The Last Mathematician from Hilbert’s G¨ ottingen: Saunders Mac Lane as Philosopher of Mathematics

While Saunders Mac Lane studied for his D.Phil inG¨ ottingen, he heard DavidHilbert’s weekly lectures on philosophy, talked philosophy with Hermann Weyl, and studied it with Moritz Geiger. Their philosophies and Emmy Noether’s algebra all influenced his conception of category theory, which has become the working structure theory of mathematics. His practice has constantly affirmed that a proper large-scale organization for mathematics is the most efficient path to valuable specific results—while he sees that the question of which results are valuable has an ineliminable philosophic aspect. His philosophy relies on the ideas of truth and existence he studied in G¨ ottingen. His career is a case study relating naturalism in philosophy of mathematics to philosophy as it naturally arises in mathematics.