If you have ever taken an introductory calculus class, then at some point you were given a list of derivative rules and expected to memorize them. Today, I want to prove and show you an easier way to use the product rule and the quotient rule. Let us start with the product rule. On a […]
Kronecker Kronecker, God and the Integers Natural numbers were created by God, everything else is the work of men — Kronecker (1823–1891). Poincaré Poincaré’s Philosophy of Mathematics Was his philosophy of mathematics underrated? Volpin The Beautiful Consistency of Mathematics — Alexander Yessenin-Volpin Mathematics is often believed to bring people to madness. We hear many stories […]
The Rubik’s Cube is a 3D permutation puzzle invented in 1974 by a Hungarian sculptor named Erno Rubik. Since its introduction to the U.S. market in 1980, the cube has become cultural icon, selling over 350 million by 2009. It is both the world’s top-selling puzzle game and the world’s best selling toy, even being featured in several movies including The […]
Modular forms are some of the most bizarre and wonderful objects in mathematics. They are one of the most esoteric entities in mathematics, and yet the twentieth-century number theorist Martin Eichler rated them as one of the five fundamental operations: addition, subtraction, multiplication, division, and modular forms. – Simon Singh, Fermat’s Enigma: The Epic Quest to […]
Perusing Hacker News last month, a particularly-captivating Ask YC popped up on the first page: what’s the most valuable thing you can learn in an hour?There was, as expected, an array of deep, well-thought-out answers. One particular answer, though, tickled the math side of my brain that gets me cranking up Medium & delving down a path of […]
Chess-players are rated according to how well they perform when facing other players. For example, reigning World Chess Champion and fellow Norwegian Magnus Carlsen is as of September 2019 rated by the International Chess Federation FIDE (Fédération Internationale des Échecs) at 2876 points, the highest in the world yet six points shy of his own peak rating […]
Philosophy Beginner’s Guide to Mathematical Constructivism The foundational crisis in mathematics along with roughly four decades following it, was likely the most fertile period in the history of logic and studies in the foundations. After discovering the set-theoretic paradoxes, such as the paradox of the set of all sets, together with the logical ones, like Russell’ History […]
On or about the 31st of January 1913, mathematician G.H. Hardy (1877-1947) of Trinity College at Cambridge University received a parcel of papers from Madras, India which included a cover letter from an aspiring young Indian mathematician by the name of Srinivasa Ramanujan (1887–1920). The cover letter discussed three topics: An introduction of Ramanujan and his precarious situation; A claim […]
There are living things we do not see. I sense organizing behaviors — order — in what I do (when writing, painting, playing music, loving). Also in things I and many others participate: scientific research, political developments, war dynamics, gaming, financial markets. In nature, its sheer variety freezes judgement. Pigeons put a strong commitment to […]
An important characteristic of the Quadratic Polynomial y=ax²+bx+c is that it retains its parabolic ax² shape and size wherever it is located in the x-y grid. The other terms, bx +c are just the, “Sit where we say”, ushers! This architectural symmetry and stability means that the gradients at the roots are of equal magnitude and opposite sign and can be used to […]
In this essay, we’re going to obsess about paths on a two-dimensional grid. Here is what such a path might look like: Fig 1: The kinds of grid paths we’ll be counting. We’ll think about counting paths that satisfy certain properties.Even though the simple joy of counting things should be motivation enough, I’ll provide some […]
Here’s a fun 2-minute guide to the infamous Axiom of Choice, one of the stranger mathematical curiosities. The short answer, not at all rigorous answer, is that the axiom of choice allows mathematicians to extract elements from an infinite number of infinitely large sets at once. This turns out to be very important, because mathematicians […]
Max Black, the author of The Nature of Mathematics (1933), thought the main task of the foundation of mathematics (and, consequently the main task of any philosophy of mathematics) would be to elucidate “and analyze the notion of integer or natural number” [1]. Is the task described by Black really so difficult to complete? Yes, […]
What are they, and why do they exist? This one is a bit technical. If you’re feeling rusty on your QC fundamentals, don’t read it. Save it. Bookmark this article for later when you’ve brushed up. You’ll be glad you did, especially if you want to understand QCS. Compare a light bulb to a candle. […]