The Art of Mathematics

Latest Episodes:

Egyptian Fractions May 22, 2024

Show notes

Neil Epstein, Associate Professor of Mathematics at George Mason University, introduces us to the fractions used by the ancient Egyptians, well before the Greeks and Romans. The Egyptian fractions all had a unit numerator. They could represent any fraction as a sum of unique unit fractions, a fact that was not proved until centuries later. These sums inspired conjectures, one of which was proved only recently, while others remain unsolved to this day. Recent work extends these concepts beyond fractions of integers. Human heritage goes way back, but is still inspiring modern research.

Da Vinci's Math Teacher: Merging the Practical and Theoretical Apr 24, 2024

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Jeanne Lazzarini joins us again to introduce us to the mathematician Luca Pacioli, whose views of numbers and shapes influenced Leonardo da Vinci, leading to a period of art and invention. His book, De Divina Proportione, is the only book ever illustrated by da Vinci. The Renaissance was a period when mathematicians studied art and artists studied mathematics. As da Vinci said, "Everything connects."

Alon Amit, sharing the mathematical journey in Quora and Math Circles Mar 27, 2024

Show notes

Alon Amit, probably the most prolific answerer of math questions on Quora, shares his reasons for his deep involvement. He seeks to share the journey, the exploration and stumbles of solving a problem. He's especially drawn to questions that will teach him things, even if he never completes the answer. He also shares his joy of problem solving with kids through Math Circles. One example problem, involving only 4 dots, can be worked on by a young child, yet affords deep exploration.

Too Much Math in the Schools? These Books Counter That Narrow View Feb 28, 2024

Show notes

Lee Kraftchick continues his tour of books about math written for the non-mathematician like himself. We also can't let go of Gödel Escher Bach. Lee cites an opinion piece in the Washington Post, titled, "The Problem with Schools Today is Too Much Math," which gives a very narrow view of what math is. He counters it with a response (see theartofmathematicspodcast.com) and more books that demonstrate that math provides "pleasures which all the arts afford." He also discusses books about math and the real world and compilations of the broad range of mathematics.

Books for the Mathematical Tourist Jan 24, 2024

Show notes

Lee Kraftchick discusses some of his favorite books for non-mathematicians to explore the breadth of mathematics. These books range from very old to current. Some discuss beautiful proofs, whether math is invented or discovered, and how to think. Lee and Carol agree on the number one greatest book for mathematicians and non-mathematicians alike. See the full list at theartofmathematicspodcast.com.

Reflecting on Kaleidoscopes Dec 27, 2023

Show notes

Jeanne Lazzarini talks about kaleidoscopes and the mathematics that makes them work. This "beautiful form watcher" uses the laws of reflection to make ever-changing repeated symmetries. The use of more mirrors, rectangles, cylinders or pyramids create even more complex patterns.

Meet the young Davidson Fellowship winners Nov 22, 2023

Show notes

Ethan Zhao and Edward Yu are the winners in mathematics of the prestigious Davidson Fellow Scholarships, awarded based on projects completed by students under 18. Ethan's project was on learning models and Edward's was on combinatorics. It was math contests and the MIT Primes program that gave them the background to do original research in high school, an experience most mathematicians don't get until graduate school. They also discussed the accessibility of math. You can come up with interesting problems while staring out the window. You can invent your own tools.

Gödel's Incompleteness, Fundamental Truths, and Reasoning in Math and Law Oct 25, 2023

Show notes

Lawyer Lee Kraftchick discusses the search for truth and basic principles in the legal community and the surprising parallels and similarities with the same search in the math community. Mathematical and legal arguments follow a similar structure. Even the backwards way an argument is created is the same.

Math and the Law Sep 27, 2023

Show notes

Lee Kraftchick, a lawyer with a math degree, discusses some of the surprising parallels between the fields. Math is used directly to make statistical arguments to rule out random chance as a cause. He gives examples from his experience in redistricting and affirmative action. Math is used indirectly in legal reasoning from what is known to justified conclusions. Math reasoning and legal reasoning are remarkably similar. He invites lawyers to set aside the usual "lawyers aren't good at math" stereotype and see the beauty of the subject.

Fabulous Fibonacci Aug 23, 2023

Show notes

Jeanne Lazzarini looks for math in the real world and finds the Fibonacci sequence and the closely related Golden Ratio. These appear as we examine plants, bees, rabbits, flowers, fruit, and the human body. These natural patterns and pleasing symmetries find their way into the arts. Does nature understand math better than we do?

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