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.

# Combinatorics

# A Beautiful Analytic Combination

Recently, I was looking for good motivating examples for complex analysis in several variables. There was already a short discussion of this question at MathOverflow. Some further searching led me to the book *Analytic Combinatorics in Several Variables* by Robin Pemantle and Mark C. Wilson. What is this all about and why did I fall in love immediately?