Francesco Caravenna - 2D KPZ, AI and collaboration

2D KPZ, AI and collaboration

A personal perspective (October 2026)

I have been involved in a large mathematical collaboration which led to the construction of a non-trivial solution to the ill-defined two-dimensional KPZ equation at criticality:

Quentin Berger, Francesco Caravenna, Jeremy Clark, Alexander Dunlap, Yu Gu, Ziyang Liu, Shuta Nakajima, Rongfeng Sun, Li-Cheng Tsai, Zuodi Xie, Nikos Zygouras
The critical 2D KPZ process
Preprint (2026) [pdf] [arXiv]

The results in this paper were obtained with substantial input from generative AI, building on a decade of work by our community. AI's most significant contributions were novel connections, tools and "tricks" of independent interest, as well as non-trivial technical improvements. Had they come from human collaborators, I would have regarded them as original and brilliant ideas. Although these contributions were not breakthroughs individually, their combination led to a solution of the problem, at a stage when most pieces of the puzzle had already been discovered.

Our interactions with AI involved successes, stalled attempts, human guidance and an element of chance. We spent considerable time and effort working through the arguments and presenting the results in a form we were happy to share with the community. A more detailed technical account is provided in Appendix C of the paper.

Interacting with AI has been a disorienting experience, both scientifically stimulating and personally stressful. Developments we expected to take years unfolded in months or weeks, raising difficult questions about authorship, credit and the meaning of our work. Working together helped put concerns about competition and priority into perspective, highlighting the collective effort behind mathematical progress. It also brought some relief from the pressures of this uncertain period.

Ours is one particular experience, and I would be cautious about drawing general conclusions from it. But I hope it can convey a positive message about collaboration and the value of understanding mathematics together.