The Queen of the Sciences: A History of Mathematics

Course Overview

Embark on a supreme intellectual adventure with award-winning Professor David M. Bressoud. This course traces the 4,000-year history of mathematics, exploring its evolution and its crucial role in understanding the universe. Drawing from exciting narratives and profound philosophical inquiries, it examines the major mathematicians and breakthroughs that have shaped our comprehension of the world.

Video Lectures

1. What Is Mathematics? – 32 min
   Introduction to the peculiar nature of mathematics and its fundamental concepts.
2. Babylonian and Egyptian Mathematics – 30 min
   Investigate early mathematical developments in ancient civilizations.
3. Greek Mathematics—Thales to Euclid – 30 min
   Survey the evolution of mathematics in ancient Greece.
4. Greek Mathematics—Archimedes to Hypatia – 31 min
   Explore contributions from key figures like Archimedes and Hypatia.
5. Astronomy and the Origins of Trigonometry – 31 min
   Learn how astronomy influenced the development of trigonometry.
6. Indian Mathematics—Trigonometry Blossoms – 31 min
   Discover significant advancements in mathematics during the Gupta Empire.
7. Chinese Mathematics—Advances in Computation – 30 min
   Examine early Chinese mathematical methods for taxation and surveying.
8. Islamic Mathematics—The Creation of Algebra – 31 min
   Trace the perfection of algebra in the Islamic Golden Age.
9. Italian Algebraists Solve the Cubic – 31 min
   Explore how Italian mathematicians addressed cubic and quartic equations.
10. Napier and the Natural Logarithm – 31 min
    Discover John Napier’s inventions and their implications for calculation.
11. Galileo and the Mathematics of Motion – 30 min
    Learn about Galileo’s innovations in studying motion mathematically.
12. Fermat, Descartes, and Analytic Geometry – 31 min
    Understand the contributions of Fermat and Descartes to analytic geometry.
13. Newton—Modeling the Universe – 29 min
    Examine Isaac Newton’s invention of calculus in understanding cosmic motions.
14. Leibniz and the Emergence of Calculus – 31 min
    Discover Gottfried Wilhelm Leibniz’s independent formulation of calculus.
15. Euler—Calculus Proves Its Promise – 30 min
    Explore Euler’s dominance in 18th-century mathematics.
16. Geometry—From Alhambra to Escher – 31 min
    Investigate the connection between geometry and art throughout history.
17. Gauss—Invention of Differential Geometry – 31 min
    Delve into Carl Friedrich Gauss’s contributions to differential geometry.
18. Algebra Becomes the Science of Symmetry – 30 min
    Learn about the evolution of algebra regarding transformations.
19. Modern Analysis—Fourier to Carleson – 30 min
    Understand the developments in analysis that solidified calculus’s foundations.
20. Riemann Sets New Directions for Analysis – 31 min
    Explore Bernhard Riemann’s influence on geometry and prime numbers.
21. Sylvester and Ramanujan—Different Worlds – 30 min
    Contrast the lives and contributions of Sylvester and Ramanujan.
22. Fermat’s Last Theorem—The Final Triumph – 31 min
    Follow the journey to proving Fermat’s last theorem over 350 years.
23. Mathematics—The Ultimate Physical Reality – 31 min
    Discover how mathematics describes physical realities and phenomena.
24. Problems and Prospects for the 21st Century – 33 min
    Conclude with a look at contemporary mathematical challenges and future directions.