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The Art of Mathematics: Daily Summaries Delivered
by Carol Jacoby
Conversations, explorations, conjectures solved and unsolved, mathematicians and beautiful mathematics. No math background required.
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- 1 weeks ago15 min
Zeno's Paradox: Is Motion Possible?
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.
- Jun 27, 202616 min
The Most Beautiful Formula
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.
- May 27, 202617 min
Math as it Should Be
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.
- Apr 22, 202612 min
Crocheting Mathematics
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.
- Mar 25, 202620 min
Pythagorean Triples and Some New Conjectures
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.
- Feb 25, 202615 min
Proofs and Buckets of Fish
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.
- Jan 28, 202614 min
Fractals: Simple rules, complex shapes
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.
- Apr 23, 202515 min
The Many Facets of Math
Alon Amit addresses the various facets of mathematics. Is it an art or a science? Both? Neither? Is it invented or discovered? Why is math that's developed for purely aesthetic reasons so often a useful tool for the real world? He likes that there are not simple, one-way answers. He challenges the listeners to post questions to Quora that surprise and delight him.
About The Art of Mathematics
Conversations, explorations, conjectures solved and unsolved, mathematicians and beautiful mathematics. No math background required.
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