"[...] now is the time of monsters."/"If you don’t want me to be nice, then I don’t have to be nice."

Usually, this blog is reserved for news of my academic day-to-day. Today, however, something far more seismic compels me to write.

It starts with September 17, 2025, when a preprint titled Discovery of Unstable Singularities [1] appeared on arXiv. A close friend of mine, an expert in the field in Lausanne, pointed it out to me. He explained that while the authors were using AI-assisted techniques to reproduce an already known result, the underlying methodology felt different: it seemed as though they were forging a genuine blade, one that might ultimately "slay" the dragon of the Navier–Stokes existence and smoothness problem. Even the typography and layout carried the unmistakable polish of a manuscript drafted for Nature or Science (as a conoscere recognizes from the layout).

Source: [1]

Since my PhD, I’ve already watched several major problems fall that once seemed completely untouchable (at least for me). A prime example is the Boltzmann equation, a topic close to my own previous work, even if my modest contribution traded rigorous limits for visually appealing figures [3]. For fifty years, the benchmark had been Oscar E. Lanford III’s result from 1974/1975. In the Boltzmann–Grad limit of a hard-sphere gas, Lanford provided the first rigorous proof that the one-particle distribution converges to the solution of the Boltzmann equation, successfully controlling the propagation of chaos.

The catch, as anyone familiar with the problem knows, was the timescale: Lanford’s proof worked only for an absurdly short fraction of the mean free time between collisions, strictly less than one-fifth of the average time between two particle collisions.

That boundary seemed practically carved in stone (again, for me as a PhD-student). But in 2024/2025, Yu Deng, Zaher Hani, and Xiao Ma finally broke through. In their paper Long time derivation of the Boltzmann equation from hard sphere dynamics (posted to arXiv in August 2024 and accepted by the Annals of Mathematics in 2025), they extended Lanford’s result to arbitrarily long times, specifically, to any finite time interval on which a sufficiently regular solution to the Boltzmann equation exists. Seeing a 50-year-old barrier collapse like that was remarkable.

And then, on September 8, 2026, the news broke: Navier–Stokes had reportedly been "slain".

Source: [4]
 

Yet the celebratory atmosphere was almost immediately eclipsed by unease. A statement published by OpenAI [4] revealed a calculated, brute-force sprint behind the scenes: "On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors and by the step change in performance of our internal model, we launched an effort to evaluate it on all open Millennium Prize problems and a few other high-impact problems."

In experimental biology, this dynamic has a notorious name: scooping. You present a brilliant, hard-earned idea at a conference; a well-funded lab with vastly superior resources, compute, or manpower catches wind of it, rushes back to the bench, and races to beat you to print. Anyone with friends doing a PhD or postdoc in the life sciences knows the quiet dread and paranoia this fosters. Mathematics, by contrast, has long prided itself on an open, collegiate, and transparent culture, one built on arXiv preprints, generous attribution, collaboration and communal trust.

Now, that protective culture seems to be fraying. Tristan Buckmaster and his collaborator Levent Alpoge, who were working on Navier-Stokes (and themselves build upon and explicitly credit foundational work by Diego Córdoba and Javier Martínez-Zoroa [2]), found themselves caught directly in the gears of this corporate machinery. According to Buckmaster's statement, OpenAI repeatedly offered him a kind of co-authorship/coordinated publication (for precise details, see [2]) on their paper, on the condition that Alpoge (employed by Anthropic) be left out. Buckmaster refused. When Buckmaster said that he would go public, he writes that he was asked why he would "ruin [his] career". He "[...] replied that I am an academic, and asked why he thought going public would ruin my career", only to receive the reply above: "I don't have to be nice."

In 2020, filmmaker David Lynch famously looked into his camera during his daily weather report and offered one of my favourite quotes by him, declaring that he saw the future and that it would be "very bright."

Source: google -> reddit. Rest in Peace David Lynch, just yesterday I finished Twin Peaks Season 1-3 for a second time.

Today, watching the collision between pure mathematical inquiry and the raw power of corporate AI labs, I find myself thinking instead of Antonio Gramsci’s famous (if rather free) quote: "The old world is dying, and the new world struggles to be born: now is the time of monsters." 

Source: google image search and "die Furche" [5]

Why write all of this down? Because mathematics, at least the parts of it I have experienced, has traditionally felt strikingly open. How the field evolves from here remains anyone's guess, but one thing is certain: mathematics may have entered a rather different era.

P.S.: I just sank several hours into this blog post instead of finishing my CERME15 submission. May the reviewers have mercy on my soul.

[1] Discovery of Unstable Singularities, arXiv preprint: arxiv.org/abs/2509.14185

[2] Tristan Buckmaster, Public Statement: cims.nyu.edu/~tristanb/statement.pdf

[3] My own venture into the Boltzmann equation (lacking a rigorous limit, but featuring nice figures): Philosophical Transactions of the Royal Society A, doi.org/10.1098/rsta.2021.0155

Source: ibid.

[4] OpenAI Announcement on the Navier–Stokes Solution: openai.com/index/navier-stokes-solution/

[5] Antonio Gramsci, Prison Notebooks (discussed e.g. in Die Furche): furche.at/feuilleton/philosophie/antonio-gramsci-wie-geht-herrschaft-17572201