RefacteUnderstanding and judgment
What a method makes possible, what an explanation establishes, and what sustains a life of inquiry.
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 essayUnderstanding, 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 essayMoral 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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