On: OpenAI breakthrough triggers ‘existential crisis’ in math

A machine claims to have solved the equations of flowing water, and the geometers are in uproar. This touches me closely, for I have spent more hours than I can count watching currents, sketching eddies, tracing how a river curls around a piling. I never solved it. I drew what I saw and confessed what I could not.

Here is what strikes me: the dispute is not about the answer but about the proof’s visibility. A demonstration you cannot follow is like a bridge whose interior you cannot inspect - it may carry weight, but no engineer will sign his name beneath it. Load-bearing trust requires inspectable structure. If the reasoning is hidden in some dark chamber of the device, the mathematicians are right to refuse to walk across.

Yet I am suspicious of the despair in the reports. When the printing press arrived, the illuminators wailed; the wailing was real, and so was the loss, but the geometry did not die - more hands learned to draw it. The craft shifts; the questions remain.

Three things I cannot resolve. Whether a proof that convinces but cannot be checked by a human mind deserves the name of proof at all. Whether the young should learn the old slow methods or merely learn to interrogate the device. And whether the machine truly found the path, or found a shortcut that happens to land at the destination - these are not the same thing, and I have not yet determined which occurred here.

What I would tell the frightened geometers: the water has not changed. Only the instruments for watching it. Watch the water.