From the Big bang to the Heat death of the universe It’s not because you’re stupid or weren’t concentrating in school Two envelopes with different amounts of money in them. Choose the better one with a higher chance than fifty-fifty! Natural numbers were created by God, everything else is the work of men — Kronecker […]
“When we met, was I walking to the faculty club or away from it? I’m wondering, because in the latter case I’ve already had my lunch” American mathematician Norbert Wiener (1894–1964) was by all accounts, a very peculiar man. After graduating from high school at 11 years old, he entered Tufts College and within three years was awarded […]
In 1896, Becquerel had registered the very first spontaneous radioactivity while working on x-rays. A mere accident allowed him to detect remarkable, not-seen-before phenomenon. To some degree, all discoveries are like rolling a dice. What, once thought out, is kind of funny; because all initial conditions must be met, without any knowledge about them. Like […]
I have a habit of throwing into the air whatever I hold. I do it so often that some call it as my addiction, yeah, it is so common to me. Depending on initial conditions, on how it left my hand, I make bare predictions: how many rotations it will make, what hight it will […]
Raymond Louis Wilder was born 1896 and died in 1982. He was an American mathematician who specialised in algebraic topology and the theory of manifolds. Wilder was professor at the University of Texas, Ohio State University and at the University of Michigan. He was also vice president of the American Mathematical Society and its president from 1955 to 1956. (He was […]
I am a student myself and not (yet) a professional mathematician. This article and the following ones go along as I am learning myself. I follow the script of my lectures and attempt to rephrase in my own words as much as possible. For more information and resources, please see the concluding notes at the […]
Being German, I have been asked about the famous German Autobahn more than once. It also means that I have a lot of discussions about (non-existing) speed limits on (some) German roads and I have spent countless hours discussing whether speed limits (on highways) are a good thing or not. Even though I mainly approve […]
There are two envelopes. You are allowed to pick one and have a look at the amount of money it contains. You take a look and see $20. I tell you that one of the envelopes contains twice as much money as the other and offer you to switch envelopes. Should you switch? Shouldn’t make […]
About 200 years BC in ancient Greece, scientists in those days were convinced that the spherical shape of the Earth, and not a flat disk, was correct. Pythagoras considered a circle perfection to be upon any other, and as such, fits best to describe the excellence of the world. Aristotle argued in his philosophical considerations […]
The book John von Neumann: Selected Letters* by Rédei (2005) is a fascinating collection of 150 of von Neumann’s correspondences starting in the 1920s until his death in 1957. Among von Neumann’s extensive communications included in the book are: Also included are seven letters to von Neumann’s friend and colleague at the Institute for Advanced Study, mathematician Oswald Veblen (1880–1960) […]
Ancient Greek philosopher Pythagoras and his followers were the first practitioners of modern mathematics. They understood that mathematical facts weren’t laws of nature but could be derived from existing knowledge by means of logical reasoning. But even good old Pythagoras lost it when Hippasus, one of his faithful followers, showed him an incredible proof. His […]
Analysis The theory of distributions , also known as generalized functions, often remains something of an enigma… 20 Sep 2020 — 15 min read The theory of distributions, also known as generalized functions, often remains something of an enigma to practicing physicists and engineers, even those working on heavily mathematical projects. This is especially true for the author, […]
The Probabilistic Method is probably best known as a book by Noga Alon and Joel H. Spencer released in 1990. I was first introduced to it around 2007, and it’s been a source of delight to return to from time to time. The technique known as the probabilistic method is mostly due to Paul Erdős, one of the […]
A metaheuristic is a high-level abstraction of established sets of mathematical rules with some randomness that leads a search process to find (near)-optimal solutions to a problem.¹ Metaheuristics are used to solve optimization problems as an alternative to exact methods like Newton’s Method or Gradient Descent. Their advantage over such exact methods is their low […]