Izar Alonso, mathematician: “String theory can never be demonstrated experimentally.”

When she was barely in elementary school, Izar Alonso (Madrid, Spain, 29 years old) discovered her love for mathematics . “I started participating in competitions and extracurricular activities. I liked it because it was very different from what we saw in school,” recalls this young woman from New Jersey (United States), a place that has been her home since 2023. It's a holiday, and for a few hours her pace slows down. In a few days, however, she will return to her office at Rutgers University, where she teaches more than 80 students of different ages. There, amidst blackboards, formulas, and questions, she continues to share that passion, which over time has translated into a brilliant academic path that has kept her connected to the fascinating world of numbers.

Alonso studied a double degree in mathematics and physics at the Complutense University of Madrid, and just a year later, she was already completing a master's degree in Pure Mathematics at the University of Cambridge (United Kingdom). Her next step took her to the University of Oxford, where she earned her doctorate in mathematics and consolidated her profile as a researcher. Her work moves into the more abstract realms of a discipline that, she asserts, "has a great deal of creativity and beauty." This perspective has earned her recognition as one of the six recipients of the Vicent Caselles Prize , awarded by the Royal Spanish Mathematical Society and the BBVA Foundation, for her significant contributions in the early years of her career.

“I felt disconnected from the Spanish mathematics community, but this has reconnected me,” she says. She anticipates remaining as Hill Assistant Professor for another year, aware that this is only part of her journey. In academia, it's common to move from one place to another. “I'm young and eager to go somewhere new,” she asserts with conviction.

Question: You have an extensive resume and a notable international career for your age. Was the support you received at home essential when you were a child?

Answer: Yes, of course. It was through my parents that they noticed my abilities and enrolled me in different activities. The first one I participated in was the Spring Math Competition held by the Community of Madrid. Later, I attended advanced classes. I find these initiatives very positive because the first phase is held in schools, and it's a good way to identify children with abilities without having to go through their parents.

I was lucky, but not everyone is. Schools' work is essential in identifying people with mathematical talent.

Q: And what was the difference between the advanced classes and what you were taught in the classroom?

A. The most intuitive example I could give is that there wasn't an emphasis on calculating. There was much more creativity; it was like solving a puzzle all the time, like constructing geometric shapes. They didn't feel like problems.

P. Over time, that led you to study a double degree in mathematics and physics…

A. I knew I wanted to study mathematics, but in the end, in high school, I decided to study physics because there was that program at Complutense University, which is quite academically intensive. In Spain, it's like studying two degrees at the same time.

Sometimes it was nice to see connections between us. Since it was a small group, the teachers gave us advanced classes, but I had to work hard.

Q. And now that you are studying pure mathematics, how would you define it?

A. It's a type of mathematics that we study for its own sake, not because we're looking for immediate practical applications. Applied mathematics, on the other hand, is based on a specific need. For example, someone might need an algorithm to solve a specific problem, or try to solve an equation used in engineering or another practical area.

In pure mathematics, we don't work with a fixed set of tools or a specific framework; rather, we start from definitions and concepts. From there, we try to prove theorems and show that certain concepts are equivalent. Sometimes this pure mathematics has applications in other pure areas, such as geometry, topology, or algebra.

Q. Your research area is also based on geometry, theoretical physics and string theory [a theoretical framework that postulates that the fundamental unit of matter is not particles, but one-dimensional filaments called strings]. Can you tell us a little more about that?

A. I work in differential geometry, with theoretical physics behind it. String theory has a very broad mathematical foundation that seeks to understand the universe, but all of this is done with models that have very complex geometric structures. I study certain high-dimensional spaces.

Q. How is that?

A: I've been doing a lot of research in the seventh dimension, where G2 structures are found, which have unique properties. My goal is to understand these structures more deeply, create clear examples, and solve equations to have more geometric structures to work with. After all, string physics is a theoretical model that can never be demonstrated experimentally.

Q. How do you apply all this knowledge to your classes? What do your students say?

A. I'm an assistant professor, but it's a postdoctoral position, and right now I have to teach three courses a year. I have students of various ages because, being a public university, the range is diverse. It's been a rewarding experience because during the Linear Optimization course, the students were motivated. It's aimed at students of computer, mechanical, and electrical engineering.

Sometimes it's a bit intense because I get several emails with questions, or sometimes they just call to explain that they're sick. You have to dedicate a lot of time to teaching, writing, and marking exams. It's a lot of responsibility.

Q. You also taught at Oxford University. What are the main differences?

A. The groups were small, two or three people. It's a very good system that's also used at Cambridge University. It helps students a lot because you can go step by step, but it requires a lot of resources.

This would be unthinkable in Spain, because there are a limited number of contracted teachers and not much money. From a pedagogical perspective, it's an excellent system.

Q. Have you enjoyed teaching over the years?

A. It's very gratifying when a student's face lights up and says, "I get it now, thank you so much." In the last class I taught, I received several messages of gratitude from students who'd learned a lot and liked the way I taught. It's a way to see a direct impact on people.

Q. And in relation to the limitations in teaching that you mentioned, where do you think there are more glass ceilings ?

A. It's transversal. After all, the mathematics community is international, and I've had to move within several countries because, in part, we're forced to relocate for short-term contracts. Then you can't stay in the same place. I've observed similar traits in the gender gaps.

Q. Have you ever experienced discrimination for being a woman?

A. The gender gap is felt, but in most cases it's more indirect because in mathematics, the number of women will be very small, and that's something that will always be felt. There's a feeling of not belonging.

The classrooms can be hostile, and inappropriate comments can arise that wouldn't be made if there were more gender balance. I haven't had any problems teaching a large class, but at one point, a student spoke to me in a less-than-professional manner. I feel like if I were a 60-year-old man, he wouldn't have spoken to me that way.

Q. Do you think it's crucial to increase the participation of girls, adolescents, and women in these spaces?

A. It would be beneficial, but I think it's important to note that this situation doesn't only exist at younger ages, but extends to contexts like mine. It's important to address this problem at all levels.

Yes, there may be changes depending on the math department. There may be more women in one area, and therefore, you may feel more comfortable. In another area, however, it may be a little more hostile, but I don't think it's a problem for individual countries, but rather a community issue.