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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

#71
post #63
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

Intelligence was always relatively cheap. You can pick up a phone and get answers for free in most academic settings.

(within limits)

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

#72
post #27
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

Once we figure out the pesky problem of how we're going to pay for housing, food, and healthcare.

I think the big names behind the AI companies already have that problem solved. A lot of people probably won't like the solution very much though.

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

#73

Earlier quoted context omitted.

What a silly and obtuse comment.

[flagged]

And that's why you aren't qualified for a customer service role but might be for something that current AI is competitive with.

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

#74
post #7

What I'm feeling is that there's a need to study how to use AI well. I've seen professors using AI, and it was amazing. In that sense, I think AI prompt input will become stratified. In the past, implementation skills were very important, but these days, concepts feel more important this is one of those things. It's not that AI brings equality, but rather that the output varies depending on how much background knowle…

I actually think people who are great at understanding problems, coming up with requirements and designing solutions (all things I would expect someone who is good at churning out MVPs would be good at) are exactly the people most empowered by the current batch of LLMs. Its the people who are only good at working on small chunks of problems that I'm concerned about..

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

#75
post #8
post #3

[flagged]

Lean is the Mizar here. For those who have no clue what this is about, Mizar [1] was an early automated theorem prover. Can't wait for HN to add AI features to explain concepts in the sideline, and autovoting. [1] https://en.wikipedia.org/wiki/Mizar_system

Mizar is an early theorem prover. It still exists, see the 2025 issue of Formalized Mathematics journal [1] that publishes math articles formally verified by Mizar (since 1990).

[1] https://reference-global.com/issue/FORMA/33/1

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

#76
I know a bit about this field. This conjecture reads as somewhat more niche than the cyclic double cover conjecture recently proved by OpenAI, but nevertheless represents a real contribution.

You want to know how long it takes to solve an optimization problem, in this case over convex, lipschitz functions. (The restriction to a spherical domain is not really a restriction, you can just change variables for any bounded domain.) Anyway, showing upper bounds on time complexity is "easy" because it's just the runtime of your algorithm. Showing (nontrivial) lower bounds is usually much harder because it requires constraining all algorithms.

This proof apparently shows that the lower bound time complexity is equal to the time complexity of an existing 30-year old algorithm: it requires Omega(d^2) function evaluations to solve over this class of functions.

My gut says likely implies that d is the minimal number of evaluations if you have a gradient oracle because you can approximate a gradient with d function evaluations, but I'm not sure how hard it is to make that rigorous.

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

#77
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

If it were commonplace, there wouldn't be a post and discussion about it. Cheap? Arguable - while it didn't cost thousands, it wasn't free. Cheap is in the eye of the beholder. Efficient...How do we even measure that? The massive infrastructure and training to take a product to the point where someone could do this is massive. Ignoring everything behind the scenes and acting like one session and result is the whole p…

Seconded on the "not cheap" argument here. I've spent $25 worth of tokens completing a one-week task in an afternoon, or rather my company spent the money. I would never have personally felt OK with throwing this much money after some prompting back and forth for a few hours, one lazy Saturday afternoon. I ran the risk of not finding the solution before the token usage would be too high for me to want to carry on, if I was my own credit card linked to the account.

Of course money in this situation is a bit of a funny measurement, right, because if I was able to take the rest of the week off as soon as I had solved the one-week problem, then I would have no problem at all throwing even $100 worth of tokens at it, so I could enjoy a nice 4-day "mini-vacation".

How cheap "cheap" is, is indeed "in the eye of the beholder".

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

#79
post #31
post #27

Earlier quoted context omitted.

Once we figure out the pesky problem of how we're going to pay for housing, food, and healthcare.

When machines are doing all the work - we no longer have to.

Is that what you're going to tell your mortgage lender?

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

#80
post #31
post #27

Earlier quoted context omitted.

Once we figure out the pesky problem of how we're going to pay for housing, food, and healthcare.

When machines are doing all the work - we no longer have to.

> the couple multi-trillioners will have all the wealth of the world, and it will all crumble down

You mistyped it.

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