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An OpenAI model has disproved a central conjecture in discrete geometry

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Re: An OpenAI model has disproved a central conjecture in discrete geometry

#571

Earlier quoted context omitted.

I think when your work is no longer required, you will probably come to regret this sentiment, not that it matters.

I think by that point humanity will having some pretty fundamental discussions about the nature of work and money.

I think you are blinded by an unprecedented optimism the rest of us simply cannot afford to entertain.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#572
post #333

Earlier quoted context omitted.

Clearly you've never supervised junior developers.

That's literally my job...

>That's literally my job...

Since you’re not in a unique position, I can confidently state that your comparison of LLMs to jr developers seems unfounded. Today, LLMs produce code that is superior to junior developer code by an order of magnitude.

Notably, they demonstrate consistent syntax, clear separation of concerns, strong test coverage, organizational rigor, idiomatic API usage, and the ability to generate and maintain documentation, among other measurable qualities.

LLMs generally operate at a staff engineer level for a number of languages and ecosystems (including polyglot projects).

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#573

See the longstanding debate on whether new math is "invented" or "discovered". Most mathematicians I knew thought it's discovered.

This is like saying a sculpture always existed, the sculptor just had to remove the superfluous material. Or like a musical octave has only 12 semitones, so all music is just a selection from a finite set that already existed. Sure the insane computation we're throwing at this changes our perspective, but still there is an important distinction.

Michelangelo never used references, instead he simply "freed" the sculptures from within the marble.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#574
post #220

Earlier quoted context omitted.

>Police officers are human. In the United States in the vast majority of cases you can't sue the police, only the community responsible for them. Police are a monopoly; nobody has a choice about which police company to use. McDonalds are not a monopoly, and many customers would prefer to eat at competitors run by entities that could be sued or jailed if they did anything particularly egregious.

You are missing the point. The point is you can still sue the McDonalds. With the police there is a human intuition to also want to sue the officer, given the officer is a human being who has free will and thus made a choice to violate your rights. The same intuition applies if you walk into McDonald's and a person there mistreats you. You want that person held responsible. But the LLM is not a person. What is there…

can you give a more concrete description of a McDonalds LLM mistreating a customer? it's gotten to abstract

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#575

As I have stated before, AI will win a fields medal before it can manage a McDonald's A difficult part was constructing a chess board on which to play math (Lean). Now it's just pattern recognition and computation. LLMs are just the beginning, we'll see more specialized math AI resembling StockFish soon.

I dunno. Is AI less than forty years old?

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#576

Earlier quoted context omitted.

Why would it excite you, rather than terrifying you? The better LLMs get at math, the closer the expertise you spent your whole life building is to being worthless. Along with all the rest of what humans find meaningful and fulfilling.

Does it terrify you to look at children? Not so many years from now, some of them will surpass you. A few years after that all (that survive to that point) will surpass you. Does that terrify you just as much?

That’s kind of a strange comparison. It’s the natural order for a population to thrive, reproduce, age, repeat. I’m not taking a side on the original comment, but the idea of human skill being completely supplanted by AI is not the same thing as having children and getting old.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#577

Speaking as a postdoc in math, I must say that this is rather exciting. This is outside of my field, but the companion remarks document is quite digestible. It appears as though the proof here fairly inspired by results in literature, but the tweaks are non-trivial. Or, at least to me, they appear to be substantial to where I would consider the entire publication novel and exciting. Many of my colleagues and I have b…

Why would it excite you, rather than terrifying you? The better LLMs get at math, the closer the expertise you spent your whole life building is to being worthless. Along with all the rest of what humans find meaningful and fulfilling.

Many of us don't do what we do for our expertise to be recognized or valued by others, rather that is a pleasant side effect. Many of us do what we do for intrinsic reasons related to the nature of the work, and would likely do it for free, or indeed, would pay for the opportunity. Many STEM-types are in this category, and as such, are compelled to continue to tinker as we fancy, and are glad for more tools to help us expand the breadth of our tinkering capabilities.

A dedicated engineer is always looking to automate themselves out of existence, so that they can move on to the next thing to automate. Ongoing repetitive work is less engineering and more akin to toiling on a line.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#578
post #153
post #46

Earlier quoted context omitted.

I disagree. It will be able to perform work deserving if a fields medal before it is capable of running a McDonalds. I think it will be running a McDonalds well before either of those things happen, and a fields medal long after both have happened.

One could hardly ask for a task better suited for LLMs than producing math in Lean. Running a restaurant is so much fuzzier, from the definition of what it even means to the relation of inputs to outputs and evaluating success.

I think Lerc is saying that LLMs will be pressed into service managing McDonald's restaurants long before they are actually capable of managing said restaurants successfully.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#579

Earlier quoted context omitted.

Because for many people who pursue these fundamental truths, the reward is not necessarily personal fame, fortune, or even personal understanding. Advancing humanity's total knowledge (even if that knowledge is by proxy through AI) is reward enough.

I think when your work is no longer required, you will probably come to regret this sentiment, not that it matters.

There's an unstated assumption there, which is that you'll have some reason to continue to want your work to be required.

In the (probably unlikely) event that AI use results in a post-scarcity economy in which there's no need to work to survive, a lot of people wouldn't regret sentiments like the ones in question.

On the contrary, it would mean they could work on whatever they please, including potentially standing on the shoulders of giants - the AIs - and seeing even further.

If we actually worked to create a society that work for the benefit of all its members, there would be a lot less reason to worry about developments like these. Much of the worry arises because for various reasons - none of them really good ones - we've ceded control of these developments to the people least suited to manage it.

Re: An OpenAI model has disproved a central conjecture in discrete geometry

#580

Earlier quoted context omitted.

People are afraid for their livelihood. What do you expect?

Well yes, but there is a choice being made here and I would love to believe we can do better. The rational response to being afraid about your livelihood isn’t to spend time filling every HN thread on LLMs with embittered negativity. Not to mention all the flat denials that LLMs can do mathematics and write decent code, which is almost a self-contradictory position if you are worried they are going to replace you. Th…

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