Terence Tao (@tao@mathstodon.xyz)

I wrote recently about how the collection of good, fruitful open problems is now being mined in a non-renewable fashion, leading to the potential scenario of these problems becoming scarce. This may seem unintuitive at first, since the set of possible problems one could ask is infinite. Perhaps the following analogy can help: a country or region can suffer a critical shortage of drinking water while simultaneously being surrounded by a massive ocean. One can easily generate any number of open problems in mathematics at will, such as working out the 10^10^10th digit of pi. But the vast majority of such problems are not worth focusing attention on: they show no particular propensity to reveal any further insights or connections to other questions, or may either be too easy or too impossible relative to known techniques to learn anything from the exercise. (1/4)

Rules for the Millennium Prize Problems

The revised rules for the Millennium Prize Problems were adopted by the Board of Directors of the Clay Mathematics Institute on 26 September, 2018.  Please read this document carefully before contacting CMI about a proposed solution.  In particular, please note that:

Navier-Stokes Equation - Clay Mathematics Institute

This is the equation which governs the flow of fluids such as water and air. However, there is no proof for the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding.

GitHub - openai/NavierStokesAndEuler at 8937a8f4cbc7abaab5e9e97d1cc7f5d2319d9538

Lean certificates accompanying Navier-Stokes and Euler results - openai/NavierStokesAndEuler

On the Navier–Stokes Millennium Prize Problem

We’re sharing an AI-generated solution to the Navier–Stokes Millennium Prize Problem, including a writeup and a formal proof in Lean.