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The Art of Mathematics

The Art of Mathematics

By Carol Jacoby
Conversations, puzzles, book reviews, conjectures solved and unsolved, mathematicians and beautiful mathematics. No math background required.
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Stereotypes of Mathematics and Mathematicians
Will Murray, chair of the math department at California State University, Long Beach, discusses popular stereotypes of mathematicians and what they do when they do mathematics. Is it all lone geniuses generating big numbers? If so many people dislike mathematical thinking, why is Sudoku so popular?
June 16, 2021
Prime numbers and their surprising patterns
Joseph Bennish talks about prime numbers, a simple concept with surprising characteristics. Are they regular or random? This takes us into unexpected realms--calculus, complex numbers, Fourier transforms and "the music of the primes."
June 2, 2021
Creativity in Mathematics
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, including an original theorem in the animated show Futurama.
May 19, 2021
The unreasonable effectiveness of mathematics
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 which purely abstract math, developed with no reference to the natural world, later is found to make accurate and useful models and predictions of the physical world.
May 5, 2021
Alternative Proofs and Why We Seek Them
Joseph Bennish discusses two famous theorems, proved long ago, and some modern alternative proofs. Why would we bother reproving something that was confirmed thousands of years ago? The answers are insight, aesthetics, and opening up surprising new areas of investigation.
April 21, 2021
Symmetry--It's More Than You Think
Scott Crass, Professor of Mathematics at CSULB, expands our vague intuition about symmetry to look at transformations of various kinds and what they leave fixed. This approach finds applications in physics, biology, art and several branches of math.
April 7, 2021
Is Math Discovered or Invented?
Saleem Watson, Professor Emeritus of Mathematics, CSULB, confronts an ancient mathematical argument. Is math a body of eternal truths waiting for an explorer to uncover them, or an invention or work of art created by the human mind? Or some of each?
March 24, 2021
That's Impossible. Oh, Yeah? Prove It.
Paul Eklof, Professor Emeritus UCI, discusses the famous impossible straightedge-and-compass constructions of antiquity that have fascinated mathematicians and attracted cranks for centuries. There are infinitely many possible constructions. How can you prove not one of them will work?
March 10, 2021
The Joy of Mathematical Discovery
Joseph Bennish, math professor at California State University, Long Beach, discusses how math is an exploration involving imagination and excitement. Kids get this. Adults can recapture this by generalizing and questioning. For example, a simple barnyard riddle leads to questions about optics.
February 24, 2021
The Monty Hall Problem
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, then Monty Hall opens one of the other doors to reveal a goat and asks whether you want to change your choice. Should you, or does it matter? Paula Sloan talks about the counterintuitive answer, and how she got the Duke MBA students in her math class to believe the answer.
February 10, 2021
What Is Mathematics? Some Surprising Answers
Brian Katz, a professor at California State University, Long Beach, approaches math as a philosopher, a linguist and an artist. It is not a science, but a byproduct of consciousness, an expression of humanity and a way to make connections.
January 27, 2021
Being a Mathematician
We talk with Kathryn McCormick, Assistant Professor at California State University, Long Beach, about why she got into this obscure field, what a mathematician really does, and where we can learn more about being a mathematician.
January 13, 2021
Math Jokes and What They Say about Mathematicians
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 mathematician, an engineer and a physicist ..."  We'll look at what these jokes say about us. The most telling is a little joke that only a mathematician would enjoy, since it gives surprising insight into how mathematicians think through all this abstraction.
December 30, 2020
The Most Famous (Formerly) Unsolved Problem
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 crackpots and obsessed mathematicians, leading through a treasure hunt across almost all branches of mathematics.
December 16, 2020
The Mathematics of Art
A surprising amount of art is inspired by mathematics. The book Fragments of Infinity describes many works of art and the mathematics behind them. Meet mathematicians who have become artists and artists who have become mathematicians, and some who have always straddled both worlds.
December 2, 2020
The Real World Is a Special Case
Abstract math is at once about nothing and about everything. The structures it builds may represent numbers, real world objects, music, or things we can barely imagine. Here we look at group theory for numbers, music, Rubik’s cubes and beyond.
November 18, 2020
How to Find Something You’ve Never Seen
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 involves “spoof” answers, trying to find the right answer (or prove it doesn't exist) by looking at wrong answers. Hey, nothing else has worked.
November 4, 2020
Beyond the Third Dimension
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 dimensions?
October 21, 2020
One Theorem, 99 Proofs
Can you really approach one mathematical statement 99 different ways? We review the wonderful book 99 Variations on a Proof. The answer is yes.
October 7, 2020
A Beautiful Theorem with an Ugly Proof
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 example of really ugly mathematics.
September 30, 2020
To Infinity...and Beyond
What is infinity, why does it seem so weird, and can you really go beyond it?
September 23, 2020
The Unsolved Is Solved...and Another
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 in the same week. What kind of skills help people make surprising connections and new discoveries?
September 16, 2020
This Podcast is Lying
We explore the mind-blowing Liar and related paradoxes and how they changed mathematics
September 9, 2020
An Impossible Easy Question
Goldbach’s Conjecture and how a statement that is easy to understand is difficult or impossible to resolve
September 2, 2020
Everything You Know About Math is Wrong
We explore some of the common misconceptions about mathematics and mathematicians.
August 26, 2020