The Art of Mathematics
Episodes
Pythagorean Triples and Some New Conjectures
25 Mar 2026
Contributed by Lukas
Ben Cornish, host of The Mathematicians Podcast, discusses Pythagorean triples, integers that can be the sides of a right triangle. There are infinite...
Proofs and Buckets of Fish
25 Feb 2026
Contributed by Lukas
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...
Fractals: Simple rules, complex shapes
28 Jan 2026
Contributed by Lukas
Krystal Taylor, Associate Professor of Mathematics at Ohio State University, discussed the surprising characteristics of fractals, "infinity in a...
The Many Facets of Math
23 Apr 2025
Contributed by Lukas
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 ...
Will AI Replace Mathematicians?
26 Mar 2025
Contributed by Lukas
Alon Amit, prolific Quora math answerer, discusses how Artificial Intelligence might change the role of the mathematician. AI will make mathematics mo...
The National Museum of Mathematics
26 Feb 2025
Contributed by Lukas
Cindy Lawrence is the Director and CEO of the National Museum of Mathematics in New York City. She and a former math professor built it up from a gras...
Contemporary Math Research for Artistic Undergrads
22 Jan 2025
Contributed by Lukas
Veselin Jungic, teaching professor of mathematics at Simon Fraser University, introduces undergraduate math minors to contemporary math research. The ...
Where do Math Concepts Come From?
25 Dec 2024
Contributed by Lukas
Joseph Bennish discusses math as a "concept factory." The concept of prime numbers came from a desire to break numbers down to their simplest atoms. T...
A Clockmaker, an Egg, and a Cathedral
27 Nov 2024
Contributed by Lukas
Jeanne Lazzarini tells us how a clockmaker used an egg to win the competition to build the dome of the Florence Cathedral. The Cathedral had had a hug...
What is a Pattern?
23 Oct 2024
Contributed by Lukas
Math is in a sense the science of patterns. Alon Amit explores the question of what exactly is a pattern. A common example is the decimal digits of pi...
What's the Big Deal about Pi?
25 Sep 2024
Contributed by Lukas
Alon Amit joins us on the antipode of Pi Day to counter the myths and mysteries of this most famous irrational number. There's nothing magical abo...
Turning Math-Hating Prisoners into Mathematicians
28 Aug 2024
Contributed by Lukas
Kate Pearce, a post-doc researcher at UT Austin, talks about her experience teaching math in a women's prison. Her remedial college algebra studen...
Stop Overselling Mathematics
24 Jul 2024
Contributed by Lukas
Alon Amit, prolific Quora math answerer, argues that an honest representation of mathematical ideas is enough to spark interest in math. It's not ...
Math for Kids: It's not a Spectator Sport
26 Jun 2024
Contributed by Lukas
Dave Cole, the author of the Math Kids series of books, talks about introducing kids to math as a fun challenge and puzzle beyond the rote memorizatio...
Egyptian Fractions
22 May 2024
Contributed by Lukas
Neil Epstein, Associate Professor of Mathematics at George Mason University, introduces us to the fractions used by the ancient Egyptians, well before...
Da Vinci's Math Teacher: Merging the Practical and Theoretical
24 Apr 2024
Contributed by Lukas
Jeanne Lazzarini joins us again to introduce us to the mathematician Luca Pacioli, whose views of numbers and shapes influenced Leonardo da Vinci, lea...
Alon Amit, sharing the mathematical journey in Quora and Math Circles
27 Mar 2024
Contributed by Lukas
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,...
Too Much Math in the Schools? These Books Counter That Narrow View
28 Feb 2024
Contributed by Lukas
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. ...
Books for the Mathematical Tourist
24 Jan 2024
Contributed by Lukas
Lee Kraftchick discusses some of his favorite books for non-mathematicians to explore the breadth of mathematics. These books range from very old to c...
Reflecting on Kaleidoscopes
27 Dec 2023
Contributed by Lukas
Jeanne Lazzarini talks about kaleidoscopes and the mathematics that makes them work. This "beautiful form watcher" uses the laws of reflecti...
Meet the young Davidson Fellowship winners
22 Nov 2023
Contributed by Lukas
Ethan Zhao and Edward Yu are the winners in mathematics of the prestigious Davidson Fellow Scholarships, awarded based on projects completed by studen...
Gödel's Incompleteness, Fundamental Truths, and Reasoning in Math and Law
25 Oct 2023
Contributed by Lukas
Lawyer Lee Kraftchick discusses the search for truth and basic principles in the legal community and the surprising parallels and similarities with th...
Math and the Law
27 Sep 2023
Contributed by Lukas
Lee Kraftchick, a lawyer with a math degree, discusses some of the surprising parallels between the fields. Math is used directly to make statistical ...
Fabulous Fibonacci
23 Aug 2023
Contributed by Lukas
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 pl...
Vowels and Sounds and a Little Calculus
26 Jul 2023
Contributed by Lukas
Brian Katz, from California State University Long Beach, invites us to explore the various layers of ordinary sounds, informed by a little calculus. T...
The Hat: A Newly Discovered "Ein-stein" Tessellation Tile
28 Jun 2023
Contributed by Lukas
Jeanne Lazzarini, who has visited us before to talk about tessellations, discusses a new mathematical discovery that even earned a mention on Jimmy Ki...
Interfacing Music and Mathematics
24 May 2023
Contributed by Lukas
Lawrence Udeigwe, associate professor of mathematics at Manhattan College and an MLK Visiting Associate Professor in Brain and Cognitive Sciences at M...
Fourier Analysis: It's Not Just for Differential Equations
26 Apr 2023
Contributed by Lukas
Joseph Bennish returns to dig into the math behind the Fourier Analysis we discussed last time. Specifically, it allows us to express any function in ...
Joseph Fourier, the Heat Equation and the Age of the Earth
22 Mar 2023
Contributed by Lukas
Joseph Bennish, Professor Emeritus of California State University, Long Beach, joins us for an excursion into physics and some of the mathematics it i...
The Ten Most Important Theorems in Mathematics, Part II
22 Feb 2023
Contributed by Lukas
Jim Stein, Professor Emeritus of CSULS, returns to complete his (admittedly subjective) list of the ten greatest math theorems of all time, with fasci...
The Ten Most Important Theorems in Mathematics, Part I
25 Jan 2023
Contributed by Lukas
Jim Stein, Professor Emeritus of CSULB, presents his very subjective list of what he believes are the ten most important theorems, with several runner...
Surprisingly Better than 50-50
28 Dec 2022
Contributed by Lukas
Jim Stein, Professor Emeritus of California State University Long Beach, discusses some bets that appear to be 50-50, but can have better odds with a ...
Fascinating Fractals
23 Nov 2022
Contributed by Lukas
Jeanne Lazzarini joins us again to discuss fractals, a way to investigate the roughness that we see in nature, as opposed to the smoothness of standar...
Approximation by Rationals: A New Focus
26 Oct 2022
Contributed by Lukas
Joseph Bennish, Prof. Emeritus of CSULB, describes the field of Diophantine approximation, which started in the 19th Century with questions about how ...
Tessellations
28 Sep 2022
Contributed by Lukas
Jeanne Lazzarini, a math education specialist, returns to discuss tessellations and tiling in the works of Escher, Penrose, ancient artists and nature...
Rational, Irrational and Transcendental Numbers
24 Aug 2022
Contributed by Lukas
Joseph Bennish returns to take us beyond the rational numbers we usually use to numbers that have been given names that indicate they're crazy or othe...
Math as Art
25 Jul 2022
Contributed by Lukas
Jeanne Lazzarini, a math education specialist, shares the connections between math, such as fractals and the golden ratio, and art. These are everywhe...
Exploration in Reading Mathematics
22 Jun 2022
Contributed by Lukas
Lara Alcock of Loughborough University shares what she learned, by tracking eye movements, about how mathematicians and students differ in the ways th...
Games for Math Learning
25 May 2022
Contributed by Lukas
Jon Goga, of Brainy Spinach Math, is using the Roblox gaming platform to bring math learning to kids using something they already enjoy. Along the way...
The Power of Mathematical Storytelling
22 Apr 2022
Contributed by Lukas
Sunil Singh, the author of Chasing Rabbits and other books, shares fascinating stories that show mathematics as a universal place of exploration and c...
The Mathematical World and the Physical World
09 Mar 2022
Contributed by Lukas
Yusra Idichchou explores the question: Does math imitate life or does life imitate math? We touch on Oscar Wilde, philosophy of both math and language...
Getting Athletes to Think Like Mathematicians
09 Feb 2022
Contributed by Lukas
Caron Rivera, a math teacher at a school for elite athletes, shares how she breaks through the myth of the "math person" and teaches athletes to think...
The Art of Definitions
12 Jan 2022
Contributed by Lukas
Brian Katz of CSULB joins us once again to discuss mathematical definitions. Students often see them as cast in stone. Prof. Katz helps them see that ...
Math Exploration for Kids
09 Dec 2021
Contributed by Lukas
Mark Hendrickson, of Beast Academy Playground, talks about how to bring young kids into the joy, creativity and exploration that mathematicians experi...
Is Mathematics an Art?
10 Nov 2021
Contributed by Lukas
Joshua Sack, mathematics professor at California State University, Long Beach, explores the breadth of art and mathematics and finds much commonality ...
Math as a way of thinking
13 Oct 2021
Contributed by Lukas
Ian Stewart, prolific author of popular books about math, discusses how math is the best way to think about the natural world. Often math developed fo...
Symmetries in 3 and 4 Dimensions
08 Sep 2021
Contributed by Lukas
Joseph Bennish joins us once again to continue his discussion of symmetry, this time venturing into higher dimensions. We explore the complex symmetry...
Symmetry, Shapes and Groups
14 Aug 2021
Contributed by Lukas
We are all born with an intuitive attraction to symmetry, through human faces and heartbeats. Joseph Bennish, of California State University Long Beac...
Freshmen and Sophomores Confront Unsolved Problems
14 Jul 2021
Contributed by Lukas
Dana Clahane, Professor of Mathematics at Fullerton College, dispels some of the misconceptions about mathematics and discusses some famous unsolved p...
Stereotypes of Mathematics and Mathematicians
16 Jun 2021
Contributed by Lukas
Will Murray, chair of the math department at California State University, Long Beach, discusses popular stereotypes of mathematicians and what they do...
Prime numbers and their surprising patterns
02 Jun 2021
Contributed by Lukas
Joseph Bennish talks about prime numbers, a simple concept with surprising characteristics. Are they regular or random? This takes us into unexpected ...
Creativity in Mathematics
19 May 2021
Contributed by Lukas
Josh Hallam shares some of the ways he uses story writing and other creative endeavors in his math classes. He also discusses math in popular culture,...
The unreasonable effectiveness of mathematics
05 May 2021
Contributed by Lukas
Saleem Watson discusses the mysterious way math predicts the natural world. Much of math is invented, and yet there are many examples of cases in whic...
Alternative Proofs and Why We Seek Them
21 Apr 2021
Contributed by Lukas
Joseph Bennish discusses two famous theorems, proved long ago, and some modern alternative proofs. Why would we bother reproving something that was co...
Symmetry--It's More Than You Think
07 Apr 2021
Contributed by Lukas
Scott Crass, Professor of Mathematics at CSULB, expands our vague intuition about symmetry to look at transformations of various kinds and what they l...
Is Math Discovered or Invented?
24 Mar 2021
Contributed by Lukas
Saleem Watson, Professor Emeritus of Mathematics, CSULB, confronts an ancient mathematical argument. Is math a body of eternal truths waiting for an e...
That's Impossible. Oh, Yeah? Prove It.
10 Mar 2021
Contributed by Lukas
Paul Eklof, Professor Emeritus UCI, discusses the famous impossible straightedge-and-compass constructions of antiquity that have fascinated mathemati...
The Joy of Mathematical Discovery
24 Feb 2021
Contributed by Lukas
Joseph Bennish, math professor at California State University, Long Beach, discusses how math is an exploration involving imagination and excitement. ...
The Monty Hall Problem
10 Feb 2021
Contributed by Lukas
You are a contestant on Let's Make a Deal, hosted by Monty Hall. There are 3 identical doors. Behind only one is the prize car. You make your choice, ...
What Is Mathematics? Some Surprising Answers
27 Jan 2021
Contributed by Lukas
Brian Katz, a professor at California State University, Long Beach, approaches math as a philosopher, a linguist and an artist. It is not a scien...
Being a Mathematician
13 Jan 2021
Contributed by Lukas
We talk with Kathryn McCormick, Assistant Professor at California State University, Long Beach, about why she got into this obscure field, what a math...
Math Jokes and What They Say about Mathematicians
30 Dec 2020
Contributed by Lukas
There are a lot of jokes that poke fun at mathematicians, how they think and how they fumble around in the real world. Many of them start, "A mathemat...
The Most Famous (Formerly) Unsolved Problem
16 Dec 2020
Contributed by Lukas
Fermat’s Last Theorem is easy to state but has taken over 300 years to prove. Fermat’s supposed “marvelous proof” has been a magnet for crackp...
The Mathematics of Art
02 Dec 2020
Contributed by Lukas
A surprising amount of art is inspired by mathematics. The book Fragments of Infinity describes many works of art and the mathematics behind them. Mee...
The Real World Is a Special Case
18 Nov 2020
Contributed by Lukas
Abstract math is at once about nothing and about everything. The structures it builds may represent numbers, real world objects, music, or things we c...
How to Find Something You’ve Never Seen
04 Nov 2020
Contributed by Lukas
Another seemingly easy problem that’s hard to solve. In fact, it's unsolved. Find an odd perfect number or prove one doesn’t exist. The search inv...
Beyond the Third Dimension
21 Oct 2020
Contributed by Lukas
The fourth dimension is a staple of science fiction and the key to relativity. What exactly is it and how can we visualize it? What about higher dimen...
One Theorem, 99 Proofs
07 Oct 2020
Contributed by Lukas
Can you really approach one mathematical statement 99 different ways? We review the wonderful book 99 Variations on a Proof. The answer is yes.
A Beautiful Theorem with an Ugly Proof
30 Sep 2020
Contributed by Lukas
The Four Color Theorem is a pretty little conjecture that has been intriguing mathematicians for more than a century. Too bad the proof stands as an e...
To Infinity...and Beyond
23 Sep 2020
Contributed by Lukas
What is infinity, why does it seem so weird, and can you really go beyond it?
The Unsolved Is Solved...and Another
16 Sep 2020
Contributed by Lukas
We consider two problems, one in tiling and one in knots. They had each had been unsolved for over 50 years and their solutions hit the popular press ...
This Podcast is Lying
09 Sep 2020
Contributed by Lukas
We explore the mind-blowing Liar and related paradoxes and how they changed mathematics
An Impossible Easy Question
02 Sep 2020
Contributed by Lukas
Goldbach’s Conjecture and how a statement that is easy to understand is difficult or impossible to resolve
Everything You Know About Math is Wrong
26 Aug 2020
Contributed by Lukas
We explore some of the common misconceptions about mathematics and mathematicians.
The Art of Mathematics trailer
26 Jul 2020
Contributed by Lukas