*Alfonso Cevallos shares his professional journey thus far after majoring in mathematics. Read more about how mathematics opened doors for him to study and work all over the world.*

My name is Alfonso and I’m excited to share my story with you. My career as a mathematician developed over five countries and has taken unexpected turns, yet has always been exciting, and landed me a job in a stimulating new industry.

I confess that I didn’t always feel a calling for math. When I started college in my home city of Quito, Ecuador, I took a Renaissance approach and registered to classes varying from philosophy to economics to fencing. I started as a physics student but eventually shifted majors to math and completed minors in physics and computer science. As a student, I was interested in learning cool new concepts and encountering challenging problems, and math was full of them and oh so elegant!

Having good grades, some money saved by working in summer jobs and a decent level of English paid off when I was offered a partial scholarship to go on exchange for a year to the University of Illinois at Urbana-Champaign in the US. This experience had a big impact on me as it gave me a thirst for travelling and learning languages. It also gave me exposure to advanced math courses and a world class research environment. I distinctly remember being blown away by Cantor’s proof that not all infinities are equal (there’s an infinity of them!) and having an animated discussion with graduate students about how you would build large arithmetic progression-free sets of numbers programmatically. There was so much to learn! And there was this lively community of smart people exploring math together. More importantly, I was excited about being able to join this community, travel, while getting paid to do so!

When I completed my undergraduate studies, I was lucky to be accepted into a masters’ program in Europe (called Erasmus Mundus ALGANT), where I focused on number theory and algebra. The program offered a full EU-funded scholarship and took me to France (U. Bordeaux 1) and the Netherlands (U. Leiden). I was equally excited about the program as I was about living in Europe for the first time, meeting new people, and learning new languages (French, Italian, and bits of Dutch). Did you know that the French say *potatoes *to describe thickly cut fries, while the German call them *pommes*? And did you know that the sum of the reciprocals of the primes not only diverges, but grows as *log log n*? In the picture, I’m taking a much-needed break in Rome, trying to absorb this slew of new information. I made lots of friends and have fond memories of this time, and I recommend the program to anyone. Perhaps unexpectedly, the topic of my master’s thesis was in cryptography, where I optimized an algorithm for computing multi-party threshold signatures. The key was looking at the communication network as a graph and computing its k-core; this trick was enough to earn me my first publication!

Back in Ecuador in 2011, I became a math teacher for first-year college engineering students. Lecturing was fun, but not as fun as I imagined a doctoral program to be (I partly blame my dad, Fernando Cevallos, a university professor, who gave me the impression that being a PhD was fantastic, akin to being an astronaut). In 2012 I was accepted as a PhD student at the École Polytechnique Fédérale de Lausanne in Switzerland, in the discrete optimization chair. The chair lies halfway between math and computer science, and in it I studied complexity theory and approximation algorithms applied to problems in graph theory and geometry. Did you know that on any n-vertex graph, the number of cliques times the number of anticliques is at most n*2^n? Or that it is NP-hard to select, out of a collection of 2n points in space, the subset of n points whose sum of pairwise distance is maximal? These are some of the theorems I proved with colleagues. In the image you can see me with my dad on the day of my PhD defense in 2016.

Switzerland is a beautiful and peaceful country. In it I developed a love for hiking in mountains and swimming in lakes, and I learned skiing and German (my skiing is considerably better than my German, although the opposite would probably be more convenient). More importantly, I developed long lasting friendships with amazing people. Therefore, after completing a postdoctoral engagement at ETH Zurich in 2018 and being confronted with the prospect of a nomadic postdoc life, I decided to stay in the country and move to the industry sector.

I currently work as a researcher in a software company that develops a blockchain network. I’m aware that *blockchain *is a buzzword that incites different reactions on people, from skepticism to curiosity to greed. However, under the buzzword and the coins lies a “boring” open-source distributed computing architecture, which I find quite fascinating. In oversimplified terms, it allows for a type of network that’s more democratic and decentralized than Facebook, and more business focused than Tor. I am a *protocol designer*: for instance, I designed an election rule for selecting authorities over the network with provable guarantees on both its computational efficiency and its fairness in voter representation, I developed a penalty-based scheme that minimizes the chance of timeout errors due to bloated data blocks, and I used Markov chains to prove that a new communication bridge across blockchains is safe because any attack will be detected with overwhelming probability. I work in a multidisciplinary team that includes experts in cryptography, computer science, network communications, game theory and economics, not to mention some cypherpunk supporters , so there is always something new to learn.

In my personal experience, it is a great time to be a mathematician working in industry, as there are plenty of exciting opportunities. That is, if you’re willing to adapt a little. For instance, a company may not necessarily post the word “mathematician” in their job advertisement, but they may be keen to hire a software developer with a math degree, or a quantitative analyst with a PhD in number theory. I, for instance, transitioned from being a “PhD graduate in combinatorial optimization” to an “expert in distributed-network algorithms with a background in optimization and cryptography” real fast. Among my mathematician friends in Switzerland, most of them, like me, struggled a bit with their first industry job for a few months, while they decided on the career path they wanted and got a foot in the door. They now work in companies such as Google, large banks, hedge funds, machine learning startups, etc., and I am happy to report that most have promising, stable and honestly interesting careers. On a personal level, I was pleasantly surprised to discover that, even though ten years ago I could have never guessed my current career, my preparation and interests matched so well with it, and I consider myself fortunate for the choices I have made.

If you, the reader, have recently started mathematics studies or are thinking about it, I can wholeheartedly encourage you to do so. Maybe apply early on for internships in different companies during your studies, so you have a better notion than I did of what’s out there. Other than that, believe in yourself and follow your passions!

### Alfonso Cevallos

Blockchain researcher,
Web3 Foundation

SWITZERLAND