Shiny Pebbles and other stuff

At secondary school and then university, we meet a variety of definitions of the derivative, all motivated by the fundam...

Greatest Common Divisor The problem is simple: given two positive integers, \(a\) and \(b\), how do we find \(\gcd(a,b)\), the greatest ...

...\(i\) wants to be a quaternion. We can think of the complex numbers as two dimensional vectors, with a rule for multip...

Where did complex numbers come from? You might think that people invented \(i\) just so that they had a solution to the quadratic equat...

I previously blogged here about the perennial discussion on \(0.\dot{9}=1\), carefully avoiding nonstandard analysis. I also blogged h...

At the early stages of mathematics, things are all very satisfying. At first you don't understand something, then you think about it,...

The problem with infinitesimals In the early development of the calculus, both Newton and Leibniz made fruitful use of infinitesimal qu...