This post is the second in the series “For the Love of Math”. Find the first one here.

This post will be a long one: full of equations, references and anecdotes about famous mathematicians. Similar to my previous post, this too will be updated as and when I get the time to do so.

A Monkey on a typewriter — you will understand this photo if you read all the way to the end of this blog!

It’s 4 AM in the morning when I write this. I woke up to the sound of mosquitoes buzzing in my ear and couldn’t sleep so I decided I’d write this. I’ll be listing some well-known but amazing theorems and results in Mathematics that amaze me in their entirety. Here we go:

1. There are more than one forms measuring distances!

Well, in fact, there is an infinite number of forms of distance measurement.

Then the Holder’s Inequality states that:

This result might appear boring to some but if you look closely, this theorem can pour out results you cannot think of! For example, we can get the generalised triangle inequality, called the Minkowski Inequality, by elementary transformations of this inequality.

If you’re still not impressed, many fundamental properties of measures in mathematical theory are developed from this inequality for example: Probability and Lebesgue Measures develop a lot of their properties from these two inequalities.