Zero to Infinity: A History of Numbers

Course Overview

This journey to infinity and beyond will be the final brush stroke on our understanding of the endless frontier of numbers. In this engaging course, Professor Edward B. Burger guides you through the fascinating evolution of the concept of number through 24 lectures. Covering historical developments and the intrinsic nature of numbers, this course will challenge your intuitions and enhance your appreciation for mathematics.

From ancient practices to modern breakthroughs, you will explore the significance of numbers in various cultures and their impact on our understanding of the world. Prepare for a captivating journey that reveals how numbers shape our lives and drive our civilization forward.

Video Lectures

1. The Ever-Evolving Notion of Number – 32 min
   Investigate the elusive definition of “number” and its historical context.
2. The Dawn of Numbers – 29 min
   Explore early numerical systems used by ancient civilizations.
3. Speaking the Language of Numbers – 30 min
   Learn how societies invented numeral systems and arithmetic.
4. The Dramatic Digits—The Power of Zero – 32 min
   Analyze the transition from additive number systems to the base-10 system.
5. The Magical and Spiritual Allure of Numbers – 31 min
   Discover the mystical significance of numbers throughout history.
6. Nature’s Numbers—Patterns without People – 29 min
   Examine the existence of numerical structures in nature, such as the Fibonacci sequence.
7. Numbers of Prime Importance – 32 min
   Dive into the world of prime numbers and their properties.
8. Challenging the Rationality of Numbers – 30 min
   Explore the emergence of irrational numbers and their implications.
9. Walk the (Number) Line – 31 min
   Understand the concept of real numbers and their characteristics.
10. The Commonplace Chaos among Real Numbers – 30 min
    Delve into the distribution and properties of rational and irrational numbers.
11. A Beautiful Dusting of Zeroes and Twos – 32 min
    Discover the Cantor Set and its fascinating properties.
12. An Intuitive Sojourn into Arithmetic – 29 min
    Overview of fundamental arithmetic operations and their significance.
13. The Story of pi – 30 min
    Trace the history and significance of the number π.
14. The Story of Euler’s “e” – 30 min
    Learn about Euler’s number and its applications in mathematics.
15. Transcendental Numbers – 30 min
    Examine the nature of transcendental numbers and their implications.
16. An Algebraic Approach to Numbers – 30 min
    Contrast algebraic and analytical perspectives on numbers.
17. The Five Most Important Numbers – 31 min
    Explore the relationship between 0, 1, π, e, and i.
18. An Analytic Approach to Numbers – 30 min
    Discover the analytical method for understanding number systems.
19. A New Breed of Numbers – 30 min
    Investigate p-adic numbers and their unique properties.
20. The Notion of Transfinite Numbers – 29 min
    Learn about different sizes of infinity and their implications.
21. Collections Too Infinite to Count – 30 min
    Explore various collections of numbers and their infinite nature.
22. In and Out—The Road to a Third Infinity – 29 min
    Assess whether there are multiple sizes of infinity and their characteristics.
23. Infinity—What We Know and What We Don’t – 28 min
    Confront the mysteries of infinity and related mathematical challenges.
24. The Endless Frontier of Number – 29 min
    Reflect on the journey through the realm of numbers and its future explorations.