# Infinite Series

Math is pervasive - a robust yet precise language - and with each episode you’ll begin to

8m 16s

There is a proof for Brouwer's Fixed Point Theorem that uses a bridge - or portal - between geometry and algebra.

9m 32s

Imagine 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?

7m 17s

What 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.

13m 2s

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?

7m 28s

What happens if you multiply things that aren’t numbers? And what happens if that multiplication is not associative?

9m 36s

When you think about math, what do you think of? Numbers? Equations? Patterns maybe? How about… knots? As in, actual tangles and knots?

10m 50s

If Fermat had a little more room in his margin, what proof would he have written there?

9m 12s

Imagine 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?

9m 36s

Symmetric 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.

10m 7s

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?

10m 21s

In the card game SET, what is the maximum number of cards you can deal that might not contain a SET?

9m 35s

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?

10m 31s

Set theory is supposed to be a foundation of all of mathematics. How does it handle infinity?

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