book
by Imre Lakatos
A classroom dialogue in which a teacher and students argue over Euler's formula for polyhedra, run into one counterexample after another, and act out in miniature how definitions really get stretched and patched to save a theorem. It is Lakatos's case that mathematics grows by conjecture and criticism rather than by deduction from axioms, and still the sharpest book on what a proof is for.
March 2, 2026
Erik Hoel on why we can't trust AI self-reports, Peter Singer's moral evolution on Philosophize This!, and the Kurzgesagt video that made infinity feel small.
April 13, 2026
Experimental History on overlooked paths to impact, Dario Amodei's five-hour conversation with Lex Fridman, and Ethan Mollick on what just happened in AI.
March 30, 2026
Veritasium tells the story of antimatter's discovery, PBS Space Time asks if we can test quantum gravity, and Experimental History on why being serious matters.
