The beauty of modeling movement with math — I recently tackled this applied mathematics problem and was quite delighted with the beauty of the answer so I thought I would share my approach to it. The problem involves a particle being launched off the top of a staircase and bouncing progressively down, hitting each step once. It’s a…

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…

There is no better way to learn mathematical induction than to work with the Fibonacci sequence — The Fibonacci sequence is a very well known and studied sequence of numbers which is often used in schools and in recreational mathematics because it can easily be understood by those with a limited technical mathematics education. The sequence is defined as follows: the first term is zero, the second…

Proving a surprising and pleasing mathematical result — Today I am going to prove a beautiful and somewhat surprising expression for π. The expression that I will prove is the following:

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…

Establishing ‘proof’ in mathematics leaves no room for error or doubt. Here are some common ways mathematicians meet this high burden — The word ‘proof’ has different implications in different contexts. In the field of jurisprudence, for example, the phrase ‘proof beyond reasonable doubt’ is a common phrase used for the burden of proof. This suggests there is room for some doubt in a conviction, as long as it is not considered…

While the debate rages about a reproducibility crisis in academia, there’s a much more common one right under our noses — There was a time when the only way I knew how to do analysis was to use a spreadsheet. I spent over 15 years building highly complex models and analytics on those screens with the rectangular boxes that so many have come to rely on. Then, in early 2016, it…

I use an Oxford Mathematics Admissions Test question about candy to demonstrate how you can ‘generalize’ or ‘abstract’ a math solution — As someone who has taken the journey from a high school math student to working in cutting edge Pure Mathematics research at the postdoctoral level, I want to highlight one key difference in how the brain operates at those different levels of training. High School students are taught to exercise…

You can derive the Golden Ratio from the Fibonacci numbers and you can generate the Fibonacci numbers from the Golden Ratio — The Golden Ratio — also know as the Divine Constant — is a fascinating natural constant. It occurs across many fields of mathematics and science and can be represented in many ways. The easiest way to describe the Golden Ratio is to take a line segment and divide it into…