How do you stack hundred-dimensional oranges? Learn about recent breakthroughs in our understanding of hyperspheres. It tackles the mysteries and the joy of mathematics. From Logic to Calculus, from Probability to Projective Geometry, both entertains and challenges its viewers to take their math game to the next level. Higher dimensional spheres, or hyperspheres, are counter-intuitive and almost impossible to visualize. Mathematician Kelsey Houston-Edwards explains higher dimensional spheres and how recent revelations in sphere packing have exposed truths about 8 and 24 dimensions that we don't even understand in 4 dimensions.
Is math real or simply something made up by mathematicians? You can’t physically touch a number yet using numbers we’re able to build skyscrapers and launch rockets into space. Mathematician Kelsey Houston-Edwards explains this perplexing dilemma and discusses the different viewpoints that philosophers and mathematicians have regarding the realism of mathematics.
Do two people on the planet have the exact same number of body hairs? How about more than two? There’s a simple yet powerful mathematical principle that can help you find out the answer. Kelsey Houston-Edwards breaks down the Pigeonhole Principle and explains how it can be used to answer some pretty perplexing questions.
There are different sizes of infinity. It turns out that some are larger than others. Mathematician Kelsey Houston-Edwards breaks down what these different sizes are and where they belong in The Hierarchy of Infinities.
You’re about to throw a party with a thousand bottles of wine, but you just discovered that one bottle is poisoned! Can you determine exactly which one it is?
Mathematician Mark Kac asked the question “Can we hear the shape of a drum?” It was a question that took over 20 years to answer. Sine waves, fundamental frequencies, eigenvalues, this episode has got it all!
You’ve always been told that pi is 3.14. This is true, but this number is based on how we measure distance. Find out what happens to pi when we change the way we measure distance.
In this episode probability mathematics and chess collide. What is the average number of steps it would take before a randomly moving knight returned to its starting square?
Mathematician Kelsey Houston-Edwards explains exactly what singularities are and how they exist right under our noses.
Mathematician Kelsey Houston-Edwards explains how to defeat a seemingly undefeatable monster using a rather unexpected mathematical proof. In this episode you’ll see mathematician vs monster, thought vs ferocity, cardinal vs ordinal. You won’t want to miss it.
Peano arithmetic proves many theories in mathematics but does have its limits. In order to prove certain things you have to step beyond these axioms. Sometimes you need infinity.
What is the math behind quantum computers? And why are quantum computers so amazing? Find out on this episode of Infinite Series.
You can find out how to fairly divide rent between three different people even when you don’t know the third person’s preferences! Find out how with Sperner’s Lemma.
How long will it take to win a game of chess on an infinite chessboard?
Only 4 steps stand between you and the secrets hidden behind RSA cryptography. Find out how to crack the world’s most commonly used form of encryption.
Classical computers struggle to crack modern encryption. But quantum computers using Shor’s Algorithm make short work of RSA cryptography. Find out how.
Using the harmonic series we can build an infinitely long bridge. It takes a very long time though. A faster method was discovered in 2009.
Can you turn your pants inside out without taking your feet off the ground?
Find out why Cantor’s Function is nicknamed the Devil’s Staircase.
What is the best voting system? Voting seems relatively straightforward, yet four of the most widely used voting systems can produce four completely different winners.
The bizarre Arrow’s Impossibility Theorem, or Arrow’s Paradox, shows a counterintuitive relationship between fair voting procedures and dictatorships.
The theory of social networks allows us to mathematically model and analyze the relationships between governments, organizations and even the rival factions warring on Game of Thrones.
What happened when a gambler asked for help from a mathematician? The formal study of Probability
The answer lies in the weirdness of floating-point numbers and the computer's perception of a number line.
Why is there a hexagonal structure in honeycombs? Why not squares? Or asymmetrical blobby shapes? In 36 B.C., the Roman scholar Marcus Terentius Varro wrote about two of the leading theories of the day. First: bees have six legs, so they must obviously prefer six-sided shapes. But that charming piece of numerology did not fool the geometers of day. They provided a second theory: Hexagons are the most efficient shape. Bees use wax to build the honeycombs -- and producing that wax expends bee energy. The ideal honeycomb structure is one that minimizes the amount of wax needed, while maximizing storage -- and the hexagonal structure does this best.
What happens when you try to empty an urn full of infinite balls? It turns out that whether the vase is empty or full at the end of an infinite amount of time depends on what order you try to empty it in. Check out what happens when randomness and the Ross-Littlewood Paradox collide.
Despite what many believe, the essence of encryption isn’t really about factoring or prime numbers. So what is it about?
Last time, we discussed symmetric encryption protocols, which rely on a user-supplied number called "the key" to drive an algorithm that scrambles messages. Since anything encrypted with a given key can only be decrypted with the same key, Alice and Bob can exchange secure messages once they agree on a key. But what if Alice and Bob are strangers who can only communicate over a channel monitored by eavesdroppers like Eve? How do they agree on a secret key in the first place?
What exactly is a topological space?
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.
There is a proof for Brouwer's Fixed Point Theorem that uses a bridge - or portal - between geometry and algebra.
You know the Golden Ratio, but what is the Silver Ratio?
What happens when you divide things that aren’t numbers?
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.
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?
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?
If Fermat had a little more room in his margin, what proof would he have written there?
In the card game SET, what is the maximum number of cards you can deal that might not contain a SET?
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?
When you think about math, what do you think of? Numbers? Equations? Patterns maybe? How about… knots? As in, actual tangles and knots?
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.
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?
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?