Who Taught the Machines Mathematics?

A few days ago, OpenAI released more than 700 mathematical manuscripts targeting some of the biggest open problems in mathematics and theoretical computer science. This has caused quite a controversy. Some mathematicians have raised concerns about the correctness of the results; others are shocked by how they were released; many wonder who is expected to do the enormous amount of work needed to check them; and some have even called for an end to cooperation with OpenAI.

As for me, I browsed the list of problems and found some I had cared about in the past, but couldn’t bring myself to read the papers. A very different experience from when I chaired one of the main conferences in theoretical computer science (FOCS) and was super-excited to see about 400 submissions from the community.

But this episode made me think about all the years I spent learning, teaching, and communicating mathematics, and the enormous amount of knowledge mathematicians pass on to one another that never appears in papers. I wonder how much of this knowledge, accumulated over generations, is now helping companies build proprietary systems that may eventually do the same work. Is this a form of extraction?

Some of the reactions within the mathematical profession also make me uncomfortable. For decades, much of the profession has increasingly focused on producing papers, proving theorems, and winning prizes.

Following up on my essay from earlier this year, I now think through these questions in a new essay:

Who Taught the Machines Mathematics?

A small note: I am now publishing my essays on my personal blog, Algorithms, Nature, and Society. I also plan to move this mailing list there soon, so subscribers here can keep receiving my writing without subscribing again.