tensorgami

September 28, 2025

Bespoke Craft vs. Framework Power: Why Nonlinear PDE Endures (and Measures Credit Differently)

Thesis. Mathematics runs on two production modes. Framework fields (many parts of algebra/geometry/topology) win by inventing reusable languages and libraries; progress compounds as more of the subject is algebraitized and “packaged.” Bespoke fields (nonlinear PDE and hard analysis at the frontier) win by inventing one‑off mechanisms – custom multipliers, weights, parametrices, resonance cuts, rigidity schemes

Mathematics under AI: why framework fields automate first while “chaotic” fields endure

TLDR. AI will keep eating execution-heavy mathematics that sits on stable formal scaffolding – think large chunks of algebraic geometry or homological algebra once the objects are defined in Lean. The parts that resist are the ones where progress depends on inventing the invariant, the weight, the parametrix, or the gluing scheme – contest combinatorics

Socratic Scoreboards: How Performative Nihilism, Contrarianism, and Demagoguery Corrode Mathematical Culture, and How to Repair It

Thesis A cluster of behaviors, performative nihilism (“I don’t care” as social pose), contrarianism-as-identity (disagreeing to signal status rather than to test truth), plausible-deniability retreats (hot takes downgraded to “just joking” when challenged), and demagogic crowd‑work, has migrated from broader Western cultural life into academic mathematics. The effect is to shift the scoreboard from logos