On: AI Has Solved One of Math’s $1 Million Millennium Prize Problems

The tap in my kitchen this morning: the stream came out glassy and smooth for an inch, then shattered into droplets. That shattering is what the fuss is about.

The claim: a computer, built by people who sell chat, has shown that the equations of fluid motion - Navier - Stokes, worth a million dollars to somebody - can blow up. Blow up means this: start with a flow as smooth as you like, and at some finite time later the speed or its slope goes infinite. The mathematics tears itself a hole.

Part of me wants to stand up and cheer. That runaway is real physics: steepen the velocity in one spot and the steepening feeds on itself, faster and faster. Anyone who has watched smoke curl has wondered whether the curling goes all the way down.

Wait - before cheering, what did they actually hand over? A proof is an argument a human can check, line by line, with nothing but patience. If the computer produced a construction too long for any person to read, nobody has solved anything; somebody has filed an enormous claim. The glory of mathematics was always that checking is cheaper than discovering. Lose that and you have not advanced the subject - you have made it unfalsifiable.

Here’s the thing you have to understand: even if true, the equations blow up - water does not. You cannot pour a singularity out of a pitcher. Real fluid has molecules; the equations forget them below some small scale. A singularity in a model is the model shouting that it has walked off its own map. Lovely to know. Not the same as knowing water.

So my test is simple: can someone else follow it? A proof nobody can read is a rumor with footnotes.