On: OpenAI claims huge maths breakthrough on a famed ‘Millennium Problem’

8 September 2026, evening

The news says a machine has mastered the motion of water. I confess I read it twice, and laughed once.

For years I filled page after page with studies of eddies: how a current striking a flat obstacle splits, curls, folds back upon itself; how the whirlpool born at a stone’s edge transmits its rotation outward until the whole river carries it. I wrote then that turbulence was a knot no straight mind could untie - one stroke of the pen and the water escapes you. If these modern calculators have truly seized the Navier - Stokes problem, they have seized the very current I chased across half a lifetime of sheets.

But observe what the claim actually is. A proof in mathematics is like a bridge arch: every stone must bear its neighbour, and if one voussoir is misshapen, the whole span drops. So far I see only the company’s own announcement - a declaration, not the arch itself. Pressure distributed through a single point of origin, one corporation bearing the entire load of verification. Columns fail suddenly; I would want a hundred hands testing each stone before I walked across.

Three things I must examine when the work surfaces: whether the proof shows the mechanism or only the conclusion, as a shadow shows the outline of a bird but nothing of the wing’s leverage; whether the machine found the solution by reasoning or by combing through a million trials as a sieve separates grain from chaff - no shame in either, but the two teach different lessons; and whether the solution holds at every scale, for fluids that run smooth in the channel misbehave in the gorge.

I have not yet determined whether a thing that computes water has understood it. That question I leave open, and it is the better question.