physics
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The Egg-Cracking Spell: On Foot Speed, Escape Velocity, and the Structural Forgetting of Foundations
There is a category error that pervades the Western mathematical establishment, and it concerns the difference between excellence and originality — or more precisely, between optimization within a paradigm and the creation of a new one. The recent death of Benedict Gross at seventy-five offers an occasion to examine this error with some care, not…
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There is a line in the classification of algebraic curves that separates two worlds. On one side lie the curves whose geometric fundamental groups are abelian — elliptic curves, the multiplicative group, the projective line with few punctures — and on the other side lie the curves whose geometric fundamental groups are non-abelian, rigid, and…
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Elite technical culture has produced a peculiar kind of intellect. It excels on examinations, dazzles in standard problem sets, and performs confidently in environments that look like clean textbook exercises. Yet it falters, sometimes catastrophically, when confronted with even slight deviations from the familiar. The same person who can solve a thousand routine engineering problems…
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There is a scene in Arthdal Chronicles where a ritual dance, drilled into a young acolyte from childhood, turns out to be a coded procedure for retrieving a hidden bell from a temple. The choreography looks like piety until the moment of use, when it reveals itself as an algorithm. Much of modern mathematics feels…
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Mathematics often advances by a prior about compressibility. Some investigators trust that with the right abstractions the world can be funneled into an additive and exact environment where one can add and subtract, take kernels and cokernels, and push information through functors without losing control. Others trust that essential difficulty lives in nonlinear and metric…
tensorgami 