Cryptography Could We Break RSA Encryption Without A Quantum Computer? We discuss a range of integer factorization algorithms that can run on classical computers and explore their future in the face of Shor’s algorithm. Applied Mathematics Algorithmic Trust Anyone? The Apple Pie Problem Cryptography Shannon Ciphers and Perfect Security A Shannon cipher, named after mathematician […]
“Although Abel shared with many mathematicians a complete lack of musical talent, I will not sound absurd if I compare his kind of productivity and his personality with Mozart’s.” — Felix Klein Niels Henrik Abel (1802–1829) died at age 26. Largely self-taught, during his short life the young Abel made pioneering contributions to variety of […]
The amount of energy expended by animals at rest, including humans, is known as the basal metabolic rate, or BMR. Think of it as the amount of fuel burned every 24 hours to keep your body at 37°C degrees as you sleep. We can estimate the rate for each individual by using the so-called Harris–Benedict equation (Mifflin and St. Jeor, […]
Bayesian Statistics A Bayesian argument for why humans will soon be extinct Photo by JEFF VRBA on Unsplash I first encountered The Carter Catastrophe in Manifold: Time by Stephen Baxter. It presented a fascinating probabilistic argument that humans will go extinct in the near future. It is called the Carter Catastrophe because Brandon Carter first proposed it in 1983. I […]
Pythagoras’ theorem provides the relationship between the sides of a right-angled triangle: the sum of the squares of the lengths of two sides equals the square of the hypotenuse. It is one of these primaries theorem of all science. Just to say about vector notation as being involved in everything. Classical mechanics, electromagnetism, relativity, quantum mechanics are […]
Everyone who has studied basic physics, mechanics, dynamics or control system have encountered the inverted pendulum. However common, students often struggle to see how understanding such an abstract device may help them in their future careers. Not many job positions call for pendulum balancing experts. You don’t see inverted pendulums in real-world devices (or do […]
There is a rich history of mathematicians, philosophers, and other thinkers invoking demons (real or imaginary) in their reasonings. The tradition goes back at least to the iconic ancient Greek philosopher Socrates, who we know through the works of Plato, Xenophon, and Aristophanes. In Plato’s dialogues, Socrates claims to have a personal δαίμων or daemon who would speak to him and let him […]
In this story, we are going to discuss how probabilities and expected values work. You will figure out how to win at Roulette — at least in the short-term. If you’re looking for a way to become rich in the long-term, I have to disappoint you though. Sorry friend, this article is not for you. […]
The methods of finding roots of a quadratic equations are quite easy and are very well understood. There are all kinds of approaches available, like algebraic, geometrical, graphical etc. The most common approach is the algebraic method, where we use the well known quadratic formula, given by This formula gives both real and complex roots, depending on the […]
A Basic Overview & Visual Introduction To The Magic Of Waves It’s warmly appropriate that Jean-Baptiste Fourier left us with the poignant quote above as a stark reminder to continuously turn to our connection with nature as a source of inspiration for knowledge. It’s appropriate because, well, Fourier’s greatest contribution, the Fourier Series, both literally […]
“Beyond the way they speak, there is only one (no two!) features of American life which I find really tiresome. The impossibility of getting a bath in the ordinary sense and their ideas on room temperature” — Alan Turing (1936) Pioneering British computer scientist and mathematician Alan Turing first arrived in America on the 28th of September 1936. […]
Mathematics The Martians of Budapest The Martians of Budapest”, sometimes referred to as simply “The Martians” is a colloquial term used to describe a group of prominent Hungarian physicists and mathematicians who emigrated to the United States following the Great Purge of 1933. Gödel Kurt Gödel’s Brilliant Madness Hungarian polymath John von Neumann (1903–1957) once wrote that […]
Calculus How to Derive the Equation of the Catenary Image by RENE RAUSCHENBERGER from Pixabay. A perfectly flexible chain in equilibrium suspended by its ends and subject to gravity has the shape of a curve called the catenary. The name was coined in 1690 by the Dutch physicist, mathematician, astronomer, and inventor, Christiaan Huygens in a letter to the prominent German […]
You meet a man on the street. He has two kids. He tells you that one of them is a boy. What is the probability of the other child being a boy as well? Before you read on, I want you to think about this problem. Maybe take a pen and a piece of paper […]