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Leiden Declaration on Artificial Intelligence and Mathematics

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Re: Leiden Declaration on Artificial Intelligence and Mathematics

#51

Post by Spacecosmonaut »

Accelerationists may argue that the eroding of proper attribution and proof verification by humans is a meaningless short term struggle of a dying field.

Mathematics seems to be entering an era where human + machine maximizes performance, much like chess in the 1990s. However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). A future where AI generates and verifies proofs without humans in the loop. Where the mathematics may be beyond human comprehension.

In that future, does it matter that early career mathematicians are inhibited by these developments? Perhaps not. Programming faces the same issue. As AI crawls up the competence ladder, does it matter that fewer people have opportunities to develop the skillset of a senior engineer? Perhaps not.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#52

Post by TimorousBestie »

SilverElfin wrote: post #35

> Technologies that draw extensively on the published mathematical commons undermine the traditional system of attribution. This just feels like something that has always been true. Defending attribution in this way feels more like a panicked gatekeeping rather than something valuable and principled. I’m a bit disappointed to see people like Terence Tao endorse this.

A career in mathematics is very unlikely to deliver fortune, fame, or even respect. Attribution is in many cases the only way we know that someone else thought our work was valuable.

The bar for being cited has never been lower in the history of mathematics: getting an arXiv account is easier than getting a lobste.rs account (at least by my experience, for I have the former but not the latter).

Tao knows what he is talking about, he was an early adopter of LLMs for proof-generation.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#53

Post by potsandpans »

Let's assume that there is an advantage to using llms. E.g. the use of an llm lends a competitive advantage in a given field.

There is no moral or ethical obligation to disclose tool use. The disclosure in of itself presents an asymmetric disadvantage to the disclosee. Especially in this charged environment where large swathes of people are champing at the bit to discredit or diminish any effort that leverages these tools.

This system incentivizes people to hide tool use to gain a competitive advantage.

This moralistic grandstanding will be seen as a reactionary movement of people trying to cope with transformative technology.

Lie about tool use, don't admit it. Use it as you see fit and rely on your taste, expertise and best judgement.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#54

Post by bcjdjsndon »

Spacecosmonaut wrote: post #51

Accelerationists may argue that the eroding of proper attribution and proof verification by humans is a meaningless short term struggle of a dying field. Mathematics seems to be entering an era where human + machine maximizes performance, much like chess in the 1990s. However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). A future where AI gene…

> However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now).

Isn't chess more popular than ever? Ai dominating the game didnt seen to matter

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#55

Post by adrian_b »

Mattasher wrote: post #44

Interesting document. Especially interesting compared to the Bourbaki movement from a century ago, which was much more focused on universality and correctness, and much less focused on process and attribution (in fact, demanded anonymity).

I consider attribution very important, less because it were associated with some merits for the humans quoted as the sources of certain new ideas, but more because it facilitates going backwards to the historical documents where those ideas were first introduced.

At least for me, in many cases I have achieved a much better understanding of various things after I studied the historical development of the ideas related to them.

Therefore I agree with the point "2." at "Potential Threats". For me a novel mathematical demonstration that is not presented in a way which disentangles its really new elements from the previously known elements, by proper quotation of all relevant older sources, has a value that is many times lower than that of a demonstration with proper attributions.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#56

Post by Spacecosmonaut »

bcjdjsndon wrote: post #54
Spacecosmonaut wrote: post #51

Accelerationists may argue that the eroding of proper attribution and proof verification by humans is a meaningless short term struggle of a dying field. Mathematics seems to be entering an era where human + machine maximizes performance, much like chess in the 1990s. However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). A future where AI gene…

> However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). Isn't chess more popular than ever? Ai dominating the game didnt seen to matter

Sure, but if we continue that analogy it does mean that there will be no human contributions to frontier mathematics.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#57

Post by bcjdjsndon »

Mattasher wrote: post #44

Interesting document. Especially interesting compared to the Bourbaki movement from a century ago, which was much more focused on universality and correctness, and much less focused on process and attribution (in fact, demanded anonymity).

Ever since I found out the french chopped their kings head off, I've had a quiet respect for those crazy frogs

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#58

Post by bcjdjsndon »

onetimeusename wrote: post #45
briandw wrote: post #28

Most of the arguments here feel like gate keeping and resistance to change. I didn't see any arguments that were directly about advancing the state of knowledge of math. “Current automated techniques can produce plausible but unreliable (or even incorrect) arguments which are difficult to distinguish from correct mathematical proofs.” That seems like a problem for mathematics with or without AI. Isn’t this a problem…

There is some of that but I wouldn't call it gatekeeping. Universities lately promote citations and publications so there's a sense that results are all that matters. Results matter, yes, but there's a human side too where we're kind of asking about human creativity and ability. To me an appropriate analogy is in climbing Mt. Everest. Proving something, or even writing a thesis, is like climbing Mt. Everest. A lot of…

It's completely antithetical to the whole enterprise to hide anything these researchers produce behind a paywall. Id be glad to see that go.

> or even writing a thesis, is like climbing Mt. Everest. A lot of the value is actually in the effort you put into it.

As an analogy, in the music industry, if you need a jingle written, you wouldn't care if someone spent five minutes or five years writing it. AI is now filling that formulaic space very well. It won't replace the top end of humans output but it completely outdoes all the boilerplate stuff humans take an age creating

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#59

Post by adrian_b »

Lerc wrote: post #49
applfanboysbgon wrote: post #10

Earlier quoted context omitted.

This appears to be a very bad faith post that intentionally misrepresents what is being said. 1. pertains to the quantity of output adding stress to review processes; LLMs can feasibly produce a million plausible but incorrect 'proofs' in the time that a human can produce one. We already see this effect in software development, with bug bounty programs shutting down and open-source software rejecting AI contributions…

> 2. is nothing about "following established traditions" but rather the general concept of crediting people for their prior work, unless you think that "not plagiarising" is a trifling established tradition. But that is the nature of establishment, when something is a sufficiently firmly established tradition, people see it as a truism. Crediting people is a social convention. Plagiarism is a social construct. It can…

In the research papers of any branch of science and technology, crediting the previous work is not some social convention, but it is very useful information for readers.

Despite the fact that there are some dishonest researchers, who attempt to create the illusion that their work is revolutionary and does not owe anything or only very little to predecessors, the truth is that almost anything novel that is published today contains only a few percent of truly new ideas that are grafted on a big body that combines many results extracted for older works.

If a new research paper separates properly its new elements from the old elements, which are properly attributed, enabling the search of the original sources, that can help a lot the readers to understand it.

I consider the fact that when you ask a question to an LLM, it is unable to accurately provide the source of the answer, as their greatest defect.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#60

Post by tcp_handshaker »

Spacecosmonaut wrote: post #51

Accelerationists may argue that the eroding of proper attribution and proof verification by humans is a meaningless short term struggle of a dying field. Mathematics seems to be entering an era where human + machine maximizes performance, much like chess in the 1990s. However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). A future where AI gene…

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