Within the world of mathematics, nothing has a profound impact on, well, everything. In “nothing”, we know that we’re effectively referring to the number zero’s (0) identity as the absence of anything. The application of zero, in a primitive sense, has been innately understood from the beginning of recorded history — even wild animals notice an absence […]
Game Theory Why politicians move to the center In microeconomics and game theory, the median voter theorem states that “In a majority rule voting system, the candidate/party most preferred by the median voter will be elected” In other words, the favorite candidate of the person in the middle of the probability distribution picks the winner of the […]
The field of Statistics and Probability is useful for a lot of things like weather forecasts, scientific research, machine learning, and data analysis. However, I recently had an experience which caused me to add one more thing to that list: guarding your laptop against theft. In the month of September last year, I suffered the […]
..and the birth of the Manhattan Project The now famous Einstein-Szilárd letter was written at the initiative of Hungarian nuclear physicist Leó Szilárd with help from Edward Teller and Eugene Wigner in 1939. It was signed by Albert Einstein and sent to the President of the United States, Franklin D. Roosevelt in October 1939. The […]
Erdős Paul Erdos is to this day remembered as the man who devoted his entire life to mathematics. Living out of a suitcase traveling from university to university, throughout his life he survived off speaking fees and modest endowments from various universities. 19 Jul 2019 — 22 min read Paul Erdős with Béla Bollobás at […]
Symmetry The Many Symmetries of Tessellations ft. Harry’s Tiles Tessellations History You Can (Literally) Count On Me The History of the Abacus Fractal (Not Only Frozen) Fractals All Around A Discussion of Fractals Ramanujan It’s Time for a Breakdown (of Numbers) Now it’s time for a breakdown… (cue En Vogue’s My Lovin’ (You’re Never Gonna […]
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 […]
This post presents a novel method for approximating 1st roots of cubic polynomials that avoids the lengthy gradient and height calculation iterations associated with Newton’s and some of my own previously posted methods. It particularly addresses the task of approximating cubic polynomial roots in ‘difficult to get to’ locations – namely where root gradients are […]
Tensors Are The Facts Of The Universe — Lillian Lieber As the popular saying goes, necessity is the mother of invention — and when it comes to math, nature never ceases to provide us with a source for this necessity. Any experienced engineer can confirm: a very real necessity for engineers of all disciplines is to precisely model physical objects & […]
The beginner’s guide to proving the Fundamental Theorem of Calculus, with both a visual approach for those less keen on algebra, and an algebraic, slightly more rigorous approach, for those keen on exactness. By the end, I hope you feel a bit more like a mathematician 🙂 Introduction, motivation and ‘hello!’ Hello! We are going to understand one of the most […]
After hearing about Eugene Wigner’s article, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” for many years, I recently decided to read and digest the article for myself. (If you’re so inclined, you can read about the results here.) Continuing this exploration of the philosophy of mathematics led me to Mario Livio’s intriguing book, Is God […]
My intention for this article is to provide a look into how the decimal expansion of some fractions yields the Fibonacci sequence. Let us first take a look at the decimal expansion of 1/89: Now, for a quick refresher on the Fibonacci sequence. You start with the numbers 0 and 1, and every number after […]
Understanding Pierre de Fermat’s observation about prime numbers If p is a prime and a is any integer not divisible by p, then p divides aᵖ⁻¹ – 1. This property of numbers discovered by Pierre de Fermat in 1640 essentially says the following: Take any prime p and any number a not divisible by that […]
Cantor’s Archive is an official directory of stories published in Cantor’s Paradise, a community-driven publication of math-, science- and technology-related essays. Why Cantor’s Archive? Cantor’s Archive includes stories published in Cantor’s Paradise which are older than 1 years old. The Story Medium ceased supporting publications in mid-2021. Medium’s founder and CEO Ev Williams resigned from […]