And the cotangent function — It has been known for a long time that the infinite series 1 - 1/3 + 1/5 - 1/7 + ⋅⋅⋅ = π/4. We are also going to see (as a side-effect of our calculations) why this is true but the main question in this article will be that of…

An indescribably beautiful proof — In this article, we will carefully try to understand why π is an irrational number. We will do this by going through what is in my opinion one of the most beautiful and creative proofs in all of mathematics. In my last article, we proved that the star of calculus…

And a thorough guide to proving it — When I first heard of this fact, I was studying mathematics at University and I was immediately intrigued by it. Let me explain why. Some mathematical facts, usually called theorems, are obvious. For example, the fact that the number 2 is the only even prime number is obvious if you…

An elusive and mythical value — It all started in 1650 when Italian mathematician Pietro Mengoli asked a question that no one (including himself) was able to solve. Pietro had earlier shown that the infinite sum 1 + 1/2 + 1/3 + ⋅⋅⋅ diverges to infinity which is a fancy way of saying that no matter…

Can energy be lost or created in our Universe? — This is a story of a woman who against all odds became one of the best mathematicians of her time and developed many of the modern theories that we use in abstract algebra today. She proved a theorem so powerful that it explains the ultimate fate of our Universe and…

Prime numbers and generalizations of the twin prime conjecture — Prime numbers are the whole number equivalent of atoms in molecules in the sense that every whole number greater than one can be written as a unique product of prime numbers just like molecules are built up uniquely by atoms (of course, the analogy is not strong enough to draw…

A hunt for the long wanted mathematical weapon — The history of algebra is more action-packed than the most action-packed American movie. It might be that no ancient Greek trashed a huge part of Paris because his daughter was kidnapped, but I can assure you that this story is even more amazing. We will see how personal secrets turned…

Operators, symmetries and the animation of “traveling” zeros — This article is about the study of functions f that has the property that for some real number α, we have f(x) = f(α - x). The motivation behind this study stems from the Riemann ξ function which has the property that ξ(1-s) = ξ(s) for all s ∈ ℂ…

Art and Science — What is beauty in math? How can mathematics be “beautiful”? I admit it… It took me quite a while to realize that this was a thing and even longer to get this feeling myself. But once it’s there, it’s there to stay and it won’t leave you - ever! It…