What happens when one pool ball strikes another? — Recently I tackled an interesting problem which involved a pool ball striking another. The problem was not straightforward to solve, but solving it involved some interesting observations about what we can expect when we play a pool shot. Among the things we will learn is: After a pool ball strikes…

The only way to learn is by trying, failing and trying again — We all love to have something to show for our efforts, don’t we? I guess that’s why graduation ceremonies are so popular. After many years of hard work, it’s great to have that moment where you can receive your diploma and celebrate reaching the finish line. Since the birth of…

Fungal infections are on the rise. Some are excruciating and deadly. — HBO’s The Last Of Us is a likely to be the first truly successful TV adaptation of a classic and popular game. Having been a fan of the game, and having watched the first two episodes of the TV show, I can see why. They have managed to keep many…

Sometimes the simplest proofs give the best insights into how mathematicians think — Fermat’s Little Theorem is a beautiful number-theoretic result which states that, for any integer a and any prime number p, aᵖ﹣a is divisible by p. For example, if a = 4 and p = 3 then aᵖ﹣a = 60 which is divisible by 3. Fermat first proposed this in a…

In a few short lines of code, we’ll get any Billboard chart for any date in history — I used to think web scraping sounded complicated. You’d have to decode a bunch of HTML and Javascript and do messy hacking to get at what you wanted. But once I took a crack at it using my favourite language of R, I realized that tools exist to make it…

This Group Theory problem was set to British 18 year olds in 1988 — If you were an enthusiastic and talented high school mathematics student in the UK in 1988, you would have studied elementary Group Theory as part of your Advanced Level (A-level) curriculum. Sadly this is not the case any more. …

How to mathematically ring in the new year 😊 — I was recently posed a new year-themed question by a friend, and I found it a fun problem to solve, so I thought I would share it with you. The question asked me to find the 2023rd derivative of the above function. My first attempt was to differentiate it directly…

The data engineer is likely to be one of the most value-adding roles to hire right now — The other day, I was invited as an expert to a call with someone who had been implementing a data system in an organization. The system had been live for a few months, and they were demoing the data extraction capabilities of this system. Basically, you could go to the…

It’s easy to be fooled by this problem — I recently came across this problem in an old Cambridge mathematics entrance paper aimed at talented high school mathematics students. I found that the question was written in a way that lulls you into a false sense of security about the solution to the problem, but in fact the problem…