Rational, Irrational and Transcendental Numbers
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 other-worldly. The Greeks were shocked to discover irrational numbers, violating their geometric view of the world. But later it was proved that any irrational number can be approximated remarkably well by a relatively simple fraction. The transcendental numbers were even more mysterious and were not even proved to exist until the 19th century.
August 24, 2022
Math as Art
Jeanne Lazzarini, a math education specialist, shares the connections between math, such as fractals and the golden ratio, and art. These are everywhere--nature, architecture, film and more. She shares hands-on mathematical activities that helped her students see math as an exploration and an art.
July 25, 2022
Exploration in Reading Mathematics
Lara Alcock of Loughborough University shares what she learned, by tracking eye movements, about how mathematicians and students differ in the ways they read mathematics. She developed a 10-15 minute exploration training, that increases students' comprehension through self-explanation. We also discuss the transition between procedural math and proofs that many students struggle with early in their college careers.
June 22, 2022
Games for Math Learning
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, he teaches them some techniques that are useful for mathematicians at any level--breaking down and building up a problem. We also discuss the "inchworm" and "grasshopper" styles of learning.
May 25, 2022
The Power of Mathematical Storytelling
Sunil Singh, the author of Chasing Rabbits and other books, shares fascinating stories that show mathematics as a universal place of exploration and comfort. Stories of mathematical struggle and discovery in the classroom help students connect deeply with the topic, feel the passion, and see math as multi-cultural and class-free.
April 22, 2022
The Mathematical World and the Physical World
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, how formal abstractions can describe the subjective physical world and various philosophies of mathematics.
March 09, 2022
Getting Athletes to Think Like Mathematicians
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 like mathematicians. Her problem solving technique applies to anything. Through it her students get comfortable with not knowing, with the adventure of seeking the answer. They build their brains in the process.
February 09, 2022
The Art of Definitions
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 they're artifacts of human choices. The student has the power to create mathematics through definitions. This is illustrated by the definitions of "sandwich" and "approaching a limit." What makes a good definition? How is mathematics like a dream?
January 12, 2022
Math Exploration for Kids
Mark Hendrickson, of Beast Academy Playground, talks about how to bring young kids into the joy, creativity and exploration that mathematicians experience. Kids enjoy art because they are free to try things and shun math for its apparent rigidness. He offers subtly mathematical games that invite even very young children to explore and question.
December 09, 2021
Is Mathematics an Art?
Joshua Sack, mathematics professor at California State University, Long Beach, explores the breadth of art and mathematics and finds much commonality in patterns, emotions and more.
November 10, 2021
Math as a way of thinking
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 for its own sake is later found useful for seemingly unrelated real-world problems. A silly little puzzle about islands and bridges leads eventually to a theory used for epidemics, transportation and kidney transplants. A space-filling curve, of interest to mathematicians mainly for being counterintuitive, has applications to efficient package delivery. The mathematical theories are often so bizarre that you wouldn't find them if you started with the real-world problem.
October 13, 2021
Symmetries in 3 and 4 Dimensions
Joseph Bennish joins us once again to continue his discussion of symmetry, this time venturing into higher dimensions. We explore the complex symmetry groups of the Platonic solids and the sphere and their relationships. We then venture into the 4th dimension, where we see that, with a change to the distance the symmetries are maintaining, we get Einstein's Theory of Relativity.
September 08, 2021
Symmetry, Shapes and Groups
We are all born with an intuitive attraction to symmetry, through human faces and heartbeats. Joseph Bennish, of California State University Long Beach, explores the mathematical meaning of symmetry, what it means for one shape to be more symmetric than another, how symmetries form mathematical groups and groups form symmetries, and hints at implications for Fourier analysis, astronomy and relativity.
August 14, 2021
Freshmen and Sophomores Confront Unsolved Problems
Dana Clahane, Professor of Mathematics at Fullerton College, dispels some of the misconceptions about mathematics and discusses some famous unsolved problems that he has freshmen and sophomores working on, learning what math is really about.
July 14, 2021
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 02, 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 05, 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 07, 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 02, 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 04, 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 07, 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 09, 2020
An Impossible Easy Question
Goldbach’s Conjecture and how a statement that is easy to understand is difficult or impossible to resolve
September 02, 2020
Everything You Know About Math is Wrong
We explore some of the common misconceptions about mathematics and mathematicians.
August 26, 2020