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 […]
I had the pleasure of witnessing this interaction the other day: two kids were locked in a battle of wits to see who could think of the highest number. Player one served with a million. Player two with an amazing return of a billion. Player one went for the smash: INFINITY. But player two caught […]
Series An Amazing Formula Generalizing Leibniz’ formula for π, the alternating harmonic series, and the Basel problem Complex Analysis Beyond Infinity Analytic Continuation and its Applications in Quantum Physics Number Theory Transcendental Numbers Into the Unknown Differential Equations Numerical Solvers for ODEs An introduction to Euler methods Number Theory The Euler-Mascheroni Constant Remember the harmonic […]
Want to win a million bucks? Just solve one of these problems. No strings attached. Ok maybe one string: the problems are somewhat hard. Scratch that, really hard. The Gauntlet is Thrown At the start of the millenium, the Clay Mathematics Institute put forward these seven problems which are deemed as some of the most […]
The terms machine learning or artificial intelligence are thrown around a lot these days. It has become fashionable to say that such and such a device has artificial intelligence. But what does this mean? My objective is to give a non-mathematical description of how AI algorithms work. Many papers on the topic quickly get bogged down in heavy duty mathematics, […]
The Indonesian Caves of Borneo Island offer an insight to the most primitive form of recorded communication. Around some 40,000 years ago, before the evolution of written language, physical illustrations on cave walls were the most precise method of recorded communication. As time progressed, the methodology of record-taking evolved from cave paintings to complex alphabets — offering complete expression […]
Captivated by the motion of waves & mesmerized by the perfectly-imperfect symmetry of leaves, it’s crystal-clear we’re a pattern-seeking species. Externally, studies have proven that we use patterns to weigh our environment of danger — a disruption in our daily routine (particularly back in hunter-&-gather societies) signals to our conscious that something is off. Internally, patterns are inscribed in […]