Frequently asked questions

I am originally from a beautiful town in north-western Spain: Oviedo. That is where I spent most of my life.

Currently, I live in Rotterdam, the second largest city in the Netherlands.

I truly have no preference — feel free to call me whichever 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 for 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 more 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 also 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.

Without any doubt, Rust. Once I started using it, I realised how much I had been missing out on, and there was no turning back.

Its rich type system leads to better-organised and more robust code, and its memory safety features make many common bugs simply impossible. In Rust, if a program compiles, you can have some confidence that it will work. And all of this comes without compromising on performance.

In addition, Rust is very versatile: you can comfortably use it to build both low-level OS components and high-level web applications with Wasm. Moreover, the Cargo package manager is a joy to use, and the Rust ecosystem is full of wonderful tools and libraries.

That being said, I should also state that, back in the day, C used to be my favourite programming language: it is minimal, it is beautiful and it gets you close to the metal. And, while I no longer use it for my personal projects, it will always have a special place in my heart.

For writing text, I use Vim (and Neovim). 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.

For coding, life has forced me to use some IDEs that I am not particularly proud of, but I still use them with Vim keybindings.