The Art of Mathematics

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1. Randomness: Can You Predict Coin Flips?

   28 oktober 2026 · 10 min

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   Joseph Bennish discusses randomness. What is randomness? Is a coin flip random? What about a lot of coin flips? How much can we infer from random processes?

2. Theorem of the Day

   24 september 2026 · 23 min

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   Robin Whitty hosts the website theoremoftheday.org, which presents a concise poster about a different theorem each day, with explanation, graphics, and links. He has been doing this for 21 years. Theorems include one by an avant-garde musician that relates to group theory, and an explanation of the intermediate value theorem applied to pancakes. We also discuss how AI might change the role of mathematicians. Lees meer

3. Life-Changing Math

   26 augustus 2026 · 17 min

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   Ted Dintersmith, author of Aftermath: The Life-Changing Math that Schools Won't Teach You, argues that much of what we learn in math can be outsourced to machines. That frees people to understand the mathematical ideas that underlie much of modern life. An example is estimation, such as political polls. Understanding the various metrics that fill the news requires creativity coupled with logic. Learning to ask the right questions is more important than, say, learning to do closed-form integrals. Lees meer

4. Zeno's Paradox: Is Motion Possible?

   22 juli 2026 · 16 min

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   Josh Cole discussed Zeno's paradox that says motion is not possible since you must go half-way, and then half of the remaining distance, and so on, infinitely. Aristotle and others struggled with this, using ideas like "potential infinity" that hint at ideas that would appear in calculus hundreds of years later. The ancient Greeks were focused on the counting numbers, so they expect things to happen in succession. In particular, the Arrow Paradox asks at what point in time does an arrow move. Lees meer

5. The Most Beautiful Formula

   27 juni 2026 · 16 min

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   Joseph Bennish discusses Euler’s formula, which involves pi, e, the imagery i, 0 and 1, a beautiful formula that unites disparate types of numbers. We can think of e raised to an exponent as compound interest or a function with a remarkable property. We can extend the properties we expect from exponentials to imaginary numbers, which gives us periodicity instead of the usual steadily rising exponential growth. Lees meer

6. Math as it Should Be

   27 mei 2026 · 17 min

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   Aris Winger, Math Professor and Executive Director of the National Association of Mathematicians, has experienced first hand how math can save students' lives by uplifting them. Our education system can move beyond workbooks and help students, all students, think crisper and understand what's happening in the world. Lees meer

7. Crocheting Mathematics

   22 april 2026 · 13 min

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   Beyza Aslan, Associate Professor of Math at the University of North Florida, crochets mathematics. This turns abstractions, such as hyperbolic geometry, into something that can be touched, felt, manipulated, and experimented with. Her work as been exhibited at the Joint Mathematics Meetings. Lees meer

8. Pythagorean Triples and Some New Conjectures

   25 maart 2026 · 20 min

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   Ben Cornish, host of The Mathematicians Podcast, discusses Pythagorean triples, integers that can be the sides of a right triangle. There are infinitely many primitive triples, as he proves. This concept has been around even before Pythagoras and across cultures. Yet, there are always new questions to ask. Answering one involves, surprisingly, complex numbers. We leave you with an open conjecture. Lees meer

9. Proofs and Buckets of Fish

   25 februari 2026 · 15 min

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   Joel David Hamkins, author of Proof and the Art of Mathematics, presents the game Buckets of Fish, which seemingly will go on forever. Yet he presents a proof that it will always come to an end. In fact, he proves it using contradiction, mathematical induction, and even transfinite ordinals. Why do mathematicians like to do multiple proofs of a single statement? He also gives a winning strategy for the game and proves it works. Lees meer

10. Fractals: Simple rules, complex shapes

    28 januari 2026 · 15 min

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    Krystal Taylor, Associate Professor of Mathematics at Ohio State University, discussed the surprising characteristics of fractals, "infinity in a box." They may have fractional dimension, which varies depending on how it's measured. An infinite perimeter may enclose a finite area. Yet they are not just mathematical oddities--they appear in nature and have practical applications. Lees meer

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