Five questions from an 1858 British school math exam — Recently I got my eyes on some examination questions from the first ever national exams set for schoolchildren by The University of Cambridge Local Examinations Syndicate in Britain in 1858. It is a source of constant debate whether school mathematics curricula and examinations are getting easier or harder, so I…

This mid-80s masterpiece still traumatizes every one of its viewers because its events are suddenly much more likely — As an eleven-year-old child, I have an enduring memory of a series of films broadcast by the BBC in the UK in August 1985 to commemorate the 40th anniversary of the atomic bombing of Hiroshima and Nagasaki. Part of this series was the first British TV screening of The War…

How survival analysis was born out of necessity — Anyone who is, like me, a fan of the US TV show Mad Men, will recall that a substantial thread of the plot and historical context of that outstanding period drama revolves around smoking. In the 1960s, the US medical establishment were pivoting towards a point of view that smoking…

Only those with a math background can truly make sense of the tsunami of analytics that is already on our shores — I trained as a Pure Mathematician. An algebraist, in fact. By the time I finished my Ph.D., I was so deep into an esoteric specialism that they struggled to even find someone to examine me. I found myself in this rabbit hole because I thought I wanted to be an…

Proving a beautiful and pleasing mathematical result — Today I am going to prove a beautiful and somewhat surprising result — that it is possible to find a mathematical expression for π that only uses the numbers 1 and 2 in the expression. The expression that I will prove is the following: where the denominator is an…

The solutions reveal a variety of interesting methods — I recently took on three interesting problems of increasing difficulty related to calculating the sums of infinite series. After I had found solutions to each part, I then went back and discovered a different approach to solving them which delivered the same result. The process of finding these alternative…

Under what conditions is this true? — A unit fraction is a fraction with a numerator of one. The ancient Egyptians used sums of unit fractions as a way of expressing more general rational numbers — leading to the term Egyptian fractions. In fact, across a wide variety of mathematics we see an interest in summing unit…

How to avoid being just plain wrong in your work — Logic — and I mean the mathematical discipline of logic — is a truly pure and beautiful subject which I studied many years ago. As a result, I am always very aware that human beings can make the most basic logical errors in their reasoning, and this can lead to…

An inspirational example of how elementary math is open to everyone — Recently, two teenage girls — Calcea Johnson and Ne’Kiya Jackson — gave a presentation to the American Mathematical Society where they demonstrated a new proof of the Pythagorean Theorem. Their proof has caused quite a stir. One reason for the stir delights me and makes me incredibly happy as a…