are seeing to prioritize the visualization, but the real eyes are constantly pulling my concentration back.

One thing you notice running NoScript is how prevalent Google is.

Even if a site doesn’t monetize with Google Ads, there’s a decent chance it’s pulling a script from ajax.googleapis.com, and Google still knows that you visited the site from the Referer of the script download.

And lucky for Google, browser vendors (including Google) even decided that caches shouldn't work cross origin so this request needs to be made for every site even if you already visited another site that used the same resource.

If what you’re saying is true, what’s the use (or even meaning) of being “all in”? You’re a rock either way.

It's not there yet, and every move we're currently making is towards an extremely inequitable future. Unless things change, not everyone is going to benefit from AI. What are you doing today to end up on the team that wins?

Once AI starts under its own direction, human brains won't be competitive. It feels like we're a breakthrough or two away, and with trillions of funding, we'll get there. Every dollar we spend on Claude subscriptions gets us closer.

> Unless things change, not everyone is going to benefit from AI. What are you doing today to end up on the team that wins?

It is going to be a tiny minority of people who "win". The other 99.5% of humans will just be losers who, what, die in the streets? This argument reminds me of Roko's Basilisk. "The humanity-ending torture-loving Basilisk is coming whether you like it or not, so come over here and help me build it!"

This is where I’m at as well. If it needs to change too much to do what I want, I take that as a sign to either (1) ask for a change that is easier to review, or barring that (2) pivot to refactoring the codebase until it becomes a change that is easy to review.

Ironically, even in this era of cheap and instant code, what works best (for me) is still to write as little code as possible.

Being “verified in Lean” doesn’t magically solve the problem of hallucinations unfortunately.

It just shifts the work from

> reading the (natural language) proof and confirming it has no errors

to

> reading the Lean code and confirming it correctly encodes the theorem

For example here is a statement of the Pythagorean theorem in Lean:

theorem EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two {V : Type u_1} {P : Type u_2} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P] [NormedAddTorsor V P] (p₁ p₂ p₃ : P) : dist p₁ p₃ * dist p₁ p₃ = dist p₁ p₂ * dist p₁ p₂ + dist p₃ p₂ * dist p₃ p₂ <-> angle p₁ p₂ p₃ = Real.pi / 2

This is just one possible way of formalizing it and it depends on other definitions, wherein you also need to understand the assumptions they make, etc.

Answering the question of “whether proving this theorem in Lean proves the Pythagorean theorem” thus requires expert judgement as well as domain knowledge of Lean’s libraries.

So if the AI says “this theorem is true, here is the proof in Lean” it’s still possible that it’s not correct, even if the Lean code compiles. The result will still be in question until a human expert reviews it.

I’ve found it depends on where I connect from. If I’m using my home WiFi, it works. If I use 4G or a VPN, I get the login prompt. Still seems to work on my WiFi at the moment.