Category: Other mathematics

This is a “what-if” document. It’s not intended as a serious suggestion for how we should write mathematical notation or for replacing current...

I was thinking about inverse function notation, and that got me thinking about function notation, and that got me thinking about operations and how meh our nota...

Theorem: Given a quadratic function with rational roots, the \(y\)-intercept is rational if and only if the stretch is rational. Proof: If \(f\) is a quadratic ...

I used to hate logarithms. They were hopelessly confusing. Sort of like this: https://www.smbc-comics.com/comic/operations This is the third year now that IR...

Mathematics is beautiful. Mathematical notation, meanwhile, is a horrid mess second only to English itself for its arbitrariness. For instance, basic arithmetic...

We tend to act as if multiplying is repeated addition. This misses a key, crucial difference between the two operations: WE CANNOT ADD UNLIKE THINGS. We can abs...

Some version of this question keeps getting asked on the internet. What is \(8\div2(2+2)\)? Some background The strength of mathematical notation is at the inte...

Euler’s Identity has been called “the most beautiful equation” in mathematics. It neatly encapsulates five key values and three operators into...

In “Burn Math Class”, Jason Wilkes spends quite a few pages deriving the value of \(e\). I did not notice him at any point mentioning compound inter...

I’m currently reading “Burn Math Class,” and it’s got me thinking about language. Yesterday, I saw an item about teaching students why c...