End of the trips in the land of math with an arduous hike. It is better to be strong on the complex plane. Because it is about an unsolved mystery of mathematics, namely: the distribution of prime numbers. Riemann made a hypothesis considered as valid but still not proven, that is to say that it is not a walk in the park. Let's go slowly...

Frank Benford observed that the number one seems to pop up a lot in both in the supermarket and on tax bills. In understanding this law, it helps to simply look at the world from a different perspective.

The Monty Hall paradox, named after a game show from the 60s, concerns the way in which information acquired during the course of a game modifies (or not) the winning statistics. Theoretically solved, the question is so disturbing to our worldview that it continues to be the subject of passionate debate to this day.

We have known for a long time that some equations can't be solved as the answers are numbers that don't exist. Fortunately, a slew of mathematicians have uncovered a new field of numbers that now play a vital role in modern mathematics.

A circle is also a triangle and a triangle is a square. Sound impossible? Not in the realm of topology, which even applies to 3-dimensional spaces and anything from donuts, UFOs and potatoes. The discipline's inventor, Henri Poincaré, created one of the most difficult problems in mathematics.

In October 1970 Scientific American magazine introduced a game under the heading “Mathematical Games” that quickly became a cult classic. The idea behind John Conway’s “Game of Life” is cellular automaton. The game’s creator hoped to help with the understanding, simulating or even recreation of life itself.

In this episode of our travels in the land of maths, we are heading towards Infinity. And even beyond, because infinity comes in many sizes. That may seem strange, but Georg Kantor and his set theory will help us come to terms with this maths concept of dizzying scale.

Statistics seem, almost by their very nature, to convey a positivist message. They are, in fact, a formidable tool in the attempt to master the complexity of the real world... But numerous "biases" threaten any discourse that refers to them without care: an over-simplistic reading of the figures can lead us - for example - to confuse correlation with causation... And more complex phenomena (notably Simpson's paradox) can distort conclusions that seem objective.

Speed is such a common term that it's easy to forget how much of a role maths plays in understanding it. Until three or four centuries ago, there was no speed at all. It was only since the Renaissance that the concept of movement crept into the world of mathematics, thanks to calculus and Isaac Newton.

In this episode, we look at the relationship between maths and truth. Maths is meant to be certain, either right or wrong. Turns out, it’s not that simple. For Gödel's theorem has proved that there are “undecidable” theories, which one can neither prove nor disprove.