PBS Infinite Series

Season 2018

Mathematician Tai-Danae Bradley and physicist Gabe Perez-Giz offer ambitious content for viewers that are eager to attain a greater understanding of the world around them. Math is pervasive - a robust yet precise language - and with each episode you'll begin to see the math that underpins everything in this puzzling, yet fascinating, universe. Previous host Kelsey Houston-Edwards is currently working on her Ph.D. in mathematics at Cornell University.

Where to Watch Season 2018

14 Episodes

  • The Mathematics of Diffie-Hellman Key Exchange
    E1
    The Mathematics of Diffie-Hellman Key ExchangeSymmetric keys are essential to encrypting messages. How can two people share the same key without someone else getting a hold of it? Upfront asymmetric encryption is one way, but another is Diffie-Hellman key exchange. This is part 3 in our Cryptography 101 series.
  • Proving Brouwer's Fixed Point Theorem
    E2
    Proving Brouwer's Fixed Point TheoremThere is a proof for Brouwer's Fixed Point Theorem that uses a bridge - or portal - between geometry and algebra.
  • Beyond the Golden Ratio
    E3
    Beyond the Golden RatioYou know the Golden Ratio, but what is the Silver Ratio?
  • How to Divide by 'Zero'
    E4
    How to Divide by 'Zero'What happens when you divide things that aren’t numbers?
  • Telling Time on a Torus
    E5
    Telling Time on a TorusWhat shape do you most associate with a standard analog clock? Your reflex answer might be a circle, but a more natural answer is actually a torus. Surprised? Then stick around.
  • What Does It Mean to Be a Number? (The Peano Axioms)
    E6
    What Does It Mean to Be a Number? (The Peano Axioms)If you needed to tell someone what numbers are and how they work, without using the notion of number in your answer, could you do it?
  • What are Numbers Made of?
    E7
    What are Numbers Made of?In the physical world, many seemingly basic things turn out to be built from even more basic things. Molecules are made of atoms, atoms are made of protons, neutrons, and electrons. So what are numbers made of?
  • What was Fermat’s 'Marvelous' Proof?
    E8
    What was Fermat’s 'Marvelous' Proof?If Fermat had a little more room in his margin, what proof would he have written there?
  • The Geometry of SET
    E9
    The Geometry of SETIn the card game SET, what is the maximum number of cards you can deal that might not contain a SET?
  • How Big are All Infinities Combined? (Cantor's Paradox)
    E10
    How Big are All Infinities Combined? (Cantor's Paradox)Infinities come in different sizes. There’s a whole tower of progressively larger "sizes of infinity". So what’s the right way to describe the size of the whole tower?
  • Unraveling DNA with Rational Tangles
    E11
    Unraveling DNA with Rational TanglesWhen you think about math, what do you think of? Numbers? Equations? Patterns maybe? How about… knots? As in, actual tangles and knots?
  • Defining Infinity
    E12
    Defining InfinitySet theory arose in part to get a grip on infinity. Early “naive” versions were beset by apparent paradoxes and were superseded by axiomatic versions that used formal rules to demarcate "legal" mathematical statements from gibberish.
  • Instant Insanity Puzzle
    E13
    Instant Insanity PuzzleImagine you have four cubes, whose faces are colored red, blue, yellow, and green. Can you stack these cubes so that each color appears exactly once on each of the four sides of the stack?
  • The Assassin Puzzle
    E14
    The Assassin PuzzleImagine you have a square-shaped room, and inside there is an assassin and a target. And suppose that any shot that the assassin takes can ricochet off the walls of the room, just like a ball on a billiard table. Is it possible to position a finite number of security guards inside the square so that they block every possible shot from the assassin to the target?

 

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