Surprised to see someone on HN arguing against open science. Seems like the opposite of the lessons we should learn from Newton and Gauss, actually, hoarding results for decades at the expense of progress.

(the Pythagorean thing isn't really competition either, is ahistorical, and from what we actually do know it's again people hoarding results instead of sharing them).

FWIW, your post comes off as a middlebrow dismissal, surface level and not actually engaging with the substance of the comment. It's also just wrong. You claim "it’s also a misstatement of mathematical history", but don't specify which part. That there's "centuries of traditions of open science"? But your examples are from centuries (and millennia) ago, and there was never any claim that these traditions are universal.

But more fundamentally, competition doesn't mean you can't also have open science. And the very long, damaging events like the Leibniz/Newton feud are exactly what make many mathematicians work to maintain a spirit of collaboration and attribution even when they're competing on approaches.

The mathematical community was very competitive in its early years, but in the last 70 to 100 years, it has been generally less competitive and very collegial. The community was in a good place, and progress has been very good. In a few cases when competitiveness was ramped up, it lead to bad behaviour and destructive fights. Few would like to return to those competitive years.

The story of the cubic equations is another great example: https://en.wikipedia.org/wiki/Cubic_equation

Dudes straight up used to hoard solutions to equations and use them in math battles.

My computer contains the prime factorization of probably several dozen (if not more) large integers, and I refuse to share them with anyone!

(Because they are my private RSA keys)

Also Andrew Wiles working in secret for 7 years out of fear of someone scooping him.

Between people.

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This is literally why we need a functional copyright system

To block progress. Got it.

Not so dissimilar to my first comment on this site (which I got piled on): https://news.ycombinator.com/item?id=48959395

Except way more nefarious than I expected

>We’re basically sharing everything we have with these companies/AI systems.

My sense of the word 'share' is that it traditionally involves agency by all parties involved. There are a lot of words in English for describing taking things without permission and profiting thereby - words like piracy, banditry, and larceny.

While AI companies have almost infinite money, they still don’t want to blow million dollar budgets on problems if there isn’t high likelihood that it will be successful.

But within next 10 years as costs drop significantly and even more improvements are made, yes it is very likely that almost every single existing math problem will get a serious AI cracking done on it

Not a mathematician.

The issue I see with a handed-over proof is tunnel-vision: you explore only the understanding of the proof.

Without a proof, your exploration branches out much further, in directions that could seem fruitless, but may uncover new understandings that are now "hidden" because the handed-over proof drastically lowered the incentives to find them.

- If you have only a fuzzy idea of how to get to your travel destination, wrong turns and alternate routes may reveal sights and places you'd never have encountered without that wandering.

- If your GPS directs you straight to your travel destination, you are now where you wanted to be but missed out on the exploration. This is the sort of consequences the AI math proofs have.

STEM research thrives on that side exploration and unearthing unexpected things along the way. James Burke's famous documentary Connections spends the middle episodes talking about the unexpected directions that exploration has taken science. It's very hard to credibly make the case that this sort of meandering exploration is not valuable.

I think you're misunderstanding the point of math problems. Mathematics is as much a process as it is a result. This is why even from early on, relatively rudimentary mathematics questions you are graded by your capacity to correctly achieve the desired process to the answer than getting the answer correct. The risk here is that AI generated proofs removes the process part of mathematics, where actually interesting concepts live (because then you can apply novel concepts to other unsolved problems and then thereby unlock new concepts that way...) Sure you can kind of try to reverse-engineer it but you lose the entire intuition and "we tried applying it in X, Y, Z ways and it didn't work" intuition, because even the non-working process can teach you about how not to apply the working process to novel problem spaces.

Basically: Tasting a delicious soup doesn't tell you how to layer the flavors, but if you want to be a good chef, you better be learning flavors more than you learn dishes!

He's saying that in such a scenario, almost all of the value is located in the analysis and just dumping the proof has "negligible or even negative value". (The negative value would occur in the cases where the proof doesn't contain enough information to reconstruct what insights would have led a person to it.)

The future sole owners of half of San Francisco’s mansions thank you for your enlightened stance.

I would expect this for service providers that provide their "free" services but the mathematicians said they paid OpenAI to help generate this result. This is a clear conflict of interest. Similar to inside trading. Or the same lawyer being hired from two opposing sides which is a big no no. There are rules and laws that already deal with this in other industries and I expect that there will have to be regulation developed for cases where there is a conflict between AI customers and AI provider interest.

> If this turns out to be true I think my take above is not correct, in the short term people will have to stop sharing updates because otherwise openai will dishonestly race to finish their work.

Which I don't see a reason for Anthropic and "Open"AI not to, given their not so stellar track record with IP of individuals/entities-that-are-not-rich-enough ;)

People who work hard to build intuition and also use AI effectively will dominate the field.

This will be literally every field, sooner or later, at least until the human and their intuition is just slowing the AI down. There’s no scenario where humans without AI beat humans with AI in the long run, unless there are fields where the “alien intelligence” somehow hurts more than it helps (like artistic pursuits perhaps?)

The difference is no one writes punchcards so the comparison is inapt. It is more like supposing AI eats everything humans attempt to do. They will take your work as you are working on it, any interaction at all. It is meta-plagiarism, on another level.

What? No, it's nothing like that. It means that if you have a critical insight and you share it out loud, somebody with no particular mathematical inclination can just spend lots of money to steal the credit from you.

It shifts power further from the worker toward those with capital.

> In other words, the "right" people need to solve it: the mathematicians who made it their job and not the people working to push AI models forward?

This is not at all what he said? I'm not sure how you got this from anything he wrote, actually.

If there are no incentives for mathematicians to work on and share progress in tough problems because they will get scooped, then they will end up quitting and in net we will see less progress overall.