William P. Thurston’s Work Algorithms

A deep 300-case reconstruction of Thurston’s mathematical method across geometrization, hyperbolic 3-manifolds, foliations, measured laminations, surface dynamics, Kleinian groups, orbifolds, rational maps, visualization, computation, education, and the philosophy of proof. The page treats each source unit as a methodological lecture: visible object, geometric language, invariant, deformation space, obstruction, proof route, and propagation channel.

33 Deep Strategies300 CasesGeometrization · Laminations · Dynamics · ProofOverlapping Prevalence
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Reconstruction method

This is a bibliographic and methodological reconstruction, not a reproduction of Thurston’s papers, books, notes, or lectures. It adapts the uploaded Logarchéon/Ahlfors/Conway/Knuth 300-case format into a Thurston-specific research instrument: strategy cards, formulas, diagnostic questions, failure modes, case traces, source-control layers, and worked demonstrations. Strategy tags overlap; percentages do not sum to 100%.

33strategies
300case lectures
12case families
900evidence tags

Core thesis

Thurston’s method is a discipline of visible structure. Start with a manipulable object, translate topology into geometry or dynamics, locate the obstruction, compress the invariant, and propagate the idea through examples, pictures, notes, and questions until a field can work with it.

Deep reading unit

Each case is read as a pipeline: object → picture/model → geometric language → invariant → obstruction → deformation/limit → theorem/program → communicable understanding.

Why this format

The page makes method operational. Cards expose strategy; formulas expose compression; rankings expose prevalence; corpus rows expose evidence; demonstrations expose how to reuse the method.

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The Thurston strategy engine

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Overlapping prevalence ranking

Bars show count divided by 300 cases. Since a case carries multiple strategy tags, the displayed prevalence is a method-frequency map rather than a probability distribution.

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Decision tree for reading Thurston as method

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300-case corpus

#CaseFamilyDeep reading moveStrategies
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Source spine as control system

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Worked demonstrations