Terence Tao

An interesting (unscientific) experiment on #MathOverflow from a few months ago, where a user gave 15 different MO problems for o1 to answer, with the aim of verifying and then rewriting the answer into a presentable form if the AI generated answer was correct. The outcome was: one question answered correctly, verified, and rewritten; one question given a useful lead, which led the experimenter to find a more direct answer; one possibly correct answer that the experimenter was not able to verify; and the remainder described as "a ton of time consuming chaos", in which the experimenter spent much time trying to verify a hallucinated response before giving up. https://meta.mathoverflow.net/questions/6114/capabilities-and-limits-of-ai-on-mathoverflow This success rate largely tracks with my own experience with these tools. At present this workflow remains less efficient than traditional pen-and-paper approaches; but with some improvement in the success rate, and (more importantly) an improved ability to detect (and then reject) hallucinated responses, I could see one soon reaching a point where a non-trivial fraction of the easier problems in MO could be resolved by a semi-automated method.

I found the discussion for possible AI disclosure policies for MO in the post to also be interesting.

I recently talked about (in https://mathstodon.xyz/@tao/113910070146861518) how solutions in a dynamical systems can be roughly divided into an effective dynamics regime, where simplifying principles such as linearity can be reasonably good approximations, and the more complicated regime of no effective dynamics, in which the behavior can be significantly more nonlinear. For instance, in linear regimes, applying a force in one direction, if followed swiftly by an equal and opposite force in the other direction, will get the state roughly back to where one started; but the same is not true in nonlinear regimes. (If one pulls a spring too far in one direction, one can end up with a broken spring, with no way to return to the initial state, regardless of how one tries to push the spring back in the opposite direction.) (1/7)

I have now had the following experience with at least three graduate students in the last ten years: in our weekly meeting, they mention that they needed to locate a key article or book for their research project, but despite searching all over the internet, they are unable to find it. I then ask if they have checked our local Science and Engineering Library, which is literally in the same building as the Math Department. Ten years ago, the response would be embarrassment that this option did not occur to them; but now, the response is surprise that a library containing physical copies of math journals and textbooks even existed.

Perhaps physical libraries are a vestigial remnant of a pre-digital era, but I do have fond memories as a graduate student of randomly browsing books next to the ones I had been looking for, or articles after or preceding the one I was initially locating. The current technological paradigm of being able to near-instantly locate nearly any article one desires (assuming one's university has a subscription to the relevant journals) is undeniably convenient, but has reduced the opportunity for serendipitious discovery. (On the other hand, there are other ways now to make such discoveries, for instance through browsing math question-and-answer sites or math-oriented social media.)

The ability of #AI tools to readily generate highly convincing "#deepfake" text, audio, images, and (soon) video is, arguably, one of the greatest near-term concerns about this emerging technology. Fundamental to any proposal to address this issue is the ability to accurately distinguish "deepfake" content from "genuine" content. Broadly speaking, there are two sides to this ability:

* Reducing false positives. That is, reducing the number of times someone mistakes a deepfake for the genuine article. Technologies to do so include watermarking of human and AI content, and digital forensics.

* Reducing false negatives. That is, reducing the number of times one believes content that is actually genuine content to be a deepfake. There are cryptographic protocols to help achieve this, such as digital signatures and other provenance authentication technology.

Much of the current debate about deepfakes has focused on the first aim (reducing false positives), where the technology is quite weak (AI, by design, is very good at training itself to pass any given metric of inauthenticity, as per Goodhart's law); also, measures to address the first aim often come at the expense of the second. However, the second aim is at least as important, and arguably much more technically and socially feasible, with the adoption of cryptographically secure provenance standards. One such promising standard is the C2PA standard https://c2pa.org/ that is already adopted by several major media and technology companies (though, crucially, social media companies will also need to buy into such a standard and implement it by default to users for it to be truly effective).

In 2017, I managed to solve a problem from the “Lviv Scottish book” in https://mathoverflow.net/a/282290/766 . The problem had a prize of “butelka miodu pitnego" (a bottle of honey mead). Today, while I was in Warsaw, some representatives from Lviv, Ukraine came (by train, as the Ukraine airspace is obviously closed) I was very touched and honored to unexpectedly receive the prize in person.

(Medien: 1)