Journey into Maths Country

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.

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.

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.

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.

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.

For centuries, geometry was based on Euclid's postulates, which seemed eternal and irrevocable. However, one of the postulates (the fifth) has always seemed "a little less natural" than the others, and hundreds of mathematicians have tried in vain to do without it by deducing it from the other postulates. In the mid-19th century, Bernhard Riemann came up with a novel idea: let's imagine it's false! This was the birth of "non-Euclidean geometries", which would later have major applications in physics.