What was it like being part of the Arab Spring?

I’ve always wondered what it’s like experiencing a historical milestone up close. Did the moment feel historical? What were people’s gut-level reactions? How did people cope with change?

While the election of Barack Obama, the 2008 financial crisis and Russia’s invasion of Ukraine all happened during my lifetime, I wasn’t in the middle of it all. However, this week I lived through what truly seems like a historical moment.

On October 6, OpenAI released proofs to 722 major open problems produced by an internal model. They’re deliberately downplaying the significance of these results: that’s decades worth of mathematical solutions. Some highlights include the Quasi-Riemann hypothesis, the irrationality exponent of $\pi$, and the Unique Games conjecture¹.

Just for the record #

The so-called ‘slop drop’² evoked different reactions, ranging from excitement to grief. On Proofs and Prompts, the community-ran blog about AI and maths, more than 100 mathematicians shared their initial thoughts.

Ryan Alweiss described the proof release as ‘wonderful’, and remarked that we’re learning more mathematics than ever before. Kevin Buzzard was equally optimistic, ending his statement with:

…I believe that truth and understanding will bubble to the top. There are plenty of important poorly-written papers by humans — bad exposition has always been with us, and mathematicians have offered translation services for free many times before. AI will get better at explaining. Mathematics has undoubtedly moved forwards this week — this cannot be denied.

Yet, most mathematicians were stunned by the speed of the development and expressed concerns about the future of the discipline. A few were mournful about ’their’ problems being solved: what about future funding opportunities? Another common theme was how to support early-career mathematicians.

Some people, including more senior members of the community, strongly condemned OpenAI’s publication of the results. One of the most damning testimonies, due to Tasmin Chu, read:

I feel a profound sense of grief for the working conditions I believed I would have. No one can take away the beauty and value of mathematical thought from me, but they can effectively disempower me in my own profession. What hurts the most is that OpenAI doesn’t even care about this result. They don’t know that our community, our intellectual thought, our knowledge is a living thing. To be frank, I find myself absolutely disgusted by the society I live in.

Another mathematician, Aleksander Skenderi, exclaimed:

Their greed knows no bounds. How much more evidence do we need? Do they need to say to us, directly to our faces, “hello, I am the Devil, and I have come here to destroy you and everything you love”?

The most poignant reaction came from the Association of Human Mathematics (AHM), formed in response to the announcement of the Navier-Stokes result. In their statement from October 7, they denounced OpenAI’s release of the problems, caustically remarking that ‘mathematicians did not ask for this work to be done’, and then lamenting that OpenAI tested their models on open problems³.

Their statement led to a huge dunkfest on Twitter, with people asking who owns problems, and whether you can legitimately prevent people from doing maths. Of course, the questions were posed with due Twitter spite, with the AHM being called ‘fucking institutional crybabies’.

Some days later, Terry Tao became a subject of derision on Twitter, after he used a clumsy analogy to illustrate the importance of human understanding. No, Terry, a cancer patient wouldn’t hesitate to try a hypothetical treatment no human understood but for which an AI had a Lean certificate it worked.

Indeed, the online discourse was rough. This was also one of the key points in Hugo Duminil-Copin’s talk at the MIAM seminar, which ended with an appeal for mathematicians to unite.

Personal remarks #

How did I react?

I felt gratitude. The 722 proofs is, by any measures, an impressive mathematical achievement. I’m thankful OpenAI took the trouble to consult an external committee, organise a GitHub repo and polish some of the writeups – it’s a lot of unpaid work. This is far from their core business.

In view of this, the second point in the guidelines from the external committee, which says that OpenAI ‘must take responsibility for ensuring that human understanding will follow’, seems unreasonable. Why should a company fund seminars, conferences and PhD positions to sustain an entire industry? While companies have some social responsibility, this is too big an ask; they’ve already done more than enough.

Mathematicians mainly provide value by teaching – not as living certificates of human understanding. If we now fail to provide value, that’s our problem. So, in their open letter from September 11, the 25 fields medalists shouldn’t have discussed the ‘severe misalignment of AI in mathematics’, but instead the misalignment between research mathematics and what society needs. There just isn’t that big public demand for research-level maths – even if it’s branded as ‘human understanding’.

I also felt calm. People are finally waking up to the social effects of AI, which is a good thing.

Honestly, I also expect AI to be less disruptive in other domains – the reactions within the maths community provide a kind of worst-case scenario. In fact, the biologists already experienced their slop drop moment in late 2020, when AlphaFold 2 solved the protein-folding problem. This didn’t lead to a field-wild existential crisis, as far as I can tell.

Let’s face it: compared with other professionals, most mathematicians are admittedly rather disconnected from the rest of society. Few researchers have had a ‘real’ job, and we’ve adapted a special set of social norms. Many maths professors are ill-equipped for any other career. No wonder, then, that mathematicians are uneasy with the changes caused by AI.

Perhaps this is what it’s like watching history unfold. Indeed, if one can speak of a Deep Blue - Garry Kasparov moment for maths, then this was it.