Inspiring Women in STEM – Celia Rubio Madrigal

The Heidelberg Laureate Forum has a single purpose: To provide some of the brightest minds in mathematics and computer science with the space and time to make connections and find inspiration. The HLFF Spotlight series shines a light on some of the brilliant young researchers attending the event, their background and research as well as their expectations for the HLF.

Celia Rubio Madrigal is a graduate in mathematics and computer science of the Universidad Complutense de Madrid in Spain, where she just completed a five-year double degree program. Motivated to work at the intersection of the two fields, she will continue to study at the University of Strathclyde in Glasgow in the Master’s program of Advanced Computer Science with Artificial Intelligence. In the interview, she describes her research projects, motivation and why she wants to be a role model for younger girls studying STEM fields.

Celia Rubio Madrigal is attending the 9th HLF in September 2022. Image Credits: Celia Rubo Madrigal

What motivated you to go into the fields of mathematics and computer science?
A main motivation for studying mathematics and physics was my father, who is a physicist. However, I did not meet the cut-off marks for physics and was placed in my second option. At first, it was honestly dramatic because I couldn’t imagine becoming a computer scientist at that point. When I discovered competitive programming, everything changed. My first-year C++ teacher, Isabel, helped me become confident at coding and promised I could travel abroad for contests if I kept practicing. This year, the promise was fulfilled, as I was able to participate in the South-Western European Regional Contest (SWERC) in Milan. My personal moral of the story is that you never really know what is for you until you learn about it. Not every rejection is a failure: sometimes, it is a brand-new opportunity.

Which research questions did you work on for your two Bachelor’s theses?
As I enjoy theoretical research on very hard questions such as the P vs. NP problem, one of the Millennium Problems, I chose to work on computational complexity for both degrees. Specifically, we are studying how to identify Boolean functions that can only be computed by big circuits, meaning with a large number of gates.
For the thesis in computer science, we used a dataset of 4 million functions as inputs for neural network training sessions. The functions were labeled according to their minimum circuit size. We wanted to understand if and how neural networks acquire enough knowledge to classify them with very high accuracy: some of them, on average, reached 99% without barely requiring any adjusting. For the thesis in mathematics, we proposed some definitions that could help find functions with super-polynomial circuits, based on the concepts of repetitiveness and endogamy. Also, we presented a potentially useful method to construct lower bounds on the size of some functions’ circuits by restricting their inputs to raise incompatibilities in their gates.

Which are the most intriguing research challenges in your field you would like to tackle in the future?
To me, the most interesting questions are the ones that no one can imagine the first approach to. The possibilities are endless: nobody can tell you which angle to start from. I enjoyed studying complexity theory and would like to thank my supervisors and mentors Ismael, Daniel, and Narciso, who sparked my motivation for research. I like topics that can cover a wide range of fields and require interdisciplinarity, which is the reason I chose to study AI for my Master’s. So, I am looking forward to finding new and exciting challenges in this research area. In general, abstraction fascinates me, such as tackling a practical topic like machine learning from a theoretical point of view. This could be done, for example, by applying mathematical research such as topology or category theory to computer science concepts such as neural networks. Here, I got inspired by my supervisor David Martín during a research stay at the Institute of Mathematical Sciences (ICMAT).

You also apply mathematics to musical theory as a hobby. What is that project about and what is your personal connection to music?
I started playing the Baroque recorder when I was six and studied it for ten years. After that, I started singing opera in my free time. As a requirement to earn the Baccalaureate of Excellence, I needed to write a research essay and chose music as my topic. I decided to formalize dodecaphonism, also called the twelve-tone music system, which is a composition method that uses permutations of the twelve notes of the chromatic scale. During my undergraduate studies, I realized I could apply the freshly learned concepts to this line of research. Hence, I used group theory to generalize the twelve-tone music system. To give an example: the note permutations can suffer some transformations – transposition, retrograde, inversion, and cyclic rotation – corresponding to the elements of D₁₂ x D₁₂ acting on that row. By chance, I met Paco, a fellow recorder player responsible for the “Music and Mathematics” column on the online journal divulgaMAT. I asked him to read my work and we turned it into a series of four articles published in 2019. 

Why do you think there are still not many women deciding to go into STEM and what is your experience as a woman in this field?
I have loved math since I was a child and always knew I wanted to be a mathematician, especially since my parents created a great environment to learn. However, during high school I started having doubts and believed I wasn’t smart enough to become a mathematician. However, in my last year of high school I had the great opportunity to become a member of the Spanish team at the European Girls’ Mathematical Olympiad (EGMO). It was a great way to recover my math self-esteem and meet girls like me in a comfortable environment. After high school, I volunteered in math contests as a jury member and guide. This year, I took part in the EGMO again as the team’s Deputy Leader serving as a mentor for the Spanish contestants, and saw that many of the young girls had similar experiences with mathematics to mine.

How can we promote women’s success in the fields of computer science and mathematics?
There are many stereotypes associated with STEM careers that many girls can’t identify themselves with. This could make them believe they don’t fit into that field. Also, sometimes young women are not confident enough in spaces where they feel like outliers, which further exacerbates the already present structural difficulties. Therefore, it is important to show examples of people and to have role models that they can identify with. To boost women’s confidence, we need to create safe spaces where they can feel comfortable. They need to be able to see that they can not only participate in STEM but – most importantly – also succeed. For that, they need to be given an initial chance to start loving the discipline.

What do you expect from the 9th HLF and who are you looking forward to meeting the most?
I have already been to Heidelberg and found it exceptionally charming, so I am delighted to be back. However, what thrills me the most is the possibility of meeting and talking to laureates I deeply admire for their work. I am lucky because many of the laureates are experts in the field I have studied. For example, Stephen Cook and Richard Karp introduced and laid the basis for the P vs. NP problem. Sanjeev Arora co-wrote the well-known book I cited the most in my theses. I am sure it will be a fantastic experience.

More inspirational stories are to come in the HLFF Spotlight series, so stay tuned.