The Art of Mathematics

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.

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.

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.

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.

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.