"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 role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding."
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 was directly used in operation planning (the birth of the field of Operations Research) as well as in cryptography.
The reason this matters is that AI is also a quintessential power-oriented technology. From the point of those providing the monetary lifeblood on which modern mathematical practice depends, the current math-AI discussion presents no issue worthy of concern.
> This has been the result of months of community input about the fundamental values and goals of the mathematical community. In retrospect, these were questions we should have been systematically discussing years ago, but in any event the exercise was extremely valuable, and the end result is excellent. I wholeheartedly endorse the statements and recommendations in this declaration.
(Mostly by theft^W piracy^W fair use of the starters planted in the Hortus Botanicus at the old University)
Such is the backstory for the logo (Top left) they have adopted for this bubbelicious topic
University PR: https://www.universiteitleiden.nl/en/news/2026/06/leiden-dec...
1. AI proofs might be incorrect and difficult to demonstrate why. This implies they are not like human proofs in these qualities.
2. AI proofs are difficult to attribute correctly, because they don't follow established traditions. Nothing to do with the math, but ok.
3. Mathematicians without AI (for political or practical reasons) will not necessarily be able to participate in AI-assisted research. This history of Mathematics is littered with people having uneven access.
4. People/orgs are publishing that AI found things are fact before they are properly evaluated. Same issue.
5. All these things are bad, because AI might muddy the field with lots of unknowns.
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 produce one. We already see this effect in software development, with bug bounty programs shutting down and open-source software rejecting AI contributions or closing altogether because LLMs flood review channels with an amount of spam for which there is no sufficient amount of human bandwidth to handle.
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.
3. is more or less accurate to the point they made, but "it has historically been this way" isn't a compelling justification for "it should always be this way and also it's okay if it gets worse"
4. An existing issue being made 100x more common is a point worth bringing attention to even if it already existed, actually
5. said nothing that could possibly be interpreted in the vein of "muddying the field with lots of unknowns" at all. Point 5 was actually about economic incentives and the risk of mathematic research becoming beholden to tech monopolies