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After Math

terrytao.wordpress.com

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Re: After Math

#161
post #7

Wouldn't AI make the field of mathematics more ambitious? In software development it feels that way: there are often tasks I can take on that would have been too risky in 2025, because it was unclear if they were worth it. Now you generate a prototype and can make much better judgement calls what is possible and what is worth pursuing.

It might feel that way, but I'll ask again: where's the payoff? Where's all the amazing software that everyone is now supposedly shipping 10x faster than before? If I look at the software I'm actually using day-to-day, or that my friends are using, all this stuff looks exactly the same as it did in 2021. Not a single product release from Google, Microsoft, or more scrappy companies in the past 6 months made me go "wo…

All vibe-coded software is complete unusable trash. There are no exceptions.

So no, we're not advancing, we're in fact regressing. The crash and disillusionment of the post-vibe-code world will be immense.

Re: After Math

#162
post #52

Earlier quoted context omitted.

> temporary state of complete loss of personal purpose and the experience of existential dread from never achieving self-actualization in spite of the tremendous time commitment towards excellence in a now automated intelligence > this will be a universal feeling for every human for the rest of existence As someone that has accepted a very long time ago that nihilism is the only self-consistent philosophy, I've made…

I’m glad you found something that works well for you. For me, nihilism is much like ice cream: I don’t want it in my fridge - not because I think it’ll taste bad, but because I think it’s gonna taste real good.

I'd rather compare it to Linux. You are in charge of your own destiny.

Re: After Math

#163
post #115

Earlier quoted context omitted.

I mean it doesn't have to bring 10x more value, but it can be a 10x better experience for existing users. There have been so many niche bugs that were never ever fixed because there's more important things to do, but because fixing a niche bug is now 1 click away that really changes the economics quite a bit especially for small teams. I'm personally working on a product solo that would not be possible without a team…

With all due respect when you strip away the noise - unless it shows up in the financials it hasn’t done anything for the firm. This is something many firms are struggling to grasp.

The world does not revolve around money, specifically non profits come to mind where this can be a huge boost in quality for everyone involved.

Re: After Math

#164

This kind of argument is always dangerous, because it essentially resorts to moving goalposts. "Oh, AI can now do X? Sure it is amazing, but it can't do Y yet, so we're totally safe!" Just because humans can't process the proof or see the advancements, it doesn't mean that it will remain that way in the future or that it will not change the field. If you only define yourself by things AI can't do yet , you're about t…

> This kind of argument is always dangerous, because it essentially resorts to moving goalposts. Nope, introspecting motivation is useful. There have been similar posts made about people using bots in PvP competitive online gaming: some people play to enjoy the game, and hopefully get better until they reach their skill ceiling. Others play (just)to win, and are open to buying aimbot hardware and software

>introspecting motivation is useful

Not if the essence boils down to moving goalpoasts to the next best thing that will likely be flown past as well within months rather than years. Sure mathematicians who do this stuff purely for the love of it will continue to exist. Just like human chess or the retro-programming scene exist for similar reasons. But if you are a professional who expects to earn a living salary on these things, your intellect will suddenly be outcompeted by orders of magnitude. Ignoring this today by saying LLM's can't do this or that will undoubtedly set you up for a rude awakening. For all we know is that there is still no fundamental limit to what they can do in theory and compute may well be the only true limit.

Re: After Math

#165

This kind of argument is always dangerous, because it essentially resorts to moving goalposts. "Oh, AI can now do X? Sure it is amazing, but it can't do Y yet, so we're totally safe!" Just because humans can't process the proof or see the advancements, it doesn't mean that it will remain that way in the future or that it will not change the field. If you only define yourself by things AI can't do yet , you're about t…

If you ask an AI if "P=NP", it will certainly give an answer. It has to, because the answer is either "yes" or "no". If you ask it to then prove its assertion, it will then certainly output the tokens that look like a plausible proof. It has to, as it is programmed too. This "proof" might even be thousands of pages of very technical looking and professional sounding jargon. It's not a real proof though, and as an art…

That's why this proof and all the other high profile AI proofs were written in lean, which allows you to verify them in a formal deterministic language. You still might not understand it as a human, but any computer with a simple processor can verify the proof's correctness. And from there you will undoubtedly see other people make sense of the proof's key steps using AI too. And the models might even pick up on further details useable for other proofs that humans didn't see. In the end I'm 100% convinced that abstract math will eventually be primarily done by computers, similar to how linear algebra and numerics have been done exclusively done by computers for a while. Noone would even consider multiplying a 100x100 matrix by hand anymore, if only because it is much more likely that you as a human will make a mistake.

Re: After Math

#166

Earlier quoted context omitted.

This is incredibly related to how people seek meaning in family, friends, or (hardly foolproof) new experiences. Because careers, skills, and other society-wide abstract purpose no longer provide a stable identity based on monthly guarantees of dopamine. In a sense, programming (et tu, mathematics) has become a bullshit job. Though, it will take some time (~6 months) before "fulltime" investors or serial SaaS founder…

There are examples of foregoing the use of known tech, like the Amish, but it really means a deep break with the western ethos and takes something like a deep committing to a religion to carry out. The default is that you work on things with the honest goal of making it work. Yes, we've become too good at making tech But a balance of camaraderie in honest effort, but not quite as much to be really successful is a kni…

Sisyphus is apt because he was "punished" by a superhuman entity for doing basically the right thing (from a mortal's pov). Doesn't it remind of alpoge, who tried to keep it as traditional as was possible? Nice one!

Then there were the brothers Epimetheus and Prometheus. One was a thief and one was implicated in the opening of Pandora's box. Who is an inspiration, who was punished? (With the caveat that it should have been climate-neutral electricity he stole, not fire.)

So the heuristic seems to be: if you come up on the wrong side of AI, you did the right thing. Ikarus was not wrong to try.

Re: After Math

#168

I think as a civilization we need to postulate a new term: “purpose death” Defined something like: temporary state of complete loss of personal purpose and the experience of existential dread from never achieving self-actualization in spite of the tremendous time commitment towards excellence in a now automated intelligence. I truly think because of the pace of innovation this will be a universal feeling for every hu…

> I’d say Terrance has recently left the denial phase, the anger phase I’m sure he wisely kept off the Internet, and is currently in the bargaining phase - ie scrambling to change the goal posts. I wonder if he will wisely keep the depression / burnout phases also off the internet. You're making up a narrative about another person. You have no clue what's happening to him, without talking to him.

Yes, I am making up a narrative. That’s why I used words like “postulate”, “think”, “I wonder”, and “I may be wrong”.

Re: After Math

#169

Earlier quoted context omitted.

> I’d say Terrance has recently left the denial phase, the anger phase I’m sure he wisely kept off the Internet, and is currently in the bargaining phase - ie scrambling to change the goal posts. I wonder if he will wisely keep the depression / burnout phases also off the internet. You're making up a narrative about another person. You have no clue what's happening to him, without talking to him.

Yes, I am making up a narrative. That’s why I used words like “postulate”, “think”, “I wonder”, and “I may be wrong”.

As a reader, it’s very off-putting. Spinning a story about someone, without first verifying whether it is at all close to the truth.

I trust the opinions of people that tend to be close to the mark. By shooting wildly, you’ve lost my trust.

Re: After Math

#170

Earlier quoted context omitted.

> This kind of argument is always dangerous, because it essentially resorts to moving goalposts. Nope, introspecting motivation is useful. There have been similar posts made about people using bots in PvP competitive online gaming: some people play to enjoy the game, and hopefully get better until they reach their skill ceiling. Others play (just)to win, and are open to buying aimbot hardware and software

>introspecting motivation is useful Not if the essence boils down to moving goalpoasts to the next best thing that will likely be flown past as well within months rather than years. Sure mathematicians who do this stuff purely for the love of it will continue to exist. Just like human chess or the retro-programming scene exist for similar reasons. But if you are a professional who expects to earn a living salary on t…

> But if you are a professional who expects to earn a living salary on these things, your intellect will suddenly be outcompeted by orders of magnitude

Which organizations do the most math research? What are their budgets, droves and culture? You may be falling victim to the pre-IPO PR razzle-dazzle by AI companies expending unreasonable resources on problems they know will get them good press and make their models appear superhuman.

A university math department will not spend $20M in one summer to solve 1 problem when it can hire 10 human mathematicians for 10 years.

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