Part 1: Disc 1. Lecture 1. What is mathematics? ; Lecture 2. Babylonian and Egyptian mathematics ; Lecture 3. Greek mathematics, Thales to Euclid ; Lecture 4. Greek mathematics, Archimedes to Hypatia ; Lecture 5. Astronomy and the origins of trigonometry ; Lecture 6. Indian mathematics, trigonometry blossoms
Disc 2. Lecture 7. Chinese mathematics, advances in computation ; Lecture 8. Islamic mathematic, the creation of algebra ; Lecture 9. Italian algebraists solve the cube ; Lecture 10. Napier and the natural logarithm ; Lecture 11. Galileo and the mathematics of motion ; Lecture 12. Fermat, Descartes, and analytic geometry.
Part 2. Disc 3. Lecture 13. Newton, modeling the universe ; Lecture 14. Leibniz and the emergence of calculus ; Lecture 15. Euler, calculus proves its promise ; Lecture 16. Geometry, from Alhambra to Escher ; Lecture 17. Gauss, invention of differential geometry ; Lecture 18. Algebra becomes the science of symmetry
Disc 4. Lecture 19. Modern analysis, Fourier to Carleson ; Lecture 20. Riemann sets new directions for analysis ; Lecture 21. Sylvester and Ramanujan, different worlds ; Lecture 22. Fermat's last theorem, the final triumph ; Lecture 23. Mathematics, the ultimate physical reality ; Lecture 24. Problems and prospects for the 21st century.
