<![CDATA[The Art of Mathematics]]>
https://theartofmathematicspodcast.com
https://d3t3ozftmdmh3i.cloudfront.net/production/podcast_uploaded/7560880/7560880-1595633788488-9cc2f697e4ceb.jpgThe Art of Mathematics
https://theartofmathematicspodcast.com
Anchor PodcastsWed, 18 Sep 2024 21:25:45 GMTCarol JacobyConversations, explorations, conjectures solved and unsolved, mathematicians and beautiful mathematics. No math background required.episodicCarol Jacobycjacoby@jacobyconsulting.comNo<![CDATA[Turning Math-Hating Prisoners into Mathematicians]]>Kate Pearce, a post-doc researcher at UT Austin, talks about her experience teaching math in a women's prison. Her remedial college algebra students came in with negative experience in math, so she devised ways to make the topics new. The elective class called, coincidentally, The Art of Mathematics, explored parallels between math and art, infinity, algorithms, formalism, randomness and more. The students learned to think like mathematicians and gained confidence in their abilities in abstract problem solving.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Turning-Math-Hating-Prisoners-into-Mathematicians-e2mqleh
fe08227d-0a3f-4a5e-9e4e-2f3d0bdcff97Wed, 28 Aug 2024 21:00:00 GMT<p>Kate Pearce, a post-doc researcher at UT Austin, talks about her experience teaching math in a women's prison. Her remedial college algebra students came in with negative experience in math, so she devised ways to make the topics new. The elective class called, coincidentally, The Art of Mathematics, explored parallels between math and art, infinity, algorithms, formalism, randomness and more. The students learned to think like mathematicians and gained confidence in their abilities in abstract problem solving.</p>
No00:22:14full<![CDATA[Stop Overselling Mathematics]]>Alon Amit, prolific Quora math answerer, argues that an honest representation of mathematical ideas is enough to spark interest in math. It's not necessary to exaggerate the role of math; the golden ratio does not drive the stock market, the solution of the Riemann hypothesis will not kill cryptography, and Grothendieck did not advance robotics. History and seeing the thought process and the struggle behind the tight finished proof are ways to make math compelling.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Stop-Overselling-Mathematics-e2lv3rd
c285169b-6639-438c-bbd5-573fce0f94d0Wed, 24 Jul 2024 21:00:00 GMT<p>Alon Amit, prolific Quora math answerer, argues that an honest representation of mathematical ideas is enough to spark interest in math. It's not necessary to exaggerate the role of math; the golden ratio does not drive the stock market, the solution of the Riemann hypothesis will not kill cryptography, and Grothendieck did not advance robotics. History and seeing the thought process and the struggle behind the tight finished proof are ways to make math compelling. </p>
No00:17:20full<![CDATA[Math for Kids: It's not a Spectator Sport]]>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 memorization they've come to expect. Kids who like to read are enticed by puzzles and mysteries. Möbius strips, Pascal's triangle, and other concepts that are new to them, make them marvel, "Is this math?" They see patterns and learn to make and even prove conjectures.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Math-for-Kids-Its-not-a-Spectator-Sport-e2ku8vu
9fbb7594-49f5-4744-9d44-dd481287df64Wed, 26 Jun 2024 20:59:00 GMT<p>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 memorization they've come to expect. Kids who like to read are enticed by puzzles and mysteries. Möbius strips, Pascal's triangle, and other concepts that are new to them, make them marvel, "Is this math?" They see patterns and learn to make and even prove conjectures. </p>
No00:21:52full<![CDATA[Egyptian Fractions]]>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 fractions of integers. Human heritage goes way back, but is still inspiring modern research.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Egyptian-Fractions-e2jv870
0b6e2853-6264-4259-a071-fda6fe92320cWed, 22 May 2024 21:29:06 GMT<p>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 fractions of integers. Human heritage goes way back, but is still inspiring modern research.</p>
No00:17:21full<![CDATA[Da Vinci's Math Teacher: Merging the Practical and Theoretical]]>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."
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Da-Vincis-Math-Teacher-Merging-the-Practical-and-Theoretical-e2ikg4n
5fb6fecb-892c-42a7-b1a1-d63f4f0b2a08Wed, 24 Apr 2024 21:00:00 GMT<p>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."</p>
No00:16:46full<![CDATA[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.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Alon-Amit--sharing-the-mathematical-journey-in-Quora-and-Math-Circles-e2gko62
1daf898b-252c-455c-bfa6-771f6d0e5adfWed, 27 Mar 2024 21:00:00 GMT<p><strong>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.</strong></p>
No00:20:26full<![CDATA[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 theartofmathematicspodcast.com) and more books that demonstrate that math provides "pleasures which all the arts afford." He also discusses books about math and the real world and compilations of the broad range of mathematics.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Too-Much-Math-in-the-Schools--These-Books-Counter-That-Narrow-View-e2g2ni1
5d337507-8fbc-4a67-b3cf-c935f6c5b29bWed, 28 Feb 2024 22:00:00 GMT<p>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 books about math and the real world and compilations of the broad range of mathematics.</p>
No00:20:59full<![CDATA[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 theartofmathematicspodcast.com.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Books-for-the-Mathematical-Tourist-e2epq0r
1d4fc832-4b78-496b-8107-3d08c2b5b340Wed, 24 Jan 2024 21:57:00 GMT<p>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.</p>
No00:20:41full<![CDATA[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.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Reflecting-on-Kaleidoscopes-e2dglko
7ff1b5f9-dfb3-43a5-8b05-bba12d52c007Wed, 27 Dec 2023 22:00:00 GMT<p>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.</p>
No00:20:18full<![CDATA[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 while staring out the window. You can invent your own tools.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Meet-the-young-Davidson-Fellowship-winners-e2bvp68
092416b9-c752-4d95-a884-9c0d88e27983Wed, 22 Nov 2023 22:00:00 GMT<p>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 while staring out the window. You can invent your own tools.</p>
No00:14:10full<![CDATA[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.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Gdels-Incompleteness--Fundamental-Truths--and-Reasoning-in-Math-and-Law-e2aq0qb
9bfcabba-f502-4774-995e-adf75d840984Wed, 25 Oct 2023 20:59:00 GMT<p>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. </p>
No00:22:07full<![CDATA[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" stereotype and see the beauty of the subject.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Math-and-the-Law-e28s7v3
bd472de7-9156-4d0a-804a-9ca14b60f76cWed, 27 Sep 2023 21:00:45 GMT<p>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" stereotype and see the beauty of the subject.</p>
No00:20:22full<![CDATA[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?
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Fabulous-Fibonacci-e27t6i4
d582de6e-3040-4c13-86e6-3a311ccdcfe1Wed, 23 Aug 2023 21:04:24 GMT<p>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?</p>
No00:20:32full<![CDATA[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 theartofmathematicspodcast.com
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Vowels-and-Sounds-and-a-Little-Calculus-e27c2hq
053dab14-6f10-4466-a598-adde7231c963Wed, 26 Jul 2023 21:00:00 GMT<p>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</p>
No00:11:38full<![CDATA[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.

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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/The-Hat-A-Newly-Discovered-Ein-stein-Tessellation-Tile-e262ppn
24fa1deb-0caf-42fb-b7f3-c6bdedb8663aWed, 28 Jun 2023 21:00:32 GMT<p>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.</p>
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No00:13:41full<![CDATA[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 the life of a mathematician among neuroscientists.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Interfacing-Music-and-Mathematics-e21shj2
9e6c0153-669e-4bdf-9e94-2ca354e6b936Wed, 24 May 2023 08:42:20 GMT<p>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 the life of a mathematician among neuroscientists.</p>
No00:21:12full<![CDATA[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.

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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Fourier-Analysis-Its-Not-Just-for-Differential-Equations-e22sq3v
62d5a720-6638-485d-8ca2-c96ca7a6d0d2Wed, 26 Apr 2023 20:50:00 GMT<p>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.</p>
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No00:18:23full<![CDATA[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 the earth too young to make Darwin's theory credible?
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Joseph-Fourier--the-Heat-Equation-and-the-Age-of-the-Earth-e206mnl
cf0a3e1f-7451-4633-8a35-e79c5b559c32Wed, 22 Mar 2023 21:07:00 GMT<p>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 the earth too young to make Darwin's theory credible?</p>
No00:17:32full<![CDATA[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.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/The-Ten-Most-Important-Theorems-in-Mathematics--Part-II-e1v9nkb
068ee368-df8f-42ae-9437-cf5ce86c1d42Wed, 22 Feb 2023 22:01:29 GMT<p>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.</p>
No00:15:37full<![CDATA[The Ten Most Important Theorems in Mathematics, Part I]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/The-Ten-Most-Important-Theorems-in-Mathematics--Part-I-e1u0lal
3a5740e9-3685-4b0f-b904-5da188ac53c4Wed, 25 Jan 2023 21:59:00 GMTJim 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.
No00:25:24142full<![CDATA[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 50-50 by taking just one sample of one of the events. Dr. Stein then discusses how mathematics shows up in some surprising places. Mathematics studied for the pure joy of it often finds surprising uses. He gives some examples from G. H. Hardy as well as his own research.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Surprisingly-Better-than-50-50-e1s2m45
201651dc-e1b6-46ad-a4f0-b70898eeb13bWed, 28 Dec 2022 22:01:25 GMT<p>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 50-50 by taking just one sample of one of the events. Dr. Stein then discusses how mathematics shows up in some surprising places. Mathematics studied for the pure joy of it often finds surprising uses. He gives some examples from G. H. Hardy as well as his own research.</p>
No00:18:15full<![CDATA[Fascinating Fractals]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Fascinating-Fractals-e1r3ls5
1a1e3df4-e838-4aae-937c-a90bc6024696Wed, 23 Nov 2022 21:59:00 GMTJeanne 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 world between 1 dimension and 2. Fractals are used in art, medicine, science and technology.
No00:21:06140full<![CDATA[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.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Approximation-by-Rationals-A-New-Focus-e1nbjvh
08b1bfef-97b4-4350-81a8-e9138ee96765Wed, 26 Oct 2022 21:00:00 GMT<p>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.</p>
No00:21:35full<![CDATA[Tessellations]]>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.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Tessellations-e1ofsks
df0c9697-f68f-4123-9e7d-32a119380fe3Wed, 28 Sep 2022 21:00:51 GMT<p>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.</p>
No00:20:47full<![CDATA[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.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Rational--Irrational-and-Transcendental-Numbers-e1mj6j9
d97a07ff-f37d-4f6b-a337-99b465ad8541Wed, 24 Aug 2022 20:17:32 GMT<p>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.</p>
No00:21:48139full<![CDATA[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.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Math-as-Art-e1lm29e
26f77d28-346c-4970-9652-843670f14160Mon, 25 Jul 2022 20:34:41 GMT<p>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.</p>
No00:18:42138full<![CDATA[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.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Exploration-in-Reading-Mathematics-e1ig6v2
0c6ee03d-7b80-406c-92fb-94ed82e9d860Wed, 22 Jun 2022 15:00:32 GMT<p>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.</p>
No00:16:31137full<![CDATA[Games for Math Learning]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Games-for-Math-Learning-e1homdg
a55a95f4-f743-4fb9-9ce0-423a3d90d8f7Wed, 25 May 2022 15:00:59 GMTJon 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.
No00:19:18136full<![CDATA[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.
]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/The-Power-of-Mathematical-Storytelling-e1h0cg4
7c965c1f-9be4-4a60-9c12-c85c72983ce9Fri, 22 Apr 2022 15:39:13 GMT<p>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.</p>
No00:16:04135full<![CDATA[The Mathematical World and the Physical World]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/The-Mathematical-World-and-the-Physical-World-e1evg07
829d04e9-1667-40a0-8085-b634e000f49bWed, 09 Mar 2022 22:00:17 GMTYusra 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.
No00:11:55133full<![CDATA[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.
]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Getting-Athletes-to-Think-Like-Mathematicians-e1dp7o6
6258e378-516c-452b-b434-c012f0a87b61Wed, 09 Feb 2022 22:00:00 GMT<p>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. </p>
No00:17:27133full<![CDATA[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?
]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/The-Art-of-Definitions-e1cmlum
233c75d8-a8d9-4754-bfb5-0ab8a052372bWed, 12 Jan 2022 22:00:00 GMT<p>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?</p>
No00:19:34132full<![CDATA[Math Exploration for Kids]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Math-Exploration-for-Kids-e1b8bal
25fc75cd-ea13-4199-8e05-021417ad73ceThu, 09 Dec 2021 06:23:08 GMTMark 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.
No00:17:50131full<![CDATA[Is Mathematics an Art?]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Is-Mathematics-an-Art-e19k6sa
4bbb5fd7-873b-41a5-aba7-f9473bf8c29dWed, 10 Nov 2021 22:00:00 GMTJoshua 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.
No00:12:10130full<![CDATA[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.
]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Math-as-a-way-of-thinking-e18f61n
efbe6566-5d89-4e9c-9356-1975bf2c548cWed, 13 Oct 2021 21:00:00 GMT<p>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.</p>
No00:19:54full<![CDATA[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.
]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Symmetries-in-3-and-4-Dimensions-e16r5lp
a085d6f8-0ed3-4fd0-a8d6-5e45113a36cbWed, 08 Sep 2021 21:00:00 GMT<p>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.</p>
No00:19:03full<![CDATA[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.
]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Symmetry--Shapes-and-Groups-e15ks9l
b0f51f2c-3b43-4188-a26a-0ed34f982222Sat, 14 Aug 2021 05:13:08 GMT<p>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.</p>
No00:19:50127full<![CDATA[Freshmen and Sophomores Confront Unsolved Problems]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Freshmen-and-Sophomores-Confront-Unsolved-Problems-e145d3l
4191ccfa-37f8-48b3-8ce5-c75a21c77182Wed, 14 Jul 2021 21:00:54 GMTDana 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.
No00:18:41126full<![CDATA[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?
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Stereotypes-of-Mathematics-and-Mathematicians-e12oouu
08375ff2-a572-4fd6-bcb1-0509bb30574aWed, 16 Jun 2021 21:00:00 GMT<p>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?</p>
No00:18:29125full<![CDATA[Prime numbers and their surprising patterns]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Prime-numbers-and-their-surprising-patterns-e11prib
13fe6b1a-5b24-47a3-9204-a2c585b172c1Wed, 02 Jun 2021 21:08:55 GMTJoseph 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."
No00:16:35124full<![CDATA[Creativity in Mathematics]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Creativity-in-Mathematics-e116r5b
11e14d37-6e9a-4266-b562-e2445105f27cWed, 19 May 2021 20:01:11 GMTJosh 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.
No00:18:20123full<![CDATA[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.
]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/The-unreasonable-effectiveness-of-mathematics-etb4vl
fd37ce37-c166-4277-ab49-a1a8dc40714fWed, 05 May 2021 21:02:57 GMT<p>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.</p>
No00:13:20122full<![CDATA[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.
]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Alternative-Proofs-and-Why-We-Seek-Them-eujqjo
b1db006a-7033-48cc-834d-0b974ddf3d27Wed, 21 Apr 2021 21:00:33 GMT<p>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.</p>
No00:17:08121full<![CDATA[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.
]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Symmetry--Its-More-Than-You-Think-euahl4
d849ce62-8414-4cf6-9a80-6b3465db1230Wed, 07 Apr 2021 21:00:00 GMT<p>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.</p>
No00:13:37120full<![CDATA[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?
]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Is-Math-Discovered-or-Invented-et9j4n
b935114f-8779-42e9-b598-90721fba9d2dWed, 24 Mar 2021 21:00:00 GMT<p>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?</p>
No00:17:21119full<![CDATA[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?
]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Thats-Impossible--Oh--Yeah--Prove-It-ermomg
efee90c6-56f9-4fdd-b434-bb8a2ff157ebWed, 10 Mar 2021 22:00:00 GMT<p>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?</p>
No00:16:44117full<![CDATA[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.
]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/The-Joy-of-Mathematical-Discovery-eph08o
1c25bc6a-8eab-4e3c-9eb4-e4f81fd4e705Wed, 24 Feb 2021 22:00:00 GMT<p>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.</p>
No00:16:35116full<![CDATA[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.
]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/The-Monty-Hall-Problem-epgvnv
d1fc7255-2b61-4c0f-a145-ba443e672eeeWed, 10 Feb 2021 22:00:00 GMT<p>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.</p>
No00:14:26115full<![CDATA[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.
]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/What-Is-Mathematics--Some-Surprising-Answers-epcm6n
1aab5ebc-becb-4c18-9e47-5b3b28879c18Wed, 27 Jan 2021 22:00:00 GMT<p>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.</p>
No00:20:47115full<![CDATA[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.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Being-a-Mathematician-eoi8pd
0a03c02d-b20d-423b-896b-37f9d04158fcWed, 13 Jan 2021 22:00:00 GMT<p>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.</p>
No00:15:53114full<![CDATA[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.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Math-Jokes-and-What-They-Say-about-Mathematicians-eo9mbl
0b2d5fbd-5713-4e50-98cd-46d0e234a6faWed, 30 Dec 2020 22:00:00 GMT<p>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.</p>
No00:16:29113full<![CDATA[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.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/The-Most-Famous-Formerly-Unsolved-Problem-emq7c2
f461f737-89be-46e5-8490-bdaea0339f3aWed, 16 Dec 2020 22:00:00 GMT<p>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.</p>
No00:16:02112full<![CDATA[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.
]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/The-Mathematics-of-Art-emk9hc
2eee96ee-fc9e-4685-a673-3a40877ae58dWed, 02 Dec 2020 22:00:00 GMT<p>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.</p>
No00:14:06111full<![CDATA[The Real World Is a Special Case]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/The-Real-World-Is-a-Special-Case-embgc0
84d0b055-289e-426e-8e49-e6f9eea3e6e4Wed, 18 Nov 2020 22:00:00 GMTAbstract 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.
No00:16:01110full<![CDATA[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.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/How-to-Find-Something-Youve-Never-Seen-ek2i7d
718befac-be8a-48f1-a2c2-ebe178624831Wed, 04 Nov 2020 17:00:00 GMT<p>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.</p>
No00:14:2519full<![CDATA[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?
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Beyond-the-Third-Dimension-ek0v60
c055d86f-3a7f-4877-b0de-e6bcd977e672Wed, 21 Oct 2020 21:00:00 GMT<p>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?</p>
No00:13:3718full<![CDATA[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.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/One-Theorem--99-Proofs-ejgb0b
163c9e48-2d53-4dd3-8087-2802cde0863aWed, 07 Oct 2020 21:00:06 GMT<p>Can you really approach one mathematical statement 99 different ways? We review the wonderful book 99 Variations on a Proof. The answer is yes.</p>
No00:08:4317full<![CDATA[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.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/A-Beautiful-Theorem-with-an-Ugly-Proof-ei2s3h
cc221133-9f77-49b4-a263-c2b5edf2d5b3Wed, 30 Sep 2020 21:00:00 GMT<p>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.</p>
No00:12:4716full<![CDATA[To Infinity...and Beyond]]>What is infinity, why does it seem so weird, and can you really go beyond it?
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/To-Infinity---and-Beyond-ei2i38
51d0de78-0504-4164-91ba-d7c611e313e9Wed, 23 Sep 2020 21:00:00 GMT<p>What is infinity, why does it seem so weird, and can you really go beyond it?</p>
No00:16:5315full<![CDATA[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?
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/The-Unsolved-Is-Solved---and-Another-ej329k
16302387-4424-4c4b-8451-063f4f25f4ffWed, 16 Sep 2020 21:00:00 GMT<p>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?</p>
No00:11:2313full<![CDATA[This Podcast is Lying ]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/This-Podcast-is-Lying-ehvkhg
7e78d211-d86e-48b2-b78f-8eedd10efdcdWed, 09 Sep 2020 21:00:00 GMTWe explore the mind-blowing Liar and related paradoxes and how they changed mathematics
No00:15:3212full<![CDATA[An Impossible Easy Question]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/An-Impossible-Easy-Question-ehu5mk
344d29d0-f9df-4047-b59b-6166a3dfafadWed, 02 Sep 2020 21:00:50 GMTGoldbach’s Conjecture and how a statement that is easy to understand is difficult or impossible to resolve
No00:14:4312full<![CDATA[Everything You Know About Math is Wrong]]>We explore some of the common misconceptions about mathematics and mathematicians.
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https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/Everything-You-Know-About-Math-is-Wrong-ehaeo6
cbe2d8e3-c177-4dac-91a6-2f75f4ee53a1Wed, 26 Aug 2020 21:00:00 GMT<p>We explore some of the common misconceptions about mathematics and mathematicians.</p>
No00:14:4811full<![CDATA[The Art of Mathematics trailer]]>
https://podcasters.spotify.com/pod/show/the-art-of-mathematics/episodes/The-Art-of-Mathematics-trailer-eh938g
dac34dcd-e315-4265-ae57-271653a0f140Sun, 26 Jul 2020 16:05:32 GMTNo00:00:57trailer