From Gauss and the birth of statistics to modern data science and machine learning — Ordinary least squares (OLS) regression is one of the first items on the menu in an introductory Statistics or Data Science course. But why do we need to square the errors? It’s a common question even high school students ask. After all, comparing the size of the errors (absolute value)…

An intuitive explanation for why sample means should be normally distributed. There have been many excellent articles and videos about the Central Limit Theorem (CLT). But besides formal proofs, I was not able to find a good intuitive explanation for why it is true. So here goes… Theorem Statement The remarkable and…

For most students of mathematics, VIDEO is the way to go. — I have noticed that given the choice between a video and a written explanation, most of my students will go for the video first. I have also noticed that Google is serving video results more than ever before. For example, if you search for “how to prove the sine rule”…

This was the final problem on Day 1 of the 2022 International Mathematical Olympiad, and the most difficult of the Day 1 problems. — The Problem Let k be a positive integer and let S be a finite set of odd prime numbers. …

The beauty of the International Mathematical Olympiad is that the problems are difficult enough to challenge the brightest young minds in the world, while only requiring knowledge of high school pre-calculus mathematics. This video/article presents Problem 1 from 2022 IMO, in the style of Plato’s Meno, where Socrates uses guiding…

Sharpen your colouring pencils… or try it as a coding challenge. — Each year, about 100 of the most outstanding high school mathematics students in Australia are invited to complete the Australian Mathematical Olympiad. The competition goes over 2 days, each day students have 4 hours to attempt 4 challenging proof-style problems. This combinatorics question was the final problem on Day 1…

Our modern society is built upon mathematics. And mathematics is built upon the achievements of thousands of outstanding individuals. Explorers, creators, problem solvers… they each pushed the boundaries of knowledge and invented new methods of thinking about the world. Who was the greatest mathematician of all time? How would you…

A fun application of graph theory and combinatorics. — Does the statement seem obvious to you? How would you prove it? It probably doesn’t seem surprising for social networks like Facebook — there are millions of Facebook users and most of them only have up to several hundred friends. But wouldn’t it be possible to construct a social network…

A spider and a fly are on opposite walls of a 30 × 12 × 12 meter room. The spider is 1 meter above the floor, the fly is 1 meter below the ceiling. They are both 6 meters from adjacent walls, as shown in the diagram below. If the…