Disc 1. Lecture 1. Understanding nature ; Lecture 2. The language of shapes ; Lecture 3. Knots and strings ; Lecture 4. Creating new knots from old ; Lecture 5. DNA entanglement ; Lecture 6. The Jones revolution -- disc 2. Lecture 7. Symmetries of molecules ; Lecture 8. The messy business of tangles and mutations ; Lecture 9. Braids and the language of groups ; Lecture 10. Platonic solids and Euler's masterpiece ; Lecture 11. Surfaces and a new notion of equivalence ; Lecture 12. Reaching boundaries and losing orientations -- Disc 2. Lecture 7. Symmetries of molecules ; Lecture 8. The messy business of tangles and mutations ; Lecture 9. Braids and the language of groups ; Lecture 10. Platonic solids and Euler's masterpiece ; Lecture 11. Surfaces and a new notion of equivalence ; Lecture 12. Reaching boundaries and losing orientations --
Disc 3. Lecture 13. Knots and surfaces -- 14. Wind flows and currents -- 15. Curvature and Gauss's geometric gem -- 16. Playing with scissors and polygons -- 17. Bending chains and folding origami -- 18. Cauchy's rigidity and Connelly's flexibility -- Disc 4. Lecture19. Mountain terrains and surface reconstruction -- 20. Voronoi's regions of influence -- 21. Convex hulls and computational conplexity -- 22. Patterns and colors -- 23. Orange stackings and bubble partitions -- 24. The topology of the universe --
Disc 5. Lecture 25. Tetrahedra and mathematical surgery
26. The fundamental group
27. Poincare's question and Perelman's answer
28. The geometry of the universe
29. Visualizing in higher dimensions
30. Polyhedra in higher dimensions
Disc 6. Lecture 31. Particle motions
35. Reclaiming Leonardo da Vinci
36. Pushing the forefront.