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No country for mediocre mathematicians

garvvee.substack.com

111–120 of 159 posts

Re: No country for mediocre mathematicians

#111

Earlier quoted context omitted.

Yes, I think we will continue to have hobbyist learners as we advance AI, but it's going to be a niche, and not a commercially viable one.

Do you think commercial viability will continue to be viable?

Who knows. I hope we figure out how to align the AI so that there's a sustainable economy for the majority of humanity, but I'm not in a position to influence that. I can just do my best to make myself less likely to be crushed.

Re: No country for mediocre mathematicians

#112
As a middle-aged mathematician, AI is provoking a serious crisis among the better mathematicians I know. Many are only half jokingly talking about retiring. We use AI a lot in research already and it's obvious that whoever doesn't will fall behind fast. At the very least it gives access to the full library in a few minutes, serving as a kind of knowledge oracle generally more useful than the expert who ought to be in the office next door but isn't. And we see what can happen when it is effectively coupled with lean to automate theorem proving and discovery.

We aren't dumb enough to see this as the end of the profesión - Esther it's clearly a shift in how we will work - but we like doing computations and playing around with examples and how one does that just changed a lot. The other problem is we know we don't have the energy of youth to learn to use AI as effectively as the kids, although we are wiser and have better judgment and do know some things.

Mathematicians who are not taking seriously how to adapt to AI are deluding themselves.

Re: No country for mediocre mathematicians

#113

Earlier quoted context omitted.

Engineers know what needs to be tested, how, to what degree, with which materials, and with what safety margin. AI can be trained on that body of work. But then AI has enough issues in output that it needs to be verified. Otherwise we'll live in a world of titan submersibles ordered by CEOs running on hopes&dreams.

Replace "AI" with "humans" and you get the same exact issues. Believe it or not, engineers don't zero shot skyscrapers either. Which is why their work gets reviewed by more engineers. Which catches the issues before they materialize. Sometimes! What's the dreaded impossible-to-replicate human advantage? Because I'm not seeing any.

I think we might be largely in agreement.

LLM's should be used to speed up the drudgery, explore creative/evolutionary ideas, but....

> What's the dreaded impossible-to-replicate human advantage?

Responsibility.

Ultimately LLM's are a tool. Someone has to be responsible for the output. You don't get to use it to create a car/plane/submarine/bridge/building/childs-toy/whatever and then if it bursts into flame, blame the LLM and walk away.

Ideally, the person signing off would "know" what they are signing off on. Which requires an engineer.

Re: No country for mediocre mathematicians

#114
post #47

Earlier quoted context omitted.

> what the point of doing research was if someone like Terence Tao could have figured out everything A similar question is now being asked: what is the point of doing research, etc. if something like AI can figure out everything? The question betrays the parochial way in which many people think about knowledge. For them, knowledge is merely an instrument or an effect. It does not occur to them that knowing is a valua…

This is why I still like solving software problems on my own. Because those solutions now live in my head, rather than being spit out by some agent and then disappearing from the Dixie Flatline's memory once the session shuts down. And they deepen and enrich my life, and my life deepens and enriches them. A brief example: When I was a teenager I had the most profound crush on a girl, as teenagers do. Gorgeous and gre…

They might be able to have that insight, but I highly doubt they would be able to have a profound crush on her. Which might matter more.

Re: No country for mediocre mathematicians

#115

Earlier quoted context omitted.

Replace "AI" with "humans" and you get the same exact issues. Believe it or not, engineers don't zero shot skyscrapers either. Which is why their work gets reviewed by more engineers. Which catches the issues before they materialize. Sometimes! What's the dreaded impossible-to-replicate human advantage? Because I'm not seeing any.

I think we might be largely in agreement. LLM's should be used to speed up the drudgery, explore creative/evolutionary ideas, but.... > What's the dreaded impossible-to-replicate human advantage? Responsibility. Ultimately LLM's are a tool. Someone has to be responsible for the output. You don't get to use it to create a car/plane/submarine/bridge/building/childs-toy/whatever and then if it bursts into flame, blame t…

What happens when the thing they have to be responsible for takes multiple lifetimes to understand on even the most basic level, let alone know deeply enough to feel comfortable taking responsibility for it?

Re: No country for mediocre mathematicians

#116
post #96

Earlier quoted context omitted.

Im going with this... scifi stuff still requires engineers. Its laughable and insulting to think these billionaire owners are going to make robots and llm loops to get real shit done https://rcsnyder.github.io/open-frontier-curriculum/ Ya "claude can you build me the next cern Thanks"

If you want AI-proof careers it seems risky to go into knowledge work at all. Robotics lag behind mere computation, so something where you do awkward work in places designed around human bodies seems a lot safer. Plumbing, landscaping or something like that perhaps.

This is a romantic and very appealing idea that flies in the face of reality. The market for skilled trade workers like plumbers, electricians, landscapers and so on is more or less in equilibrium, and the demand side of it is relatively inelastic. Dumping hundreds of millions of new workers into these trades will not increase demand sufficiently to let anyone earn a viable living from them.

Re: No country for mediocre mathematicians

#117

Earlier quoted context omitted.

I think we might be largely in agreement. LLM's should be used to speed up the drudgery, explore creative/evolutionary ideas, but.... > What's the dreaded impossible-to-replicate human advantage? Responsibility. Ultimately LLM's are a tool. Someone has to be responsible for the output. You don't get to use it to create a car/plane/submarine/bridge/building/childs-toy/whatever and then if it bursts into flame, blame t…

What happens when the thing they have to be responsible for takes multiple lifetimes to understand on even the most basic level, let alone know deeply enough to feel comfortable taking responsibility for it?

Again, engineers know what needs to be tested, how, to what degree, with which materials, and with what safety margin.

Your widget that mankind may never understand. Well, that's just like anything else in the world. Engineers didn't understand building foundations to anywhere like the degree we do now. Or how to build earthquake proof buildings for a long time. It didn't stop stuff getting built. But it sure affected the confidence in it.

And when they honestly don't know, they don't have to approve it.

I cited the Titan sub example because one engineer refused to sign off on it and was fired for it. Whoever signed off on it has deaths to weigh on their conscience/reputation - for whatever societal good that is worth.

If the latest electric vehicle car never needs to charge but might catastrophically explode randomly between 2-15 years, then the car company doesn't get to take money for the car but handwave away the deaths caused. Legally someone is on the hook. In this case, the engineer who signed off on the magic involved - whether they understood it or not - is at fault.

But honestly, people sign off on shit they don't understand all the time. It's a matter of:

1. did their gamble not pay off?

2. were they negligent?

If your answer to 2. is "the LLM made a mistake I never checked for in regulation approved ways", then you are negligent.

Re: No country for mediocre mathematicians

#118
post #96

Earlier quoted context omitted.

If you want AI-proof careers it seems risky to go into knowledge work at all. Robotics lag behind mere computation, so something where you do awkward work in places designed around human bodies seems a lot safer. Plumbing, landscaping or something like that perhaps.

This is a romantic and very appealing idea that flies in the face of reality. The market for skilled trade workers like plumbers, electricians, landscapers and so on is more or less in equilibrium, and the demand side of it is relatively inelastic. Dumping hundreds of millions of new workers into these trades will not increase demand sufficiently to let anyone earn a viable living from them.

There is nothing that can absorb millions of new workers. If AI destroys jobs to that degree pitchfork manufacturers will be the only ones left in business.

Where I live at least right now it is quite hard to find contractors for anything and many are close to retirement age and have a hard time finding replacements.

Re: No country for mediocre mathematicians

#119

Earlier quoted context omitted.

> Is there’s something more to that? Yes: this is about building the quotient field (field of fractions) [1] for some integral domain, or more generally, building the localization ([2], [3]) of a commutative ring with respect to some given set that is closed under multiplication (the special case of the quotient field for a ring R is obtained when one chooses R\{0} as such a set). -- [1] https://en.wikipedia.org/w/in…

Don't we still teach kids that e.g. 3/4=6/8, that they need to make a common denominator to add, and that they should cross multiply to check equality? I suppose we don't teach zero divisors, but otherwise, jargon aside, I'd be hard pressed to explain how we don't teach kids that fractions are members of ZxZ* mod (ad-bc). Lies to children are like... time-reversal symmetry.

I don’t think it is lying, it’s just simplified so they could learn one skill at a time.

Re: No country for mediocre mathematicians

#120

> We're all frustration addicts. We just want to bang our heads against problems we don't yet know how to solve. I've been tapering off AI lately. I think I've realized that conquering the struggle is the fun part, and accomplishments just don't hit the same if AI is smoothing over every friction and cordoning off all the pitfalls and rabbit-holes.

I hate struggling. I hate the realization that comes after the struggle about how easy was the problem I tried to solve. I hate realizing that I only reduced the number of problems from infinity + 1 to infinity, and have to do it again, forever.

Yet I also hate when I get away from solving problems and feel like I'm wasting my life with nothing to show for it.

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