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GPT-5.6 used a prompt to close a 30-year gap in convex optimization

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Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#141

Post by bwestergard »

mw67 wrote: post #14

Crazy how intelligence is cheap, efficient and commonplace now. We humans better refocusing our energy on our core values/principles, given most of our skills are becoming irrelevant

A counter argument: A strong distinction between "intelligence" (understanding what is) and "values/principles" (understanding what ought to be) was characteristic of much early modern European philosophy from Descartes to Kant, which received its influential strong formulation from David Hume.

But trying to maintain this distinction leads to insuperable difficulties. Our conceptual framework for understanding the world are always value-laden. There is no "view from nowhere", no historically unconditioned set of values or concepts. Your framing, in which "values" are external to "intelligence" and must be imposed on it (on pain of intelligence being "value-neutral"), leads inevitably to the dead end of "AI Alignment", "superintelligence", etc. Which is a kind of pseudo-theology.

"We humans better [be] refocusing our energy on our core values/principles, given most of our skills are becoming irrelevant."

In light of the untenability of a strong fact/value or intelligence/ethics distinction, I would suggest this alternative advice: humans should focus on critical appropriation and extension of the received wisdom, whether that comes to us directly from human beings or indirectly through an LLM. Perhaps this is compatible with the spirit of your original suggestion.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#142

Post by slashdave »

mw67 wrote: post #14

Crazy how intelligence is cheap, efficient and commonplace now. We humans better refocusing our energy on our core values/principles, given most of our skills are becoming irrelevant

Iteratively leaning on lean to prove a conjecture is not intelligence, it is automation

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#143

Post by jethkl »

amelius wrote: post #70
mw67 wrote: post #14

Crazy how intelligence is cheap, efficient and commonplace now. We humans better refocusing our energy on our core values/principles, given most of our skills are becoming irrelevant

Everybody can be an armchair mathematician now. Just fling some thoughts in the direction of your AI setup and let it do breadth first search with AI based pruning heuristics.

I generally agree, though direction, intuition, and domain knowledge are still relevant. Your breadth-first-search framing feels right, but you still need a sense of which paths are worth following, and you need to know when to trust the results.

I’ve been doing more math as a hobby in the past few weeks — working on lesser-known conjectures and exploring proofs of hard theorems — than I could have managed over the previous several years. It’s an exciting time.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#144

Post by slashdave »

sashank_1509 wrote: post #116

This is all a depressing and bleak future that I don’t look forward to. One solution is to ban LLM’s, to artificially create a demand for human thought, that just feels like living in an artificially constructed zoo. Another solution is humans don’t do anything that AI can do better , / doesn’t need the human touch. So I suppose we will all become artists, sportsmen or politicians, the only jobs that will remain exce…

There is more to human life than programming and math proofs.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#145

Post by xorcist »

p-e-w wrote: post #139
Quothling wrote: post #88

Earlier quoted context omitted.

Around here AI isn't really more of a threat to juniors than it is to seniors. It's a threat to the people who have been taught "recipies" rather than applied computer science. You can have excellent seniors who can do TDD, DRY, SOLID and so on, who also happen to have no idea what a L1 cache miss is. The current AI models know all of those things, but they struggle applying them correctly without someone piloting th…

Unless you’re claiming that AIs will suddenly (and very soon) stop improving, they are obviously a threat to everyone’s job. Calling notable conjectures that have been open for decades “low-hanging fruit” is an act of desperation. Most professional mathematicians couldn’t have proved those conjectures if their lives depended on it.

The thought that anything could improve without bounds would be absurd. We are living in the physical world after all. The (open, interesting) question is how close we are to the limit.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#146

Post by slashdave »

threethirtytwo wrote: post #108

Genuine question: If you still or did think LLMs are just stochastic parrots that just summarize everything and have no form of creativity, what do you think after seeing results like this? I'm very curious how people reconcile their fear/hatred of AI with actual objective reality. This is actually what interests me most about the whole AI thing. How we tell ourselves what we tell ourselves.

Must be nice knowing you have a clear understanding of "objective reality" that others don't.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#147

Post by zarzavat »

Quothling wrote: post #88
rakel_rakel wrote: post #29

> I don't think researchers in math/TCS will be made obsolete, but I think it will instead no longer make sense to work on any low-hanging, or even medium-hanging (you know what I mean) fruit. We'll be needed for problems where actual novel approaches are needed. I wonder how this compares to what we see happening with "juniors" in software development? In math research, do you also get the training for the professio…

Around here AI isn't really more of a threat to juniors than it is to seniors. It's a threat to the people who have been taught "recipies" rather than applied computer science. You can have excellent seniors who can do TDD, DRY, SOLID and so on, who also happen to have no idea what a L1 cache miss is. The current AI models know all of those things, but they struggle applying them correctly without someone piloting th…

AI is a threat to everyone. People who claim that AI will never be able to do X have consistently been proven wrong.

The only people who are safe are those whose jobs depend in some way on their humanity. e.g. yoga teachers, bouncers, etc

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#148

Post by skybrian »

p-e-w wrote: post #139
Quothling wrote: post #88

Earlier quoted context omitted.

Around here AI isn't really more of a threat to juniors than it is to seniors. It's a threat to the people who have been taught "recipies" rather than applied computer science. You can have excellent seniors who can do TDD, DRY, SOLID and so on, who also happen to have no idea what a L1 cache miss is. The current AI models know all of those things, but they struggle applying them correctly without someone piloting th…

Unless you’re claiming that AIs will suddenly (and very soon) stop improving, they are obviously a threat to everyone’s job. Calling notable conjectures that have been open for decades “low-hanging fruit” is an act of desperation. Most professional mathematicians couldn’t have proved those conjectures if their lives depended on it.

I wouldn’t call it “low hanging fruit” but it’s easy to think of problems that seem harder. Apparently solving notable math conjectures is easier than building a practical robot to deliver a package to someone’s porch?

So, yes, AI is a big deal and we don’t know what it’s going to affect, but the goal of replacing everyone’s job is extremely ambitious and there’s a long way to go.

This has to be assessed separately for each kind of job.

Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization

#150

Post by tripleee »

mw67 wrote: post #14

Crazy how intelligence is cheap, efficient and commonplace now. We humans better refocusing our energy on our core values/principles, given most of our skills are becoming irrelevant

how much can I bill for having good core values?
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