Contemporary Math Research for Artistic Undergrads

The Art of Mathematics

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Understanding the Elegant Math Behind Modern Machine Learning 1:14:43

12 hari yang lalu1:14:43

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Artificial intelligence is evolving at an unprecedented pace—what does that mean for the future of technology, venture capital, business, and even our understanding of ourselves? Award-winning journalist and writer Anil Ananthaswamy joins us for our latest episode to discuss his latest book Why Machines Learn: The Elegant Math Behind Modern AI . Anil helps us explore the journey and many breakthroughs that have propelled machine learning from simple perceptrons to the sophisticated algorithms shaping today’s AI revolution, powering GPT and other models. The discussion aims to demystify some of the underlying mathematical concepts that power modern machine learning, to help everyone grasp this technology impacting our lives–even if your last math class was in high school. Anil walks us through the power of scaling laws, the shift from training to inference optimization, and the debate among AI’s pioneers about the road to AGI—should we be concerned, or are we still missing key pieces of the puzzle? The conversation also delves into AI’s philosophical implications—could understanding how machines learn help us better understand ourselves? And what challenges remain before AI systems can truly operate with agency? If you enjoy this episode, please subscribe and leave us a review on your favorite podcast platform. Sign up for our newsletter at techsurgepodcast.com for exclusive insights and updates on upcoming TechSurge Live Summits. Links: Read Why Machines Learn, Anil’s latest book on the math behind AI https://www.amazon.com/Why-Machines-Learn-Elegant-Behind/dp/0593185749 Learn more about Anil Ananthaswamy’s work and writing https://anilananthaswamy.com/ Watch Anil Ananthaswamy’s TED Talk on AI and intelligence https://www.ted.com/speakers/anil_ananthaswamy Discover the MIT Knight Science Journalism Fellowship that shaped Anil’s AI research https://ksj.mit.edu/ Understand the Perceptron, the foundation of neural networks https://en.wikipedia.org/wiki/Perceptron Read about the Perceptron Convergence Theorem and its significance https://www.nature.com/articles/323533a0…

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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.

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#Science #Math #Carol Jacoby

The Art of Mathematics

Contemporary Math Research for Artistic Undergrads

The Art of Mathematics

13 subscribers

published sekitar setahun yang lalu

MP3•Beranda episode

70 episode

#Science #Math #Carol Jacoby

Semua episode

The Art of Mathematics

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The National Museum of Mathematics 17:52

13 hari yang lalu17:52

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

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Contemporary Math Research for Artistic Undergrads 14:13

7 weeks yang lalu14:13

14:13

The Art of Mathematics

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Where do Math Concepts Come From? 20:37

11 weeks yang lalu20:37

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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

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

15 weeks yang lalu14:02

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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

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What is a Pattern? 12:46

20 weeks yang lalu12:46

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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

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

24 weeks yang lalu17:36

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

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Turning Math-Hating Prisoners into Mathematicians 22:14

28 weeks yang lalu22:14

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

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Stop Overselling Mathematics 17:20

33 weeks yang lalu17:20

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

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

37 weeks yang lalu21:52

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

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Egyptian Fractions 17:21

42 weeks yang lalu17:21

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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

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

46 weeks yang lalu16:46

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

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

50 weeks yang lalu20:26

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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

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

1 year yang lalu20:59

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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.…

The Art of Mathematics

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Books for the Mathematical Tourist 20:41

1 year yang lalu20:41

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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.…

The Art of Mathematics

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Reflecting on Kaleidoscopes 20:18

1 year yang lalu20:18

20:18

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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