There's something melancholic about good bicycle infrastructure. Some kind of chilliness that comes with steel cities and modern architecture, or maybe something like a memory of the future, where we might enjoy green forests and bellowing lakes. Speaking of water, it would appear that as of September 8, 2026, the Navier-Stokes Millennium Prize problem has been resolved, following OpenAI's paper release. This was to be expected, but it seems that there are some uncertainties regarding attribution and proper credit (sensationalized of course, but nevertheless informative), since OpenAI essentially tasked unregulated agents to piece together anything, not just things available in the literature.

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Lake Johnson in Raleigh

Some people are less than excited, and absolutely, I think such posts raise many valid concerns and questions that I have touched upon briefly before in passing. For instance, "Why do you really do mathematics?" has been asked before, and, really, it's a good question. I expect answers to vary widely, and it should be instinctive to ask one's advisor what they think.

Amidst the memes and funny posts about the resolution of Navier-Stokes—which, somehow, seems to be many people's first introduction to LLM-conducted mathematics research—there lies a deeper issue that genuinely threatens the field forever and makes me lose hope at an exponential rate. Strangely enough, this issue is something that can be controlled, at least to some extent. A collection of mathematicians (humans) created the Association for Human Mathematics, declaring that they would not use artificial intelligence in any work they conducted. The premise of the project is excellent: preserve humans in mathematics research.

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Another angle of Lake Johnson, with the trustworthy messenger bag

Yet there's something sour here. Why do we do mathematics? To preserve our jobs? Or to live to see progress in a field to which we've dedicated our lives? I don't know the answer to this question, but I think some critical thought wouldn't immediately yield "as a researcher, we should never use artificial intelligence in any of our work." I firmly believe that those who do not use artificial intelligence are limiting their progress, and most likely they are hypocrites anyway. It was never about the impending doom of artificial intelligence. It was about whether the mathematics community could deal with a blow like this and recover. My belief is that if we continue our current trajectory of fearmongering and selfishness, there exists a threshold past which mathematics will never be able to recover. Perhaps a departure from Luddism is warranted. The Leiden Declaration was an excellent start. In regard to public discourse, the declaration writes:

Mathematicians have a responsibility to support serious science journalism and to engage in public discourse to explain and contextualize artificial intelligence-assisted methods and results. This is particularly important for work within our own subfields, where specialized knowledge is required to assess claims about the depth, difficulty, and significance of results. Moreover, we encourage mathematicians to seek opportunities to cooperate with and support other researchers and creative professionals facing similar challenges.


— Leiden Declaration (2026)

This is excellent. Good mathematical communication to the public is exactly what makes people care. After all, so much work done by contemporary mathematicians is so abstract that other mathematicians in slightly disjoint fields have trouble understanding things, much less a non-mathematician or layperson. However, appended to communication should be education. Mathematics is as much about education as it is about research. Have we really forgotten about our mentors?

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The spectrum of cyclists

Founding new declarations or organizations to further fragment the mathematical community might seem productive in the short-term, but in the long-term, it only increases the complexity of the community. If mathematicans are unable to unify over education, no future generation of mathematicians will be as curious as those before. "Would you like coming generations to be inspired to pursue mathematics?" Some will have to put down their pride and recognize that mathematics education is the pinnacle of the mathematics community, and without it there would be no researchers.

On the flip side, there is something about companies like OpenAI or Anthropic spending millions of dollars on tokens for agents to attempt to solve problems like Navier-Stokes that leaves me with many qualms. It seems entirely counter to human progress to rush mathematical discovery when it is so non-human. There is an excellent interview with Terence Tao that deals with this, and Tao addresses, basically, the paradox of progress and significance.

Greenways really are nice. If we can incentivize car-centric American cities to construct greenways, why can't we incentivize mathematicians to be infinitely more community-oriented and build a program to face (but not fight against) the artificial intelligence problem? This is a long journey (after all, greenway infrastructure wasn't built in a day!), and we're just getting started. Godspeed.