Mathematician Terence Tao Comments on ChatGPT
Terence Tao, an Australian-American mathematician of Chinese ethnicity and Fields Medal winner, recently announced that he has decided to try incorporating AI tools into his workflow in different ways, including GPT-4 and others. On April 10, Tao wrote on the decentralized social network Mastodon: “Today was the first day that I could definitively say that GPT-4 has saved me a significant amount of tedious work. I am now looking forward to native integration of AI into the various software tools that I use, so that even the cut-and-paste step can be omitted.”
During the past few days, he discovered many hidden features of ChatGPT, such as searching for formulas, parsing documents with code formatting, and rewriting sentences in academic papers. For example, sometimes ChatGPT can perform a semantic search on an unfinished mathematical problem to generate some hints. Tao also asked ChatGPT to identify Kummer’s theorem from its description. Although it could not provide the correct answer, it gave an approximate answer based on Legendre’s formula. Regarding this matter, Tao said that AI plays a role in mathematics by providing an initial approximate answer which can then be combined with traditional search engines to easily find the correct answer.
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Tao also discovered the highlights of ChatGPT in handling mathematical problems, which can describe the recommended pronunciation of proper nouns in various languages, in a manner that does not require knowledge of phonetics. In addition, ChatGPT can be requested to convert a pile of references obtained from MathSciNet and format them as .\bibitems in the LaTeX bibliography environment.
However, in a proof problem about the infinitude of primes, Terence Tao found that the answer given by ChatGPT was not entirely correct. On the other hand, he discovered that the AI argument does imply that the infinitude of squarefree numbers implies the infinitude of primes, and the former statement can be proven by a standard sieve argument.
Terence Tao also released some further minor use cases for ChatGPT that he has discovered recently. “Firstly, it is quite good at parsing documentation for a code format (in this case the API for arXiv search) and then returning a correctly formatted query for that code (and it also later provided some working python code to call this API in the fashion I requested, although I had to manually install a package to make it run).”
“Secondly (and not pictured here), I asked it to come up with some questions that a bright student might ask in an undergraduate linear algebra class (for which I provided a few sample topics), and it came up with some good examples that stimulated ideas for possible directions for the course, as well as potential assignment questions.”
“In general, I am finding that while these AI tools do not directly assist me in core tasks such as trying to attack an unsolved mathematical problem, they are quite useful for a wide variety of peripheral (but still work-related) tasks (though often with some manual tweaking afterwards).”