From Iceberg Melting to a Proof: A Month with LLMs

Levent Alpöge and the author publicly released three finite-time blowup results with smooth forcing, for incompressible porous media、Boussinesq flows, and 3D incompressible Euler — though the hypo-dissipative Navier-Stokes case awaits Lean verification and isn't included yet.

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• The program behind the work was initiated by Diego Córdoba and Luis Martínez-Zoroa, whom the author credits with the core ideas — includinga perceived Fields Medal-worthy contribution from Martínez-Zoroa
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• Large Language Models (Claude, Codex/GPT-5.6, and Astra) were central to pushing the results from rough to smooth forcing, especially August 15th breakthrough; the first LLM-generated proof was"horrendous"yet verified in Lean on August 22nd.

• The author is apologetic about the papers' presentation quality, calling the Euler writeup"AI slop,"attributing haste to outside pressure (a September 3rd rumor and tip that progress details had leaked to OpenAI).

• The deeper significance, per the author, is a:"Deep Blue-Kasparov moment"for mathematics — a human mathematician和an LLM achieving this in a month,demanding unhurried community discussion on training, credit, refereeing, and attention.

• The work is apurely personal collaboration,with no institutional agreements; the author explicitly notes the program was not proposed by an LLM,but the models were used tohconsume and extend prior human work.

Source: https://cims.nyu.edu/%7Etristanb/statement.pdf