There are a lot of reasons why I’m writing this, one of them is I could never understand Borel Sets, I got introduced to them on day one of my adventures in Probability Theory, there was something about the way it was portrayed, it didn’t make sense to me, like at all. So I broke […]
I love these three math problems! The first one requires very little math skill — but it is maybe the most difficult one. The second one only requires basic geometry. For the third one, you need to know elementary algebra. Problem 1: The 316 problem I call this problem “the 316 problem” because 316 is […]
In this article we explore how the principle of relativity may apply to curvilinear movements. Our aim will be to achieve a transformation analogous to that obtained by Einstein on his paper On the electrodynamics of moving bodies [1], the Lorentz Transformation, but referred to systems on rotational movement respect each other. For that sake we will first […]
Here’s a conjecture with a lot of really smart people working on it that has a fairly intuitive statement, and yet almost no one knows about it. Seriously, there isn’t even a Wikipedia page. The idea is to quantify how weird 1-dimensional sets can be. We’ll make these notions more precise in a bit, but […]
Puzzle This Math Trick Only Works for Everyone at the End of the Year So it’s the perfect way to usher in the new year Field Theory A Finite Number Of “Numbers” What exactly is arithmetic on a field of numbers which are merely elements in some set? Babylonian A Modern Look at Square Roots […]
Economics is widely recognized as an independent branch of knowledge, but this was not the case before Adam Smith’s The Wealth of Nations publication in 1776. Since the Sixteenth Century, Mercantilism had been the dominant school of thought among economists. The mercantilistic perspective views economy, which is already under governmental control, as a means at the […]
Before we begin, be aware that talking about electromagnetism in any meaningful way means talking about vector calculus. Please don’t be intimidated, even if you don’t have the first idea what any of the symbols or terms mean. Vector calculus is hard but its core ideas are intuitive and I will explain everything as we […]
The Goldbach conjecture is one of the most captivating unsolved mysteries in mathematics. In this article, I will take you on a journey through time and mathematics. I will present some other ways of looking at the conjecture than the original definition. Both visually and algebraically. We will prove an equivalence and investigate it a […]
Hypothesis testing has some similarities with one of the simplest methods of proof from mathematical logic: Proof by contradiction. Hypothesis testing can be thought of as being the probabilistic counterpart of proof by contradiction. Let us refresh our memories first about this method. How does proof by contradiction work? Let’s say we want to prove a […]
A theorem by two mathematical greats, which anybody, no maths experience required, can understand! An amazing and beautiful result accompanied by some pretty hand-coded visualisations! Regardless of your experience with math, this theorem can be understood, and the elegance of the solution appreciated. Throughout I will both use diagrams to explain concepts where possible. Where I use […]
Hilbert The Hardy space has three equivalent definitions. Each of them emphasizes a different aspect of the space and all three of these aspects… G.H. Hardy (1877–1947) and David Hilbert (1862–1943), whom Hardy- and Hilbert spaces are named after The Hardy space has three equivalent definitions. Each of them emphasizes a different aspect of the […]
Arguably the most important unsolved problem in pure mathematics today is to prove (or disprove) the Riemann hypothesis, which is intimately connected to the distribution of prime numbers. One of the basic techniques needed to understand the problem is called analytic continuation, which is the topic of this article. Analytic continuation is a technique from a branch of mathematics […]
In mathematics, especially when it comes to number theory, there are many basic things that we don’t know. Simple questions that we can’t answer. This can be realized by considering a few of the famous unanswered questions that we mathematicians would like to know the answer to. A few of them are Are there infinitely many […]
Kronecker Kronecker, God and the Integers Natural numbers were created by God, everything else is the work of men — Kronecker (1823–1891). Number Theory Perfect Numbers An ancient riddle Prime Numbers The Goldbach Conjecture An Equivalent Formulation of an Unsolved Mystery Number Theory The Euler Totient Function A Probabilistic Approach Number Theory Transcendental Numbers Into […]