Leiter Reports: A Philosophy Blog

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  1. Luis Marxuach's avatar

    ‘Some mathematicians are still wary, however. “The big story now in mathematics is that nobody wants to share anything,” Buckmaster…

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  3. Mark's avatar

    Sorry, I don’t follow? The whole point of the open letter is that these AI engines *are* producing innovative solutions…

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“A Severe Misalignment of AI in Mathematics”

A statement by 25 Fields Medalists in mathematics. Some of their case applies, I would venture, to philosophy. An excerpt, but do read the whole statement:

[T]he push by AI companies to solve mathematical problems as a benchmark is detrimental to the science of mathematics, and to the mathematical community. The goals of the AI companies and the goals of the mathematical community are severely misaligned. We see these as part of broader alignment issues impacting other scientific and creative professions, as well as the whole of society….

The mathematical community functions, in many ways, as a miniature version of humanity. It consists of individuals using a wide variety of different approaches, joined by core values. The most precious resources of our profession are students and ideas, and these we nurture with great care. We feel responsible to let them grow to their full potential, until they can live a life of their own in the mathematical world. For students we often suggest problems with the core intention of developing skills making them well-positioned for advances in research and elsewhere. Our ideas we disseminate in talks, private discussions and careful writeups, connecting them to the previous ideas of others. These processes invariably take time and are based on human interaction….

[T]he success of AI in solving major mathematical problems has made headlines even outside mathematical circles. But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may turn the tool against the primary goal. Indeed, the mass production at faster and faster pace of “true/false” statements could destroy fertile ground instead of breathing life into new ideas.

Often these solutions are announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others. As in all creative professions, this raises severe attribution and plagiarism questions. Moreover, without the willing mathematicians who must take care of their development and integration into the mathematical canon, AI-conceived ideas would never become fully alive and the crucial human transmission chain between mathematicians would be lost.

We are witnessing a general threat to intellectual work, with misalignment between the outcome of the use of AI and its initial purpose. In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such work directly, and these goals cease to align. The issues the mathematical community faces now are similar to issues that other scientific and creative professions are facing, and indicate issues that all of humanity might face: how to make sure that, as AI changes the way work is done, we do not lose sight of what that work was meant to achieve in the first place.

What do readers think about the application of these points to philosophy and other scholarly fields? Do they apply (if so, how; if not, why not)?

(Thanks to Michael Clune for the pointer.)

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4 responses to ““A Severe Misalignment of AI in Mathematics””

  1. I used to think it was a drawback of philosophy that we don’t have anything like Hilbert’s Problems—a list of open questions that everyone agrees are important.

    Now, I think it’s a valuable defense against AI encroachment. There’s less potential for “AI solves X”-type headlines in philosophy.

  2. I can’t get past “The mathematical community functions, in many ways, as a miniature version of humanity.”

  3. This issue – the difference between getting an answer from AI and actually understanding it – is why I started reading philosophy, and thus started haunting this blog’s comments…

    How far this will go, I’m not sure. I think other STEM fields are probably going to be effected, although it may take a while. The problem is collecting training data. This is relatively easy for math and CS, but considerably harder when an experiment requires manipulating things in the physical world. However, there’s a lot of work right now on automated wet labs and the like. I don’t have enough understanding (natch) of those fields to tell how successful these efforts will be, or over what time scale. Given enough effort, adequate training data can probably eventually be put together, but it may take a long time.

    Philosophy and other fields in the humanities and social sciences may, ironically, be more resistant to this intrusion than hard sciences. How would one collect training data for philosophy? What would that even mean, given that philosophy often doesn’t have a “right” answer? Plus, it’s not really a high priority for the frontier labs. They’re trying to automate coding because replacing software engineers will make them a lot of money. There’s not as much market for replacing philosophers.

    That said, the above analysis assumes we don’t see much domain generalization. If we train an AI to be a genius at math, how much of that “intelligence” transfers to making it better at tasks like philosophy? Probably some, but we don’t know how much. I don’t know of any studies that have tested domain generalization at the scale that would be needed to meaningfully answer the question. If I had to guess, I would guess we’ll see very little domain generalization of this sort, implying philosophy will be safe for some time to come, but as far as I am aware we really don’t know.

    So I think philosophy is probably safe for now, at least from this issue, but we really don’t know what the future is going to bring…

  4. I remember in grad school in 1976 Ian Hacking (visiting UCLA at the time) reporting that the 4-color theorem had been proven by a computer. He expressed reservations about this un-surveyable “proof”. I suppose that was a forerunner of this issue. But whatever “proof” procedures we have in philosophy, it is hard to imagine them taking on a recognition-transcendent life of their own, the way they have in mathematics.

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