Where do Math Concepts Come From?

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."

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Episoder(81)

Theorem of the Day

Theorem of the Day

Robin Whitty hosts the website theoremoftheday.org, which presents a concise poster about a different theorem each day, with explanation, graphics, and links. He has been doing this for 21 years. Theo...

24 Sep 22min

Life-Changing Math

Life-Changing Math

Ted Dintersmith, author of Aftermath: The Life-Changing Math that Schools Won't Teach You, argues that much of what we learn in math can be outsourced to machines. That frees people to understand the ...

26 Aug 16min

Zeno's Paradox: Is Motion Possible?

Zeno's Paradox: Is Motion Possible?

Josh Cole discussed Zeno's paradox that says motion is not possible since you must go half-way, and then half of the remaining distance, and so on, infinitely. Aristotle and others struggled with this...

22 Jul 15min

The Most Beautiful Formula

The Most Beautiful Formula

Joseph Bennish discusses Euler’s formula, which involves pi, e, the imagery i, 0 and 1, a beautiful formula that unites disparate types of numbers. We can think of e raised to an exponent as compound ...

27 Jun 16min

Math as it Should Be

Math as it Should Be

Aris Winger, Math Professor and Executive Director of the National Association of Mathematicians, has experienced first hand how math can save students' lives by uplifting them. Our education system c...

27 Mai 17min

Crocheting Mathematics

Crocheting Mathematics

Beyza Aslan, Associate Professor of Math at the University of North Florida, crochets mathematics. This turns abstractions, such as hyperbolic geometry, into something that can be touched, felt, manip...

22 Apr 12min

Pythagorean Triples and Some New Conjectures

Pythagorean Triples and Some New Conjectures

Ben Cornish, host of The Mathematicians Podcast, discusses Pythagorean triples, integers that can be the sides of a right triangle. There are infinitely many primitive triples, as he proves. This conc...

25 Mar 20min

Proofs and Buckets of Fish

Proofs and Buckets of Fish

Joel David Hamkins, author of Proof and the Art of Mathematics, presents the game Buckets of Fish, which seemingly will go on forever. Yet he presents a proof that it will always come to an end. In fa...

25 Feb 15min

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