Yes, you are reading this correctly: a triangle can have four sides. If this sounds strange, I have to agree: this statement could be formulated in a more nuanced way: when we look from the point of view of the associated circles to the sides of a triangle, the fourth...

## Differential equations ODEs versus PDEs

Differential equations came paired with the invention of calculus and have been around for a long time. They are still the main study of a lot of mathematicians. Many famous mathematicians such as Newton, Leibniz, d’Alembert, Euler and Lagrange have made discoveries...

## The Infinite Monkey Paradox

To most people the notion of infinity is unfathomable. That has to do with the strange behavior some things demonstrate when the concept of infinity is introduced. Think for example of an infinite time horizon. No one knows what it feels like for an infinite amount of...

## What God’s number has to do with a Rubik’s Cube

The Rubik’s Cube: we have probably all tried to solve it. Some of us failed to do it and some of us have found real successes. The 3-D combination puzzle was invented in 1974 by the Hungarian sculptor and professor of architecture Ernő Rubik. As of March 2021, over...

## The Legacy of Frank Ramsey

In history, there have been numerous influential scholars in the field of economics and econometrics. Think for instance of John Maynard Keynes, who is known for his influence in macroeconomics through the Keynesian School. Or think of Adam Smith, who introduced the...

## Diophantine equations

Diophantine equations are polynomial equations over the integers. These are useful in many fields of mathematics such as group theory and operations research.

## Discovering the Frequencies in Financial Markets

Wavelet analysis stems from the 19th century when Joseph Fourier studied the heat equation. From his work, a foundation was set for Fourier transformations (FT). However, FT requires conditions such as stationarity of the data set and it only gives frequency...

## Is math discovered or invented?

Mathematics has been used and researched since ancient times. The point of view on what mathematics is shifts from being an invention, a discovery to an artefact, by the influence of time and people. -Britt Brugts

## Zeno’s paradox

It’s a calm and sunny day as Achilles is walking through the city when he comes across a tortoise that approaches him. “Hi Achilles, I have a rather interesting question for you.”, says the tortoise. “Would you like to have a sprint race against me? I will get a head...

## A road to mathematics

Remember when you were young and you were too excited to sleep because you were going on vacation the next day? Your parents would wake you up very early the next morning because they wanted to drive all the way to the south of France in one day. Then, sometime during...

## The raven paradox

The raven paradox Econometricians face difficult problems. One of the hardest problems one can encounter is a paradox. The raven paradox is such a problem and was first proposed by logician Carl Gustav Hempel. The paradox has its basis in statististics. In this...

## The math conference

Two mathematicians, Simon and Blume, are at a conference dinner, fighting over the last few pieces of lobster and steak, when another mathematician walks up to them. Having heard about the brilliance of the two, he decides to present them a riddle. After thinking for...

## The World of Sports Betting

It’s Saturday evening and you’re watching a football game with a couple of friends. Unfortunately, the game is between mediocre teams, so you don’t expect to see a great match. However, one of your friends has an idea to spice it all a bit up and to make the game more...

## Newcomb’s paradox

Let's suppose that we have a game with two players. One is a person that will make a decision and the other is a supercomputer that will try and predict that decision beforehand. This computer has been tested many times and the testers have worked out that the...

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