The Power of Involutions

Time and again, there are moments when mathematics just feels magical.
For me, one example for this is given by generating functions (and that is why they can be found on this blog).
Today, I want to talk about another such example: involutions. We will look at how they are used to prove in one sentence that primes of the form can be written as a sum of squares, in the proof of the wonderful Lindström-Gessel-Viennot lemma, and in the proof of Euler’s pentagonal number theorem.