Knowledge sharing is hard — Can we get serious now?… I was once at a concert with Simon&Garfunkel and I clearly remember Paul walking up to the microphone saying “I need to say this”… All 40,000 spectators went pin-droppingly quiet and listened carefully to his next sentence. I always thought that this was a badass…

The key to unlocking the secrets of the primes — Euler products are very interesting mathematical objects. In some sense, they act as dictionaries between two worlds — the multiplicative and additive worlds of numbers. They are both number theoretic and analytic. Number theoretic because they are products over prime numbers and analytic because they are analytic (complex differentiable) functions.

Learn the inner workings of calculus by understanding a more general version and watch as the beauty unfolds — Not too long ago I was writing an article about the Planck length — a hypothetical shortest length in our Universe. …

A place where time becomes space and space becomes time — Let’s start with the most challenging task: explaining what a black hole is as we understand it with our best physical theories at the time of writing. A black hole is a point of infinite density and curvature surrounded by an event horizon where time is frozen and where spacetime…

The Smallest Scale of the Universe — Let’s start out by asking an innocent question: Why does the Sun shine? The other day, my three-year-old son asked me why the Sun is yellow. I laughed and told him that that was a very good question! …

With applications to the sum of divisors functions and the prime counting function — In this article, we will try to devise a formula for counting divisors of a number. In the process, we will check our calculations with the programming language Python. …

What is energy? — Energy is everywhere. We use it to power every bit of technology from computers, phones, and light, to transport and life itself. But what exactly is energy and why is it so crucial in almost all processes in the Universe? In this article, we will tackle these daunting-looking questions by…

Number theory and distributions - an introduction — In this article, we are going to use the theory of distributions to study functions of interest in the field of analytic number theory, thus we are going to unite two very different areas of mathematics. Specifically, we will use the Heaviside step function and its distributional derivative the Dirac…

A crazy object with finite volume but infinite surface area — This interesting puzzle is one of those “ wonders of mathematics” that we mathematicians tend to hide from our more inexperienced students for as long as possible together with other gems like the Basel problem and the “evaluation” of divergent series. I first heard of this apparent paradox when studying…