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The logarithm - the instrument the joints share
floor
Two trees: Napier's table (1614) and Saint-Vincent's hyperbola (1647) - a number's logarithm as a tabulated count, and as an area. They become one function in Euler's Introductio (1748): e, and exp and log as inverses. From there the logarithm enters each of the seven questions as the instrument that turns a product into a sum (log zeta, Euler 1737 and Riemann 1859), a size into a count (the height of a point, Weil 1929 and Néron 1965), a scale into a step (the running coupling, Gell-Mann-Low 1954), a profile into a line (the law of the wall, von Kármán 1930), a number into its length (Cobham 1965), a pole into a form (Deligne 1971), a count of states into an entropy (Boltzmann 1877, Shannon 1948, Perelman 2002). Found, cited; sealed where it is arithmetic (tools/tick.py logarithm_chain).
- part of → The Floor of Discovery — one floor, and by its design the fear of God — the logarithm chain rests on the one Floor of Discovery
- has part → Napier 1614 — Mirifici logarithmorum canonis descriptio — a root of this chain - one of the two trees it began from
- has part → Saint-Vincent 1647 — Opus geometricum quadraturae circuli et sectionum coni — a root of this chain - one of the two trees it began from
- has open end → The Riemann hypothesis — the open question this chain reaches
- has open end → The Birch and Swinnerton-Dyer conjecture — the open question this chain reaches
- has open end → Navier-Stokes existence and smoothness — the open question this chain reaches
- has open end → Yang-Mills existence and the mass gap — the open question this chain reaches
- has open end → P versus NP — the open question this chain reaches
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