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Podcast Profile: The Art of Mathematics

podcast imageTwitter: @CarolJacobyPhD
59 episodes
2020 to present
Average episode: 17 minutes
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Categories: Interview-Style • Math

Podcaster's summary: Conversations, explorations, conjectures solved and unsolved, mathematicians and beautiful mathematics. No math background required.

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List Updated: 2024-Apr-20 06:27 UTC. Episodes: 59. Feedback: @TrueSciPhi.

2024-Mar-27 • 20 minutes
Alon Amit, sharing the mathematical journey in Quora and Math Circles
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, the exploration and stumbles of solving a problem. He's especially drawn to questions that will teach him things, even if he never completes the answer. He also shares his joy of problem solving with kids through Math Circles. One example problem, involving only 4 dots, can be worked on by a young child, yet affords deep exploration. | | --- | | Send in a ...
2024-Feb-28 • 21 minutes
Too Much Math in the Schools? These Books Counter That Narrow View
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. Lee cites an opinion piece in the Washington Post, titled, "The Problem with Schools Today is Too Much Math," which gives a very narrow view of what math is. He counters it with a response (see and more books that demonstrate that math provides "pleasures which all the arts afford." He also discusses books about m...
2024-Jan-24 • 21 minutes
Books for the Mathematical Tourist
Lee Kraftchick discusses some of his favorite books for non-mathematicians to explore the breadth of mathematics. These books range from very old to current. Some discuss beautiful proofs, whether math is invented or discovered, and how to think. Lee and Carol agree on the number one greatest book for mathematicians and non-mathematicians alike. See the full list at | | --- | | Send in a voice message:
2023-Dec-27 • 20 minutes
Reflecting on Kaleidoscopes
Jeanne Lazzarini talks about kaleidoscopes and the mathematics that makes them work. This "beautiful form watcher" uses the laws of reflection to make ever-changing repeated symmetries. The use of more mirrors, rectangles, cylinders or pyramids create even more complex patterns. | | --- | | Send in a voice message:
2023-Nov-22 • 14 minutes
Meet the young Davidson Fellowship winners
Ethan Zhao and Edward Yu are the winners in mathematics of the prestigious Davidson Fellow Scholarships, awarded based on projects completed by students under 18. Ethan's project was on learning models and Edward's was on combinatorics. It was math contests and the MIT Primes program that gave them the background to do original research in high school, an experience most mathematicians don't get until graduate school. They also discussed the accessibility of math. You can come up with interesting problems w...
2023-Oct-25 • 22 minutes
Gödel's Incompleteness, Fundamental Truths, and Reasoning in Math and Law
Lawyer Lee Kraftchick discusses the search for truth and basic principles in the legal community and the surprising parallels and similarities with the same search in the math community. Mathematical and legal arguments follow a similar structure. Even the backwards way an argument is created is the same. | | --- | | Send in a voice message:
2023-Sep-27 • 20 minutes
Math and the Law
Lee Kraftchick, a lawyer with a math degree, discusses some of the surprising parallels between the fields. Math is used directly to make statistical arguments to rule out random chance as a cause. He gives examples from his experience in redistricting and affirmative action. Math is used indirectly in legal reasoning from what is known to justified conclusions. Math reasoning and legal reasoning are remarkably similar. He invites lawyers to set aside the usual "lawyers aren't good at math" stereo...
2023-Aug-23 • 21 minutes
Fabulous Fibonacci
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 plants, bees, rabbits, flowers, fruit, and the human body. These natural patterns and pleasing symmetries find their way into the arts. Does nature understand math better than we do? | | --- | | Send in a voice message:
2023-Jul-26 • 12 minutes
Vowels and Sounds and a Little Calculus
Brian Katz, from California State University Long Beach, invites us to explore the various layers of ordinary sounds, informed by a little calculus. The limited frequencies that come out of the wave equation are what separates sounds that communicate (voice, music) from noise. These higher notes are in the sound itself and you can hear them (but alas, not on this compressed podcast audio). Brian has provided links to hear these layers of pitches at | | --- | | Send in a voi...
2023-Jun-28 • 14 minutes
The Hat: A Newly Discovered "Ein-stein" Tessellation Tile
Jeanne Lazzarini, who has visited us before to talk about tessellations, discusses a new mathematical discovery that even earned a mention on Jimmy Kimmel. It's a shape that can be used to fill the plane with no gaps and no overlaps and, most remarkably, no repeating patterns. | | | --- | | Send in a voice message:
2023-May-24 • 21 minutes
Interfacing Music and Mathematics
Lawrence Udeigwe, associate professor of mathematics at Manhattan College and an MLK Visiting Associate Professor in Brain and Cognitive Sciences at MIT, is both a mathematician and a musician. We discuss his recent opinion piece in the Notices of the American Mathematical Society calling for "A Case for More Engagement" between the two areas, and even get a little "Misty." He's working on music that both jazz and math folks will enjoy. We talk about "hearing" math in jazz and ...
2023-Apr-26 • 18 minutes
Fourier Analysis: It's Not Just for Differential Equations
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 terms of sines and cosines. Fourier analysis appears in nature--our eyes and ears do it. It's used to study the distribution of primes, build JPEG files, read the structure of complicated molecules and more. | | | --- | | Send in a voice message:
2023-Mar-22 • 18 minutes
Joseph Fourier, the Heat Equation and the Age of the Earth
Joseph Bennish, Professor Emeritus of California State University, Long Beach, joins us for an excursion into physics and some of the mathematics it inspired. Joseph Fourier straddled mathematics and physics. Here we focus on his heat equation, based on partial differential equations. Partial differential equations have broad applications. Fourier developed not only the heat equation but also a way to solve it. This equation was used to answer, among other questions, the issue of the age of the earth. Was t...
2023-Feb-22 • 16 minutes
The Ten Most Important Theorems in Mathematics, Part II
Jim Stein, Professor Emeritus of CSULS, returns to complete his (admittedly subjective) list of the ten greatest math theorems of all time, with fascinating insights and anecdotes for each. Last time he did the runners up and numbers 8, 9 and 10. Here he completes numbers 1 through 7, again ranging over geometry, trig, calculus, probability, statistics, primes and more. | | --- | | Send in a voice message:
2023-Jan-25 • 25 minutes
The Ten Most Important Theorems in Mathematics, Part I
Jim Stein, Professor Emeritus of CSULB, presents his very subjective list of what he believes are the ten most important theorems, with several runners up. These theorems cover a broad range of mathematics--geometry, calculus, foundations, combinatorics and more. Each is accompanied by background on the problems they solve, the mathematicians who discovered them, and a couple personal stories. We cover all the runners up and numbers 10, 9 and 8. Next month we'll learn about numbers 1 through 7. --- Send...
2022-Dec-28 • 18 minutes
Surprisingly Better than 50-50
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 tiny amount of seemingly useless information. Blackwell's Bet involves two envelopes of money. You can open only one. Which one do you choose? We learn about David Blackwell and his mathematical journey amid blatant racism. Another seeming 50-50 bet is guessing which of two unrelated events that you know nothing about is more likely; you can do better than 50-...
2022-Nov-23 • 21 minutes
Fascinating Fractals
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 standard mathematics. Fractals are built of iterated patterns with zoom similarity. Examples include the Koch Snowflake, which encloses a finite area but has infinite perimeter, and the Sierpinski Triangle, which has no area at all. Fractals have fractional dimension. For example, The Sierpinski Triangle is of dimension 1.585, reflecting its position in the nether wo...
2022-Oct-26 • 22 minutes
Approximation by Rationals: A New Focus
Joseph Bennish, Prof. Emeritus of CSULB, describes the field of Diophantine approximation, which started in the 19th Century with questions about how well irrational numbers can be approximated by rationals. It took Cantor and Lebesgue to develop new ways to talk about the sizes of infinite sets to give the 20th century new ways to think about it. This led up to the Duffin-Schaeffer conjecture and this year's Fields Medal for James Maynard. | | --- | | Send in a voice message: https://podcasters.spotify....
2022-Sep-28 • 21 minutes
Jeanne Lazzarini, a math education specialist, returns to discuss tessellations and tiling in the works of Escher, Penrose, ancient artists and nature. We go beyond the familiar square or hexagonal tilings of the bathroom floor. M.C. Escher was an artist who made tessellations with lizards or birds, as well as pictures of very strange stairways. Roger Penrose is a scientist who discovered two tiles that, remarkably, can cover an area without repeat, as well as a strange stairway. | | --- | | Send in a vo...
2022-Aug-24 • 22 minutes
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. | | --- | |...
2022-Jul-25 • 19 minutes
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. | | --- | | Send in a voice message:
2022-Jun-22 • 17 minutes
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. | | --- | | Send in a voice message:
2022-May-25 • 19 minutes
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. --- Send in a voice message:
2022-Apr-22 • 16 minutes
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. | | --- | | Send in a voice message:
2022-Mar-09 • 12 minutes
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. --- Send in a voice message:
2022-Feb-09 • 17 minutes
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.  | | --- | | Send in a voice message:
2022-Jan-12 • 20 minutes
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? | | --- | | Send in a voice message: ...
2021-Dec-09 • 18 minutes
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. --- Send in a voice message:
2021-Nov-10 • 12 minutes
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. --- Send in a voice message:
2021-Oct-13 • 20 minutes
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 math...
2021-Sep-08 • 19 minutes
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. | | --- | | Send in a voice message:
2021-Aug-14 • 20 minutes
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. | | --- | | Send in a voice message:
2021-Jul-14 • 19 minutes
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. --- Send in a voice message:
2021-Jun-16 • 18 minutes
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? | | --- | | Send in a voice message:
2021-Jun-02 • 17 minutes
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." --- Send in a voice message:
2021-May-19 • 18 minutes
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. --- Send in a voice message:
2021-May-05 • 13 minutes
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. | | --- | | Send in a voice message:
2021-Apr-21 • 17 minutes
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. | | --- | | Send in a voice message:
2021-Apr-07 • 14 minutes
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. | | --- | | Send in a voice message:
2021-Mar-24 • 17 minutes
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? | | --- | | Send in a voice message:
2021-Mar-10 • 17 minutes
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? | | --- | | Send in a voice message:
2021-Feb-24 • 17 minutes
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. | | --- | | Send in a voice message:
2021-Feb-10 • 14 minutes
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. | | --- | | Send in a voice message:
2021-Jan-27 • 21 minutes
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. | | --- | | Send in a voice message:
2021-Jan-13 • 16 minutes
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. | | --- | | Send in a voice message:
2020-Dec-30 • 16 minutes
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. | | --- | | Send in a voice message:
2020-Dec-16 • 16 minutes
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. | | --- | | Send in a voice message:
2020-Dec-02 • 14 minutes
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. | | --- | | Send in a voice message:
2020-Nov-18 • 16 minutes
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. --- Send in a voice message:
2020-Nov-04 • 14 minutes
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. | | --- | | Send in a voice message:
2020-Oct-21 • 14 minutes
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? | | --- | | Send in a voice message:
2020-Oct-07 • 9 minutes
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. | | --- | | Send in a voice message:
2020-Sep-30 • 13 minutes
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. | | --- | | Send in a voice message:
2020-Sep-23 • 17 minutes
To Infinity...and Beyond
What is infinity, why does it seem so weird, and can you really go beyond it? | | --- | | Send in a voice message:
2020-Sep-16 • 11 minutes
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? | | --- | | Send in a voice message:
2020-Sep-09 • 16 minutes
This Podcast is Lying
We explore the mind-blowing Liar and related paradoxes and how they changed mathematics --- Send in a voice message:
2020-Sep-02 • 15 minutes
An Impossible Easy Question
Goldbach’s Conjecture and how a statement that is easy to understand is difficult or impossible to resolve --- Send in a voice message:
2020-Aug-26 • 15 minutes
Everything You Know About Math is Wrong
We explore some of the common misconceptions about mathematics and mathematicians. | | --- | | Send in a voice message:
2020-Jul-26 • 1 minutes
The Art of Mathematics trailer
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