alt Hacker NewsLeiden Declaration on Artificial Intelligence and Mathematics
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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.
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 with human proofs as well?
“Many current models are also built on data obtained by systematically exploiting licenses and access arrangements that were not made with artificial intelligence in mind, or indeed by simply violating copyright protections”
Copyright? The copyright arguments have been hard to make in domains where copyright is much stronger, mathematical knowledge isn’t even subject to copyright.
“Technologies which affect the way in which mathematics is practiced may disturb the current system of incentives”
Resistance to change again.
“Proper evaluation is endangered if results are communicated through informal channels”
Gatekeeping again.
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).
> Terence Tao - Professor, University of California, Los Angeles
> 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.
> Recommendations for policymakers in government and elsewhere
> 2. Don’t believe the hype
> 3. Regulate the artificial intelligence industry1. 'incentives' hmm
"Now, here, you see, it takes all the running you can do, to keep in the same place."
(Leiden being the town in the Netherlands where Leiden University is.)
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.
So they are recommendations. At global level.
In a word, they're cooked
> 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.
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1. first they ignore you <<<< GPT-4 can barely add too numbers without making a mistake
2. then they laugh at you <<<< the International Math Olympiad is basically just high school math
3. then they fight you <<<< this declaration
4. then you win
The potential threats section reads like panic, rather than a critique of AI. I can see where #2 has some legs, if I thought tradition was sacrosanct.
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.
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 role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding."