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Isn't it the passage of mathematics from the age of craftsmanship to the age of industrial making ?

My recent take on AI is that people haven't adapted to the new huge potential of the tool, and don't dream big enough (yet).

It's like seeing a car engine for the first time, lamenting about the future of horses, and not realizing it'll also help us fly.

To a first approximation I agree that it’s similar to industrialization. However there’s a key factor which distinguishes this case, and which makes the analogy less than perfect: there isn’t a profit motive in mathematics, so there was no push for this development from inside the field. Instead, the industrialization was entirely exogenous, from companies which do in fact have that profit motive and view math as a means to achieve it.

There might be a “proof motive” in math which one could argue will drive the full automation of theorem proving. But we must recognize that profit is more universally valuable (i.e. it has value outside the industry in which it was created), whereas proofs are only valuable inside the math community (at least the pure math proofs the labs have been publishing thus far).

It's more like opera. Math has always been opera.

Do rich people like opera? Yes. Is that a profit motive? No... but it's a shibboleth for wanting to be rich. Do you get it?

It's ridiculous to say, no profit motive in mathematics. It's like saying, no profit motive in LISP. But cmon, you think the Collison brother who took Math 55 and liked LISP: I know that in a pedantic sense what you mean. But in terms of academic departments where people say they are no interested in money and it turns out they want to become billionaires... Math Department ranks pretty highly. Always has.

I agree that being technically gifted has been a great way to make boatloads of cash in the past few decades, and that this correlates with being good at math. But I don’t see why this implies that enjoying math means someone is more money-minded than others. If anything, the students in pure math departments are intentionally forgoing the potential cash conferred by their technical abilities in favor of the academic pursuit. In anticipation of a reply observing that math PhDs regularly go into quant, I counter that quant programs reach out to interview students in many other fields, and more to the point, spending half a decade studying algebraic number theory is surely not even close to an efficient way to build wealth. In response to your second point: even if mathematicians desired wealth more than other professionals, how does this demonstrate the existence of some kind of profit motive in math?
>and don't dream big enough

People have been dreaming running PS5 games on PC for a long time. Just when AI starting to become capable of doing that, Anthropic shut it down.

Yeah you can dream, but only what we allow.

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1. That’s a legal grey area that could result in significant legal exposure for Anthropic.

2. Even if someone wants to do something that’s in a legal grey area, or more (hacking others, another item limited by Anthropic), is the idea that such people won’t have the ability to use AI to do those things? I don’t understand the criticism that just because one company might institute some guard rails that those who want to conduct legally grey or black activities will be unable to use other AIs to do so?

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This is really well put, I totally agree with you.

There’s an immediate resistance towards change rather than embracing it and finding opportunities to improve and work with it.

How do you expect mathematicians to "embrace" OpenAI having unreleased models that are much better at solving big-ticket problems than they are?

Maybe some math departments could pay OpenAI for access to their models, but I doubt OpenAI would want to deal with most of them.

That is a great example, car engines (and derivatives) did create tremendous economical value but are in the process of making our planet unhabitable.

Maybe we should listen to people that care about negative externalities more often, and actually mitigate them.

Unfortunately, I cannot think of a single politician right now who is a thought leader on regulating technology, which is exactly the kind of person we should be looking for. People who understand that we don't need every website to give us an annoying popup saying that they are using tracking cookies but we do need the option to opt out of AI features for basic services.
> every website?

What? Only websites that want to track you before opting in have cookie banners. HN doesn't have a cookie banner, in case you haven't noticed. I'd say your issue isn't with consumer protection, but with pushy marketing people (or worse). But they're good at marketing, hence the cookie banner nonsense complaints, which redirect the anger towards laws requiring that creeps announce their presence, rather than the creeps themselves.

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Two possible walls for advancing math with AI: first, it could be that the kind of problems that AI solves are the ones that don't open new avenues to concepts and ideas, and second, problems complexity is usually not linear, and the new and interesting problems to solve could be at a level of complexity beyond what AI can currently solve. Perhaps mathematicians could work to find ways to help AI cope with those walls.
How you get somewhere is important and tools change how you get there.

You can drive 1000 miles and arrive at the destination on the highway quickly.

Or you can take the slow road and walk. You discover unrelated things, make new relationships, see the scenery, listen and smell what is around you and have time to contemplate things which may or not be related.

This particular tool economy robs us of all these things in the rush to the destination.

I'd sacrifice "progress" a little for some of the better bits of humanity.

Do you feel robbed of your scenic expeditions because vehicles and highways exist?
Not OP, but actually I do because I have been forced to live in places where it’s dangerous to walk and where all the scenic landscape has been replaced with asphalt.

I get your point in general, but I think vehicles are a poor analogy because in many ways they have changed the places we live for the worse (and yes I’ll concede occasionally for the better). It turns out we need places to park all of these vehicles and they compete for space with humans.

Not really. I feel sad for the people who miss them.
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The thing is that if you don't learn to drive some destinations are unachievable. And destination is more important than the journey unless you travel for pleasure or personal development.
There are many more places you can't drive. I've walked to quite a few of them.

That analogy holds too.

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No one forces you to drive. You can still walk.
But it now takes 3 times as long because you constantly have to cross roads.
They build cities around the car, they defund public transit, they close down rail lines, they build new housing a 5 km away from your closest grocery store, and 20 km away from any cafés and other cultural venues. Your job is located 50 km north of where you live, your partner’s job is 60 km in the other direction, and your child’s school is 10 km in the third direction.

They neglect to build sidewalks, and force you to walk 1-2 meters from cars racing at 70 km/h. With all the noise and high risk stressing you up to the level you just wanna scream.

stevenhuang: No one forces you to drive. You can still walk.

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It's pretty well documented they deliberately made things impractically large distances apart and scrapped the idea of footpaths, to encourage car sales, paid for by car companies to your local city government several decades ago.
But Terry T said I have to drive or die.

Or has he changed his mind again.

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Yes, this. Unless there is a true singularity where no more questions are ever asked, there will be definition be infinitely many problems to solve, and most of them we have not even glimpsed yet.

Singularity? Probably not.

Tech bro dictatorship? Unfortunately a bit more likely.

None of the above? Then we have a small shot at a great future.

Having a machine that solves hard problems must be a good thing.

Solving the hardest problems doesn't always result in the best outcomes unless the answers are shared equitably and implemented compassionately.
Absolutely. This is an aspect of the tech bro dictatorship.