Great Thinkers, Great Theorems by The Great Courses

Mathematics is filled with beautiful theorems that are as breathtaking as the most celebrated works of art, literature, or music. They are the Mona Lisas, Hamlets, and Fifth Symphonys of the field—landmark achievements that repay endless study and that are the work of geniuses as fascinating as Leonardo, Shakespeare, and Beethoven. Here is a sample:

• Pythagorean theorem: Although he didn’t discover the Pythagorean theorem about a remarkable property of right triangles, the Greek mathematician Euclid devised an ingenious proof that is a mathematical masterpiece. Plus, it’s beautiful to look at!
• Area of a circle: The formula for the area of a circle, A = π r², was deduced in a marvelous chain of reasoning by the Greek thinker Archimedes. His argument relied on the clever tactic of proof by contradiction not once, but twice.
• Basel problem: The Swiss mathematician Leonhard Euler won his reputation in the early 1700s by evaluating an infinite series that had stumped the best mathematical minds for a generation. The solution was delightfully simple; the path to it, bewilderingly complex.
• Larger infinities: In the late 1800s, the German mathematician Georg Cantor blazed the trail into the “transfinite” by proving that some infinite sets are bigger than others, thereby opening a strange new realm of mathematics.

You can savor these results and many more in Great Thinkers, Great Theorems, 24 half-hour lectures that conduct you through more than 3,000 years of beautiful mathematics, telling the story of the growth of the field through a carefully chosen selection of its most awe-inspiring theorems.

Approaching great theorems the way an art course approaches great works of art, the course opens your mind to new levels of math appreciation. And it requires no more than a grasp of high school mathematics, although it will delight mathematicians of all abilities.

Your guide on this lavishly illustrated tour, which features detailed graphics walking you through every step of every proof, is Professor William Dunham of Muhlenberg College, an award-winning teacher who has developed an artist’s eye for conveying the essence of a mathematical idea. Through his enthusiasm for brilliant strategies, novel tactics, and other hallmarks of great theorems, you learn how mathematicians think and what they mean by “beauty” in their work. As added enrichment, the course guidebook has supplementary questions and problems that allow you to go deeper into the ideas behind the theorems.

About the Author

Dr. William Dunham is the Truman Koehler Professor of Mathematics at Muhlenberg College in Allentown, Pennsylvania. He earned his undergraduate degree from the University of Pittsburgh and his M.S. and Ph.D. in Mathematics from The Ohio State University. Before his current appointment at Muhlenberg, Dr. Dunham taught at Hanover College in Indiana, receiving teaching awards from both institutions as well as the Award for Distinguished College or University Teaching from the Eastern Pennsylvania and Delaware Section of the Mathematical Association of America.

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