“Nadie te quita lo bailado.” (No one can take from you what you’ve danced.)

For Federico Ardila, this Latin American expression epitomizes his approach to life and mathematics. It’s the driving force behind the parties he DJs in venues across the San Francisco Bay Area, where people dance till morning to the beats of his native Colombia. The dance floor is a place “where you have your freedom and you have your power, and nobody can take that away from you,” Ardila said.

He taught the expression to his students at San Francisco State University, where he is a math professor, after giving them a punishingly hard exam. San Francisco State has a highly diverse student body, and Ardila, who just turned 40, is a prominent voice in the mathematics community about how to make students from underrepresented groups — such as women and people of color — feel that they belong. But on this occasion, as he looked around at his students’ demoralized faces, he knew he had missed the mark.

“Nadie te quita lo bailado,” Ardila told his students.

“I think that’s a very powerful message — that nobody can take away from you the joy that you’ve had doing mathematics,” he told Quanta Magazine in an interview last month. “And people can give you grades, but that’s not going to take away the freedom that you felt and the fulfillment that you felt.”

The expression also applies to Ardila’s research, though not always in ways he would have chosen. Four years ago in Portland, Oregon, a thief smashed his car window and made off with a backpack containing, as luck would have it, five years’ worth of work — all of Ardila’s notes from a sweeping new paper he was developing. Proofs, examples, counterexamples and conjectures were all gone.

But the thief couldn’t steal the mathematics Ardila had “danced” in his mind. Over the past few years, Ardila and his coauthor, Marcelo Aguiar of Cornell University, have painstakingly reconstructed their work unifying the geometric and algebraic sides of combinatorics — the study of discrete structures like a social network, a sudoku puzzle or a phylogenetic tree. They finally posted their 113-page paper online in September, and in January Ardila will be presenting their work in an invited address at the Joint Mathematics Meetings, the biggest annual math conference in the United States.

Quanta spoke with Ardila at the Mathematical Sciences Research Institute in Berkeley, California, where he is visiting for the fall semester, about the mathematics he has danced and taught. The interview has been condensed and edited for clarity.

Your mathematical talent was identified quite early — in fourth grade, you got the highest score in your age group in a national math competition in Colombia.

It was actually my sister, Natalia, who first showed great promise in mathematics. I was just the little brother. She and my cousin Ana María, they both performed really, really well in this national math competition. And I think the organizers probably said, “OK, these two women are very good, and then here’s the little brother who’s coming along to the awards ceremony. Maybe he’s OK also.”

I feel like from a young age, they were paying attention to me. I never enjoyed mathematics in school very much, but my experience through the Math Olympics was much more creative and much more playful.

And it turned out that it was, as many of these spaces are, a very male-dominated space, and eventually both my sister and my cousin felt uncomfortable with this space. I mean, they’re doing amazing things now; my cousin is an engineer and my sister is a music pedagogy professor. But I do think it’s kind of interesting — that was a space where I felt very comfortable and that felt very nurturing to me, and it didn’t feel so to other people. It was a space that was very “othering” for them. I think that’s always served to remind me of the role of a mathematician, of an educator, in curating the culture of a place. That’s why that’s been such a theme in my work.

You’ve said that you were surprised to get into the Massachusetts Institute of Technology, where you did your undergraduate and doctoral studies. What’s the story there?

I had never heard of MIT. And it hadn’t crossed my mind to study abroad. I was already enrolled in the local university. But my classmate told me MIT had awesome financial aid and said the math there was really good. I wanted to learn more math, so I decided to play along and apply.

At that moment I was failing most of my classes in high school. It was not clear that I was going to graduate. I had a little bit of an attitude problem. I was very interested in a lot of things but I did not like being told, “Read this” or “Think this way.” I just kind of wanted to do things on my own terms.

I was failing, I think, six out of eight subjects. Had I known what MIT was, I should have known not to apply. There is no way I should have applied with that kind of transcript.

I like telling this story to my students because I think we often close doors to ourselves by thinking that we’re not eligible or that we’re not good enough. And especially if you’re somebody who feels “othered” in your discipline or who feels like you’re lacking confidence, it’s easy to close doors on yourself. There’s a lot of people in life who are ready to close doors for you, so you can’t do it for yourself.

When you came to the United States, as an undergraduate at MIT, it was your turn to feel like the “other.”

It’s not that anybody did anything to mistreat me or to doubt me or to explicitly make me feel unwelcome, but I definitely felt very different. I mean, my mathematical education was outstanding and I had fantastic access to professors and really interesting material, but I only realized in retrospect that I was extremely isolated.

There’s a system in place that makes certain people comfortable and others uncomfortable, I think just by the nature of who’s in the space. And I say that without wanting to point fingers, because I think you can be critical about the spaces that “other” you, but you also have to be critical about the ways in which you “other” other people.

I think because mathematics sees itself as very objective, we think we can just say, “Well, logically, this seems to make sense that we’re doing everything correctly.” I think sometimes we’re a little bit oblivious as to what is the culture of a place, or who feels welcome, or what are we doing to make them feel welcome?

So when I try to create mathematical spaces, I try to be very mindful of letting people be their full human selves. And I hope that will give people more access to tools and opportunities.