S2018 E1 • The Mathematics of Diffie-Hellman Key Exchange

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. This is part 3 in our Cryptography 101 series.

Première diffusion : 11 janvier 2018

S2018 E2 • Proving Brouwer's Fixed Point Theorem

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

Première diffusion : 18 janvier 2018

S2018 E3 • Beyond the Golden Ratio

You know the Golden Ratio, but what is the Silver Ratio?

Première diffusion : 25 janvier 2018

S2018 E4 • How to Divide by 'Zero'

What happens when you divide things that aren’t numbers?

Première diffusion : 1 février 2018

S2018 E5 • Telling Time on a Torus

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.

Première diffusion : 15 février 2018

S2018 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?

Première diffusion : 27 février 2018

S2018 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?

Première diffusion : 1 mars 2018

S2018 E8 • What was Fermat’s 'Marvelous' Proof?

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

Première diffusion : 8 mars 2018

S2018 E9 • The Geometry of SET

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

Première diffusion : 15 mars 2018

S2018 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?

Première diffusion : 23 mars 2018

S2018 E11 • Unraveling DNA with Rational Tangles

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

Première diffusion : 29 mars 2018

S2018 E12 • Defining Infinity

Set 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.

Première diffusion : 13 avril 2018

S2018 E13 • Instant Insanity Puzzle

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?

Première diffusion : 26 avril 2018

S2018 E14 • The Assassin Puzzle

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?

Première diffusion : 17 mai 2018