An elegant proof using Coulomb’s Law, infinite series, and conditional convergence — When we ask the question, “Does order matter?”, we are very ambiguous. Sometimes it does, sometimes it doesn’t. This depends on what the situation is, so let’s narrow it down to mathematics. Does order matter in mathematics? Unfortunately, narrowing down doesn’t change our answer, it still depends on the situation…

Using maths to prove a well-known property of an A4 piece of paper — Many of you may have heard of the phrase “you can’t fold a piece of paper 8 times” and I bet many of you have tried at least once only to be faced with the harsh reality after your 7th fold that you can’t achieve the 8th fold. I found…

We look at the AM-GM, what it is, how to prove it, and what it’s used for — The AM-GM inequality stands for arithmetic mean-geometric mean. Probably more people are familiar with the notion of the arithmetic mean than the geometric mean. I will briefly explain both to ensure everyone can follow later on. Take a set S={2,6,11,17}. To calculate the arithmetic mean we find the sum of…

Investigating a geometric series problem from the STEP I 2004 paper — Depending on where you are in your mathematical education, you may or may not have seen series and in particular geometric series. If you haven’t seen the series before I suggest looking at them as they are very useful in mathematics. Series are a way to write a summation of…

I look at a brief history of the events during World War II following Alan Turing and the breaking of the enigma code — World War II The year is 1939. Tensions were high with unresolved political issues from World War I, the Great Depression loomed over the economy and Nazi Germany has just invaded Poland. World War II has started. With estimated casualties of 50 to 80 million deaths over the course of 7 years, World…

I tackle a question from the 2019 STEP 3 Paper that only requires you to use familiar methods that most mathematics students can follow — As a student wanting to study mathematics at degree level in the future, I try to look at mathematics entrance exams for schools like Cambridge that require me to have deeper understanding of topics and apply these topics differently to how I usually would. The Cambridge entrance exam is called…

I look at an A1 question from the William Lowell Putnam Mathematical Competition that could be solved by most first year mathematics A Level students — What Is The Putnam Mathematical Competition The Putnam Competition was founded by Elizabeth Lowell Putnam in memory of her Husband William Lowell Putnam. The competition began in 1938 and commences annually on the first Saturday of December. The competition is open to all undergraduate students in the United States and Canada and are in teams representing…

Looking at an infamous problem posed by Srinivasa Ramanujan and an integral with a golden solution — One part of mathematics that I find fascinating however hard to grasp are infinite series, summations and nested radicals. Probably my first encounter with infinite nested radicals was from Srinivasa Ramanujan’s work. Arguably, his most infamous nested radical which he proposed to the ‘Journal of the Indian Mathematical Society’