# Believe in numerical magic

The more I learn about it, the more I feel fascinated by numerical methods. Why? Let me give you some background.

My secret ambition would have been to be a pure mathmetician. My life would have evolved proving theorems with very ambiguous relevance to the real world. Mathematics as a closed system; how logic connects assumptions to results, how it generate patterns and structures the mind, and making all that working around.

My second best ambition would have been to be an applied mathematician. Something fascinating about mathematics is that all that stuff that shows up in the reall analysis books connects with the world, describe real patterns. I had that feeling recently as I was reviewing the gamma function and euler number. The first time I saw complex numbers, I really could not get why the heck that would ever be useful. It took me a while to understand that complex number operations, and all the corpus of theory that is linked to it, was just a simple way of keeping track of two dimensions. Voilá!  In one equation:

exp(ix)=cos xsin x

you can connect to any two dimensions representation. A similar feeling of Eureka! occurs when you learn PCA for the first time and realize that eigenvalues, that esoteric product of the mathematical mind, have in fact a very direct quantitative use. And a similar feeling happened to me when I understand, much earlier, that derivatives -god, I still remember my what-the-hell-is-this face when I first saw a derivative in high school- could be use to find an analytical closed form solution for a maximum -which is in turn the corner stone of much economic theory.

Unfortunately, I’m not gifted and for me writing proofs feels too much like moving in a dark room and feeling how frustration hit on my self esteem. Iam however  happy of the time I invested learning math to be, at least, able to appreciate the magic and beauty -not to say be able to use it- of these arrangement.

But as I was saying, this is a piece on numerical methods. Imaging you come from that background. You have gone through all that experience of fascination with how the human mind can perform that magic making use of its privileged intuition and intelligence. You feel amazed about that quasi-mystical experience. And then, you discover that you can teach a machine, lacking any of that intelligence whatsover, through a finite number of stupid predetermined steps, to essentially approximate the same solution, to get through a different path to the same place, and that doing it yourself is actually relatively straightforward, not a science fiction operation.

As I said in a previous piece this is something that can’t leave intact your perception of the world.