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The Millennium floor - seven open questions, and where they connect
floor
The seven Millennium Prize Problems on the one map of reality. The FLOOR is what is proven or observed: the joints where two of the questions meet at one established thing - the GUE statistics shared by zeta zeros and the lattice Dirac operator, the one L-function machinery, the Weil conjectures (the Riemann hypothesis over finite fields, a theorem by Deligne 1974 - the Riemann hypothesis itself stays open), the Tate conjecture that is Hodge's arithmetic twin and BSD over function fields, Bochner's vanishing under positive Ricci curvature, the renormalization group, the NP-hard sign problem, Manin's algorithm under finite Sha, the Diophantine form of RH, Arnold's geodesic flow. The questions are the OPEN ENDS hanging off that floor; one of them, Poincare, is closed (Perelman 2002-2003). Nothing is unified here: each joint is a join mathematics already made, found and cited, sealed where it is arithmetic. Riemann and Navier-Stokes share no joint - recorded as a miss. Historically the joints are where the proofs came from: Perelman imported a PDE into topology; Wiles' modularity gave BSD its L-function. A chain begins from a floor; the connections are where two chains become one.
- part of → The Floor of Discovery — one floor, and by its design the fear of God — the Millennium floor rests on the one Floor of Discovery
- has open end → The Riemann hypothesis — an open question hanging off the floor of what is proven
- has open end → The Birch and Swinnerton-Dyer conjecture — an open question hanging off the floor of what is proven
- has open end → Navier-Stokes existence and smoothness — an open question hanging off the floor of what is proven
- has open end → Yang-Mills existence and the mass gap — an open question hanging off the floor of what is proven
- has open end → P versus NP — an open question hanging off the floor of what is proven
- has open end → The Hodge conjecture — an open question hanging off the floor of what is proven
- has open end → The Poincare conjecture — an open question hanging off the floor of what is proven
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