An ongoing essay series
Axioms
Essays on the History and Philosophy of Mathematics
How did mathematics come to trust its objects, methods, and proofs? This series begins with concrete mathematical questions and follows them toward the assumptions underneath.
Begin here
A question before the first axiom
The introduction sets out the route through the series and the tension between describing a mathematical object and establishing that it exists.
Part I
From Infinity to Axioms
Six essays move from Cantor's comparison of infinite sets through paradox, type theory, and ZFC to the distinction between formal proof and interpretation.
The wider route
Where the series goes next
Later parts will consider the limits of formal systems and the philosophical questions that remain when mathematics turns to models, structures, and the world beyond its axioms. Titles and order may change as the essays develop.