Infinite Series

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 m

The answer lies in the weirdness of floating-point numbers and the computer's perception of a number line.

What happened when a gambler asked for help from a mathematician? The formal study of Probability.

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.

The bizarre Arrow’s Impossibility Theorem, or Arrow’s Paradox, shows a counterintuitive relationship between fair voting procedures and dictatorships.

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.

What does the inside of a tesseract look like? Pascal’s Triangle can tell us.

Can you turn your pants inside out without taking your feet off the ground?

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.

Classical computers struggle to crack modern encryption. But quantum computers using Shor’s Algorithm make short work of RSA cryptography. Find out how.

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.

Can you produce a rational number by exchanging infinitely many digits of pi and e?

At one time, Wolverine served on four different superhero teams. How did he do it? He may have used graph coloring.

To understand finance, search algorithms and even evolution you need to understand Random Walks.

What is Pick's Theorem and how can we prove it?

How long will it take to win a game of chess on an infinite chessboard?

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.

What is the math behind quantum computers? And why are quantum computers so amazing? Find out on this episode of Infinite Series.

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.

How do you defeat a creature that grows two heads for every one head you chop off? You do the math.