Frequently asked questions

I am from a beautiful town in north-western Spain: Oviedo. Here is where I currently live and where I have spent most of my life.

I truly have no preference — feel free to call me however you prefer. I switch randomly between both, but I tend to call myself Samuel in writing and Sam in speech.

Just like all Spaniards, I have two surnames: one from my father (González) and one from my mother (Castillo). Thus, my legal last name is "González Castillo". This has been a source of confusion for some people, who have mistaken my first surname by a middle name. That's why, following the guidelines issued by FECYT, I join my two surnames with a hyphen when I am writing in English.

Some people try to pronounce my last name as it would sound in Spanish. While I appreciate the effort, you can pronounce it just as you would likely read it: /gɒn'zælez kæs'tɪləʊ/. Honestly, don't worry. As long as I know it's me who you're calling, it's fine!

Unlike in any other field of knowledge, in mathematics everything has a reason. Everything can be logically deduced from some definitions or axioms. If you are stuck with something, it probably just means that there's a broken link in your chain of reasoning.

My advice is for you to go as deep as you can into whichever problem you are trying to solve. Break it down into its smallest pieces and identify what doesn't fit. Then you can ask somebody (myself included).

This process may take time — perhaps there are several things that you need to relearn! But be patient and keep trying. I can assure you that everything can and will make sense if you make the effort. Mathematics is perfectly self-contained and consistent... at least at the user level! Maybe we can leave the chat about Goedel's incompleteness theorem for another time.

This question is hard to answer, but I will try my best.

As Maryam Mirzakhani once said, "the beauty of mathematics only shows itself to patient followers". Indeed, when you give mathematics a chance, it's hard to ignore its sheer beauty and greatness. Mathematics is not only the footprint of Truth in our world, but it is vast far beyond our imagination. Furthermore, there is a unique feeling of certainty and safety that one can find within mathematics, for in the World of Thought the right questions always have a unique unambiguous answer. Of course, at the foundational level, even mathematics can reveal some uncertainties within itself, but these are insignificant compared to those of any other discipline.

Plenty, but these would be my top three in alphabetical order: David Hilbert, Euclid and Nicolas Bourbaki. The latter had a troublesome life and a rather rebellious son.

In terms of programming languages, my absolute favourite is C. It is minimal, it is beautiful and it gets you close to the metal. What else could you ask for? If you want a comprehensive introduction to C, the C notes for professionals handbook might be a good starting point.

Needles to say, the fact that C is my favourite language in no way means that C is my go-to language for any kind of project. There are many other languages that I use and enjoy, and some are better suited than others for different tasks.

Vim. I use it for everything and I strongly recommend it. The learning curve is a little bit steep when you start using it, but, trust me, it pays off in the long run. In particular, if you are writing LaTeX, Vim-LaTeX is a game changer.