The Art of Mathematics

Carol Jacoby
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The Art of Mathematics

Conversations, explorations, conjectures solved and unsolved, mathematicians and beautiful mathematics. No math background required.

  1. 25.12.2024

    Where do Math Concepts Come From?

    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."

    21 мин.

  2. 27.11.2024

    A Clockmaker, an Egg, and a Cathedral

    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.

    14 мин.

  3. 23.10.2024

    What is a Pattern?

    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.

    13 мин.

  4. 25.09.2024

    What's the Big Deal about Pi?

    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.

    18 мин.

  5. 28.08.2024

    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.

    22 мин.

  6. 24.07.2024

    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.

    17 мин.

  7. 26.06.2024

    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.

    22 мин.

  8. 22.05.2024

    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.

    17 мин.
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Conversations, explorations, conjectures solved and unsolved, mathematicians and beautiful mathematics. No math background required.

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  • Автор
    Carol Jacoby
  • Годы выхода
    2020 - 2024
  • Выпуски
    68
  • Ограничения
    Без ненормативной лексики
  • Авторские права
    © Carol Jacoby
  • Сайт подкаста
    The Art of Mathematics

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