This market will be resolved to:

**YES **-- if by the 1st of January, 2030 a proof recognized by the Clay Mathematics Institute is published

**NO **-- otherwise

## Related questions

All seven questions and my comments

Birch and Swinnerton-Dyer conjecture (1960s --): Mostly number theory, rational points on elliptic curves. Quick literature search did not turn up any relevance to elliptic curve cryptography.

Hodge conjecture (1930s --): algebraic topology. Not sure who is interested other than algebraic topologists and geometers (two of the most abstract fields of modern mathematics...).

Navier–Stokes existence and smoothness (1850? -- ): It has strong connection to classical mechanics. Presumably physical intuitions can help. Terence Tao has constructed (2016) a singular solution for averaged NS equation that allows liquid computer that constructs a smaller and faster copy of itself, and so on, allowing finite-time blowup. He believes it's possible for this to work with NS itself. See https://www.nature.com/articles/s42254-019-0068-9

P versus NP problem (1971--): Extremely difficult. Implications across all computer science, mathematics, and possibly philosophy. See

*Why Philosophers Should Care About Computational Complexity*.~~Poincaré conjecture~~(1904 -- 2003): Solved by the Ricci curvature flow (PDE on manifolds).Riemann hypothesis (1859--): Strong connections with number theory and complex analysis. Mathematicians typically say this is the most difficult one.

Yang–Mills existence and mass gap (1960s --): A problem in axiomatic Quantum Field Theory. I have no intuition for how difficult it is, but considering how many mathematical physicists there are, probably it's very difficult?

There have been 500 years of cumulative problem time, and only 1 solution, so the baseline rate is 1/500 per year. This gives a probability of 6/500 * 7 = 9% of any solution before 2030.

All seven questions and my comments

Birch and Swinnerton-Dyer conjecture (1960s --): Mostly number theory, rational points on elliptic curves. Quick literature search did not turn up any relevance to elliptic curve cryptography.

Hodge conjecture (1930s --): algebraic topology. Not sure who is interested other than algebraic topologists and geometers (two of the most abstract fields of modern mathematics...).

Navier–Stokes existence and smoothness (1850? -- ): It has strong connection to classical mechanics. Presumably physical intuitions can help. Terence Tao has constructed (2016) a singular solution for averaged NS equation that allows liquid computer that constructs a smaller and faster copy of itself, and so on, allowing finite-time blowup. He believes it's possible for this to work with NS itself. See https://www.nature.com/articles/s42254-019-0068-9

P versus NP problem (1971--): Extremely difficult. Implications across all computer science, mathematics, and possibly philosophy. See

*Why Philosophers Should Care About Computational Complexity*.~~Poincaré conjecture~~(1904 -- 2003): Solved by the Ricci curvature flow (PDE on manifolds).Riemann hypothesis (1859--): Strong connections with number theory and complex analysis. Mathematicians typically say this is the most difficult one.

Yang–Mills existence and mass gap (1960s --): A problem in axiomatic Quantum Field Theory. I have no intuition for how difficult it is, but considering how many mathematical physicists there are, probably it's very difficult?

There have been 500 years of cumulative problem time, and only 1 solution, so the baseline rate is 1/500 per year. This gives a probability of 6/500 * 7 = 9% of any solution before 2030.