Reflecting on Kaleidoscopes

The Art of Mathematics

#Science #Math #Carol Jacoby

51:57

On the Season 2 debut of Lost Cultures: Living Legacies , we travel to Bermuda, an Atlantic island whose history spans centuries and continents. Once uninhabited, Bermuda became a vital stop in transatlantic trade, a maritime stronghold, and a cultural crossroads shaped by African, European, Caribbean, and Native American influences. Guests Dr. Kristy Warren and Dr. Edward Harris trace its transformation from an uninhabited island to a strategic outpost shaped by shipwrecks, colonization, the transatlantic slave trade, and the rise and fall of empires. Plus, former Director of Tourism Gary Phillips shares the story of the Gombey tradition, a vibrant performance art rooted in resistance, migration, and cultural fusion. Together, they reveal how Bermuda’s layered past continues to shape its people, culture, and identity today. You can also find us online at ⁠travelandleisure.com/lostcultures Learn more about your ad choices. Visit podcastchoices.com/adchoices…

about a year ago 20:18

M4A•Episode home

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.

72 episodes

Reflecting on Kaleidoscopes

The Art of Mathematics

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published about a year ago

M4A•Episode home

72 episodes

#Science #Math #Carol Jacoby

All episodes

The Art of Mathematics

1
The Many Facets of Math 15:54

7 weeks ago15:54

15:54

Alon Amit addresses the various facets of mathematics. Is it an art or a science? Both? Neither? Is it invented or discovered? Why is math that's developed for purely aesthetic reasons so often a useful tool for the real world? He likes that there are not simple, one-way answers. He challenges the listeners to post questions to Quora that surprise and delight him.…

The Art of Mathematics

1
Will AI Replace Mathematicians? 20:11

11 weeks ago20:11

20:11

Alon Amit, prolific Quora math answerer, discusses how Artificial Intelligence might change the role of the mathematician. AI will make mathematics more efficient but it can't do math in a deep sense at present. It can't perform logical reasoning or even know if it's wrong. However, there are recent advances in proof verifiers. They may eventually be able to check complex proofs like the recent alleged proof of the ABC Conjecture.…

The Art of Mathematics

1
The National Museum of Mathematics 17:52

15 weeks ago17:52

17:52

Cindy Lawrence is the Director and CEO of the National Museum of Mathematics in New York City. She and a former math professor built it up from a grass-roots museum started by math teachers. The Museum, soon to move into a 30,000 square foot space, appeals to both those who love and hate math. Attendees learn that math is beautiful, fun, and surprising--"That's so cool!"…

The Art of Mathematics

1
Contemporary Math Research for Artistic Undergrads 14:13

20 weeks ago14:13

14:13

Veselin Jungic, teaching professor of mathematics at Simon Fraser University, introduces undergraduate math minors to contemporary math research. The focus is Ramsey theory, an area of current research activity that brings together multiple areas of math, deals with big ideas, proves complete chaos is impossible, and is built on human stories. Some students extended or corrected ongoing research. Others used their artistic talents to express the patterns of mathematics through, for example, a graphic novel or a poem.…

The Art of Mathematics

1
Where do Math Concepts Come From? 20:37

24 weeks ago20:37

20:37

Joseph Bennish discusses math as a "concept factory." The concept of prime numbers came from a desire to break numbers down to their simplest atoms. This simple concept led to simple questions like the twin prime conjecture that no one has been able to answer. Those questions in turn led to deep research. The concepts of new geometries grew out of failed attempts to prove that Euclid's geometry was the only geometry. Gauss' "most wonderful theorem" of surfaces led to Riemann's higher dimensional manifolds. This, combined with Minkowski's space-time geometry, led to Einstein's relativity, "the most beautiful theory of physics."…

The Art of Mathematics

1
A Clockmaker, an Egg, and a Cathedral 14:02

28 weeks ago14:02

14:02

Jeanne Lazzarini tells us how a clockmaker used an egg to win the competition to build the dome of the Florence Cathedral. The Cathedral had had a huge gaping hole for a hundred years since no one knew how to build such a large dome. His solution involved the equation for a hanging chain and parallel lines that meet.…

The Art of Mathematics

1
What is a Pattern? 12:46

33 weeks ago12:46

12:46

Math is in a sense the science of patterns. Alon Amit explores the question of what exactly is a pattern. A common example is the decimal digits of pi. The statement that they have no pattern seems to be either obvious or completely untrue. We explore the spectrum of pattern-ness from simple repetition to total randomness and finally answer the question about pi. We also discuss analogy, which powers mathematical exploration.…

The Art of Mathematics

1
What's the Big Deal about Pi? 17:36

37 weeks ago17:36

17:36

Alon Amit joins us on the antipode of Pi Day to counter the myths and mysteries of this most famous irrational number. There's nothing magical about a non-repeating string of digits. The real and profound mystery is the ubiquity of pi. It shows up in places that have nothing to do with circles, such as the sum of the reciprocals of the squares of the integers and the normal bell-shaped curve.…

The Art of Mathematics

1
Turning Math-Hating Prisoners into Mathematicians 22:14

41 weeks ago22:14

22:14

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.…

The Art of Mathematics

1
Stop Overselling Mathematics 17:20

46 weeks ago17:20

17:20

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.…

The Art of Mathematics

1
Math for Kids: It's not a Spectator Sport 21:52

50 weeks ago21:52

21:52

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.…

The Art of Mathematics

1
Egyptian Fractions 17:21

1 year ago17:21

17:21

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.…

The Art of Mathematics

1
Da Vinci's Math Teacher: Merging the Practical and Theoretical 16:46

1 year ago16:46

16:46

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."…

The Art of Mathematics

1
Alon Amit, sharing the mathematical journey in Quora and Math Circles 20:26

1 year ago20:26

20:26

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.…

The Art of Mathematics

1
Too Much Math in the Schools? These Books Counter That Narrow View 20:59

1 year ago20:59