Leiden Declaration on Artificial Intelligence and Mathematics • Hacker News Board

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#71

Post by mimd » Wed, Jun 03, 2026, 5:42 PM UTC

So, no one's buying our textbooks anymore, it's getting costly to do our work, stop over claiming results for your marketing and insulting our work? I would have stuck with that.

Everything else seems to be organizational or standard politics. I would have avoided the political sections as it just sets those signatories up for getting into those fights, having not realized what they cosigned.

The issue of attribution is a hard problem that has festered for a while, that has mostly been obscured by the inability to discern an authors entire body of ingested information. I would be careful as, the proposed opt-out restrictions will be eventually imposed on people, which sorta blows up the whole math enterprise of universities/etc. Ie. the proposed leads to a book author revoking a person's ability to reference their arguments in a mathematic paper for money, spite, etc.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#72

Post by palmotea » Wed, Jun 03, 2026, 5:46 PM UTC

pfdietz wrote: post #11

curt15 wrote: post #3

It's worth remembering Thurston's essay on mathoverflow ( https://mathoverflow.net/questions/43690/whats-a-mathematici... ): "The product of mathematics is clarity and understanding. Not theorems, by themselves. Is there, for example any real reason that even such famous results as Fermat's Last Theorem, or the Poincaré conjecture, really matter? Their real importance is not in their specific statements, but their ro…

That's the product of math from the point of view of mathematicians. But is it the point of view of those funding math? I suggest if one looks at the history of funding for mathematics and science, the product of these efforts is not understanding, but rather power. Funding went way up after WW2 when the war demonstrated that power flows from them. Math not only contributed to the scientific weapons of the way, but w…

> That's the product of math from the point of view of mathematicians. But is it the point of view of those funding math?

That's AI in a nutshell: the only point of view that matters is the point of view of people with a lot of money, and we've finally developed a technology that will allow all those other points of view to be squashed and discarded. The powerful won't need to be bothered with them anymore.

For them, math is an instrument. Disagree? Fuck you, you don't matter anymore. Be excited about the future!

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#73

Post by Mattasher » Wed, Jun 03, 2026, 6:14 PM UTC

adrian_b wrote: post #55

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…

> 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.

Completely agree with this. Math, and especially related studies like probability/stats, are presented as laws of the universe, when quite often they represent branching paths that could have gone a different way. What we take as correctness is often just one specific metric, or one justifiable epistemological pathway, among many, and it's worth understanding why we ended up where we are, and what those other forking paths might have been, and often still are.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#74

Post by Jblx2 » Wed, Jun 03, 2026, 7:17 PM UTC

enugu wrote: post #32

pfdietz wrote: post #11

Earlier quoted context omitted.

That's the product of math from the point of view of mathematicians. But is it the point of view of those funding math? I suggest if one looks at the history of funding for mathematics and science, the product of these efforts is not understanding, but rather power. Funding went way up after WW2 when the war demonstrated that power flows from them. Math not only contributed to the scientific weapons of the way, but w…

Power depends on understanding - Seeing a larger scale view of what is happening as opposed to an arbitrary sequence of manipulations. The foundations of the WW2 technologies you cite were dependent on previous theoretical efforts (ex:relativity) to develop a good understanding. Without understanding, you get brittle demos which fail as the environment or problem description changes.

Which WW2 technologies had even a cursory dependency on Special or General Relativity?

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#75

Post by magimas » Wed, Jun 03, 2026, 7:29 PM UTC

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…

I don't know, I don't think this "effort for effort's sake" is a very convincing argument. In particular, I think it's very much affected by recency bias in a way?

What we perceive as "effort worth taking" instead of "dull occupational therapy" is very prone to change with technology.

If you would argue that modern photographers need to take the time to physically develop their photos and use chemicals to get their effects rather than applying photoshop filters, you'd not be taken very seriously - in the 80s and 90s it would have been a very different discussion where people saw photoshop as "taking the helicopter to the summit of Mt Everest".

Same even with paper writing. I still had old school teachers in the 90s and early 2000s who insisted that writing anything on a computer was a "shortcut" that would encourage worse writing because you could undo stuff etc. They did all their handouts and worksheets on their old typewriters.

There is a discussion to be had on AI in maths, but I don't think it's this one. I think mathematicians should be talking about what the future of their field is supposed to look like in a time where AI will be able to find the proofs. Maybe maths will turn into a more "experimental" science, where you already know the proof of a theorem, but you want to find a particularly elegant way that helps humans understand it or find other ways to apply the knowledge. Or rewrite old theories from different angles based on all the new proofs generated by AI. I don't know, but I think there's a lot of mathematics to do out there for humans even in a time with AI.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#76

Post by pfdietz » Wed, Jun 03, 2026, 7:32 PM UTC

Jblx2 wrote: post #74

enugu wrote: post #32

Earlier quoted context omitted.

Power depends on understanding - Seeing a larger scale view of what is happening as opposed to an arbitrary sequence of manipulations. The foundations of the WW2 technologies you cite were dependent on previous theoretical efforts (ex:relativity) to develop a good understanding. Without understanding, you get brittle demos which fail as the environment or problem description changes.

Which WW2 technologies had even a cursory dependency on Special or General Relativity?

The atomic bomb certainly had a cursory dependence on special relativity. E = mc^2, you know.

Klystrons were used in WW2, and the beam current of a klystron scales as the beam voltage to the 3/2 power (due to space charge limits). Modern klystrons operate with relativistic electron beams, but I don't know if any of the WW2 ones did.

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#77

Post by Jblx2 » Wed, Jun 03, 2026, 7:52 PM UTC

pfdietz wrote: post #76

Jblx2 wrote: post #74

Earlier quoted context omitted.

Which WW2 technologies had even a cursory dependency on Special or General Relativity?

The atomic bomb certainly had a cursory dependence on special relativity. E = mc^2, you know. Klystrons were used in WW2, and the beam current of a klystron scales as the beam voltage to the 3/2 power (due to space charge limits). Modern klystrons operate with relativistic electron beams, but I don't know if any of the WW2 ones did.

Is there any part of the theory or design or implementation of the atomic bomb that depends on E = m*c^2? Or is it: "if you could theoretically weigh the end-products, you would get a slightly smaller answer than the before-products". Seems like it would have been known that there was a lot of electrical potential energy stored in the nucleus (after the discovery of the proton).

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#78

Post by 1970-01-01 » Wed, Jun 03, 2026, 8:35 PM UTC

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…

It is said that every discipline, every task, will eventually be challenged by AI. I see it simply as an adapt-or-die situation. There is no rule in Principia Mathematica stating this field of philosophy is rightly reserved only to humans. Hopefully, this is just evidence of the old-guard culture starting to break.

https://en.wikipedia.org/wiki/Philosophi%C3%A6_Naturalis_Pri...

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#79

Post by nh23423fefe » Wed, Jun 03, 2026, 9:32 PM UTC

palmotea wrote: post #72

pfdietz wrote: post #11

Earlier quoted context omitted.

That's the product of math from the point of view of mathematicians. But is it the point of view of those funding math? I suggest if one looks at the history of funding for mathematics and science, the product of these efforts is not understanding, but rather power. Funding went way up after WW2 when the war demonstrated that power flows from them. Math not only contributed to the scientific weapons of the way, but w…

> That's the product of math from the point of view of mathematicians. But is it the point of view of those funding math? That's AI in a nutshell: the only point of view that matters is the point of view of people with a lot of money, and we've finally developed a technology that will allow all those other points of view to be squashed and discarded. The powerful won't need to be bothered with them anymore. For them,…

When did people with no power matter?

Re: Leiden Declaration on Artificial Intelligence and Mathematics

#80

Post by Lerc » Wed, Jun 03, 2026, 9:57 PM UTC

adrian_b wrote: post #59

Lerc wrote: post #49

Earlier quoted context omitted.

> 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 t…

>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.

I covered that aspect. Those are thing that the writer does to increase the utility of their work. It is one of many ways that improvements may be done. That this particular way is compulsory and the others are not suggests that this is not the reason for the choice to make it compulsory.