From nothing but the definitions of derivatives and limits, we’ll prove one of the first derivative rules you’ll learn in undergrad calculus. All pictures made by me with LaTex, tikz, and GIMP unless otherwise specified. If you wish to make an apple pie from scratch, youmust first invent the universe. — Carl Sagan When most students first see […]
Every physicist would agree that the greatest paradigm shift of the last century was the quantum. Quantum mechanics has changed the face of science. It can explain everything. Electricity? Yes. How birds fly in one direction? Yes. Gravity? No. But, today we won’t get to that. Instead we will talk about another conflict in the […]
“There is a rumor in America that there are two intelligent races on Earth: Humans and Hungarians” — Isaac Asimov 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 […]
Chess Chess and Mathematics At first glance, these two disciplines may seem unrelated. However, mathematics and chess have a large amount of unexpected connections. Computer Science Babbage, Lovelace, and The First Computer Long before Alan Turing revolutionized the field of computation, there was Charles Babbage and his difference engine. Babbage was a man of many skills, most notably in machinery […]
Set Theory My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. — Georg Cantor 06 Nov 2020 — 12 min read Image source My theory stands as firm as a rock; every arrow directed against it will return quickly to its archer. — Georg Cantor As quoted […]
Linear Algebra SVD decomposition and a demo of an image compression. Photo by Daniel Plan on Unsplash I structured this article in a way that you are gonna need your focus at the first section when I explain about the SVD decomposition and just after that you’ll get your reward which will be watching how it works in […]
The Dartmouth Summer Research Project on Artificial Intelligence was a summer workshop widely considered to be the founding moment of artificial intelligence as a field of research. Held for eight weeks in Hanover, New Hampshire in 1956 the conference gathered 20 of the brightest minds in computer- and cognitive science for a workshop dedicated to the conjecture: […]
History The Limit of Logic and The Rise of The Computer AI since Aristotle (Part 2) Analysis Cantor’s Diagonal Argument “Diagonalization seems to show that there is an inexhaustibility phenomenon for definability similar to that for provability” — Franzén… Philosophy Platonist Roger Penrose “Sees” Mathematical Truths What does Roger Penrose mean when he claims to “see” mathematical […]
Quantum Mechanics Cats and Collapses: Interpreting Quantum Mechanics Everyone’s heard of Schrödinger’s Cat. But what can it tell us about the meaning of Quantum Mechanics? Quantum Physics Schrödinger’s Equation “So do any of you guys know quantum physics?” Paul Rudd in Avengers: Endgame Quantum Mechanics What is Wave-Particle Duality? Why we need quantum physics. History […]
In this time of deep political, economic, and public health crisis, another terrible ill has recently befallen us: the death of a great and prolific mathematician, Ronald Graham (1935–2020). We were blessed with his presence and genius from October 31, 1935 to July 6, 2020. While this is truly a sad moment for mathematics, I […]
Using only elementary methods we will prove the Fundamental Theorem of Algebra. Along the way, we’ll befriend some key ideas from elementary analysis and catch a glimpse into the beautiful world of complex numbers. Motivation Regardless of anything else, it’s been a great quarantine project for me:) The aim of theory really is, to a great extent, […]
Ever wondered what happens to a raindrop during its journey from clouds to the ground? It does not stay intact. It deforms and breaks as it comes down. According to Villermaux and Bossa, the raindrop flattens as it comes down and forms a bag-like structure before it breaks (I strongly recommend watching the supplementary movie on this page for the […]
Relativity A Light Intro To Tensors A Framework For Defining Geometric Objects In Space Relativity The Lorentz Transformation And how to repair physics Relativity How to Compute the General Relativistic Correction to Time General relativity is one of the most technically difficult physics theories, as it requires uncommon knowledge and mathematical skills. However, it is […]
An omnipresent problem observed by all scientific intellectuals from Aristotle to Galileo is that modeling the real world is, well, nearly impossible. While dot-diagrams, differential equations & vector calculus bring us closer & closer from theory to reality, it’s clear that an additional degree of complexity lurks. A fascinating branch of discrete math that attempts […]