RefacteUnderstanding and judgment
Mathematical explanation, AI and research strategy, and the institutions that shape intellectual life.
Featured essay · Research strategy
Why abstraction is no refuge, and where sparse numerical computation offers a stronger research bet
The old refuge in abstraction is over. I argue for discovering better diagnostic and repair rules where spectral graph algorithms, matrix analysis, and numerical analysis meet, and explain how a specialist must earn an advantage beyond strong AI.
What a proof makes possible, and what an explanation establishes.
Old theorems and the changing means of understanding
How new proofs of familiar theorems expose mechanisms, improve estimates, and connect mathematical subjects. Comparing the arguments reveals why their constructions work, where they generalize, and what further questions they open.
Read the essayExpertise, explanation, and the scope of judgment
How to test whether a description retains what a conclusion needs, through eigenvalues, naturality, and the scope of judgment.
Read the essayResearch strategy, the value of understanding, and the conditions that sustain it.
AI research and the remaining human advantage is featured above.
Understanding, judgment, and the freedom to inquire
How people acquire the means to understand and pursue mathematics, and how AI changes the responsibilities of institutions that cultivate and judge those capacities.
Read the essayUnderstanding, employment, and independent capability
How the value of mathematical understanding connects to paid expertise, and what arrangements can sustain the independent capabilities on which mathematical life depends.
Read the essayHow authority, incentives, and accountability shape intellectual life.
Moral authority and the permanent defendant
How accusations acquire institutional force, why scrutiny can become costly, and what makes consequential judgments open to challenge and correction.
Read the essayPrestige, incentives, and the reproduction of intellectual conformity
How credentials, performance measures, prestige, and research incentives can reproduce academic authority while weakening independent judgment.
Read the essayKnowledge, Belief, and Freedom in Villeneuve’s Dune
How learned competence, extraordinary knowledge, and collective hope become claims to command in Villeneuve’s Dune.
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