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Pablo Freire, a student at IES As Lagoas, in Ourense, earned a gold medal in the 2025 Spanish Math Olympiad while still in 10th grade. Thanks to this achievement, he will represent Spain at the IMO 2025. Today, he tells us how he did it.
How did you start learning mathematics?
I started preparing for the Olympiad in the summer of 2023, working on easy problems and gradually increasing the difficulty of the ones I chose.
Was there anyone in particular who inspired you to take part in competitions?
The math teacher at IES As Lagoas (the school I attend), Carlos Ferreiro García, was the one who prepared me for the Olympiads in the workshop he holds every Wednesday for two hours. I also improved through online workshops led by former top-level Olympians from different parts of Spain, especially Catalonia.
When you started learning mathematics, did you expect to win a gold medal in the Spanish National Olympiad while in 10th grade?
No. Initially, I only aimed to reach the national phase someday.
How did you prepare for these Olympiads?
At first, I worked on problems from previous Olympiad editions. Once I reached a sufficiently high level, I began using books to study, which teach theorems, tricks, and lemmas useful for solving problems.
Before participating in these Math Olympiads, had you taken part in previous editions of these Olympiads or other math competitions?
I participated in the Estalmat program for three years, where mathematics is taught outside the regular school curriculum in a very engaging way. I also took part in the Kangaroo Math and Pangea competitions, which focus on solving problems quickly.
In 8th grade, I competed in the Agapema Math Olympiad, a contest designed for 8th-grade students that involves solving problems with reasoning. In Galicia, it consisted of a regional phase and a final phase with higher difficulty. Since I placed second in the final phase, I qualified for the national phase held in late June in Tenerife, where I received an honorable mention for finishing among the top four.
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How did you manage to win the gold medal in the 2025 Math Olympiad?
Studying and practicing a lot. It’s the only way, because although creativity and ingenuity are important in the competition, you also need to know a lot of things.
In a few words, how would you describe your experiences in these Olympiads? Why?
It’s wonderful because it definitely helped me discover my calling. Also, the participants in the Olympiad are very nice and friendly people, and we form a kind of community since we all share the same passion: mathematics.
Do you plan to participate in other math Olympiads in the future?
Of course, I will be able to participate in the math Olympiads in high school, since there is an edition of the Olympiads every year, both at the national and international levels.
How are you preparing for the 2025 International Mathematical Olympiad? Do you expect to stand out there?
I’m practicing a lot with problems of similar difficulty to those that usually appear in the International Mathematical Olympiad. I’m also still studying with books, although not as much as before, because I consider practicing with past IMO problems more important.
Since the problems are very challenging for my current level, I don’t expect to stand out much.
If a student asked you for advice on how to successfully participate in math Olympiads, what would your advice be? And why?
The first thing is that you need to like mathematics. I never studied math without feeling passionate about it. When practicing, it’s best to work on problems that are just slightly above your current level—that’s the most effective way to improve. If, after doing many problems, you’re able to solve ones of a certain difficulty, that’s great—it means you’re making progress. And if not, you’ll always learn something from them, even if you don’t realize it at the time.
It’s important to understand that improvement is slow; it never happens overnight. I don’t feel much better than I did a month ago, but I do feel a clear difference compared to six months ago. Also, the better you get, the harder it becomes to keep improving.
When it comes to studying, it’s absolutely essential to truly understand what you’re learning and to solve lots of problems where you apply that technique or theorem, so you internalize it and don’t end up using it in problems where it doesn’t apply.
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