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.
GPT-5.6 used a prompt to close a 30-year gap in convex optimization
71–80 of 414 posts
Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization
#72Crazy 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.
Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization
#73Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization
#74What 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…
Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization
#75[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
Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization
#76You 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
#77Crazy 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…
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
#78Crazy 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
Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization
#79Re: GPT-5.6 used a prompt to close a 30-year gap in convex optimization
#80Earlier 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.
You mistyped it.