The Art of Mathematics

00:17:21

Egyptian Fractions

The Art of Mathematics ·

2024/05/22

Neil Epstein, Associate Professor of Mathematics at George Mason University, introduces us to the fractions used by the ancient Egyptians, well before the Greeks and Romans. The Egyptian fractions all had a unit numerator. They could represent any fraction as a sum of unique unit fractions, a fact that was not proved until centuries later. These sums inspired conjectures, one of which was proved only recently, while others remain unsolved to this day. Recent work extends these concepts beyond

en

00:16:46

Da Vinci's Math Teacher: Merging the Practical and...

The Art of Mathematics ·

2024/04/24

Jeanne Lazzarini joins us again to introduce us to the mathematician Luca Pacioli, whose views of numbers and shapes influenced Leonardo da Vinci, leading to a period of art and invention. His book, De Divina Proportione, is the only book ever illustrated by da Vinci. The Renaissance was a period when mathematicians studied art and artists studied mathematics. As da Vinci said, "Everything connects."--- Send in a voice message:

en

00:20:26

Alon Amit, sharing the mathematical journey in Quora...

The Art of Mathematics ·

2024/03/27

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

en

00:20:59

Too Much Math in the Schools? These Books Counter...

The Art of Mathematics ·

2024/02/28

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 theartofmathematicspodcast.com) and more books that demonstrate that math provides "pleasures which all the arts afford." He also discusses

en

00:20:41

Books for the Mathematical Tourist

The Art of Mathematics ·

2024/01/24

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 theartofmathematicspodcast.com.--- Send in a voice message:

en

00:20:18

Reflecting on Kaleidoscopes

The Art of Mathematics ·

2023/12/27

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: https://podcasters.spotify.com/pod/show/the-art-of-mathematics/message

en

00:14:10

Meet the young Davidson Fellowship winners

The Art of Mathematics ·

2023/11/22

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

en

00:22:07

Gödel's Incompleteness, Fundamental Truths, and...

The Art of Mathematics ·

2023/10/25

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: https://podcasters.spotify.com/pod/show/the-art-of-mathematics/message

en

00:20:22

Math and the Law

The Art of Mathematics ·

2023/09/27

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

en

00:20:32

Fabulous Fibonacci

The Art of Mathematics ·

2023/08/23

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: https://podcasters.spotify.com/pod/show/the-art-of-mathematics/message

en

00:11:38

Vowels and Sounds and a Little Calculus

The Art of Mathematics ·

2023/07/26

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 theartofmathematicspodcast.com --- Send in a

en

00:13:41

The Hat: A Newly Discovered "Ein-stein" Tessellation...

The Art of Mathematics ·

2023/06/28

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: https://podcasters.spotify.com/pod/show/the-art-of-mathematics/message

en

00:21:12

Interfacing Music and Mathematics

The Art of Mathematics ·

2023/05/24

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

en

00:18:23

Fourier Analysis: It's Not Just for Differential...

The Art of Mathematics ·

2023/04/26

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: https://podcasters.spotify.com/pod/show/the-art-of-mathematics/message

en

00:17:32

Joseph Fourier, the Heat Equation and the Age of the...

The Art of Mathematics ·

2023/03/22

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

en

00:15:37

The Ten Most Important Theorems in Mathematics, Part II

The Art of Mathematics ·

2023/02/22

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: https://podcasters.spotify.com/pod/show/the-art-of-mathematics/message

en

00:25:24

The Ten Most Important Theorems in Mathematics, Part I

The Art of Mathematics ·

2023/01/25

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

en

00:18:15

Surprisingly Better than 50-50

The Art of Mathematics ·

2022/12/28

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

en

00:21:06

Fascinating Fractals

The Art of Mathematics ·

2022/11/23

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

en

00:21:35

Approximation by Rationals: A New Focus

The Art of Mathematics ·

2022/10/26

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:

en

All Episodes

Similar Podcasts

The Deep Dive Lab: Unraveling Materials Science

Son Hoang

New Books in Political Science

New Books Network

Station 151

Pale Matter | Realm

Beyond the Divide

Koala Moon

StarTalk with Neil deGrasse Tyson

Neil deGrasse Tyson