“Ximena Catepillán, Mathematical Ambassador to the Americas”
by: Daniel Coxson (Richard Montgomery High School)
Interviewee: Ximena Catepillán (Millersville University)
At 4 AM, they headed up the mountain. The archaeologists, mathematicians, and various other experts had to get to the top of Machu Picchu before the Sun, taking hours of trekking and setting up equipment in the pitch-black night. Ximena Catepillán set up her station, poised to track the Sun’s course over the various structures nestled in the mountains.
Ximena Catepillán was born in Chile, coming from a family descended from the Huilliche natives. Her father and grandfather were both engineers, so math ran in her blood. In her own words, she had loved math since she “first noticed numbers”. She credits her years at an all-girls school with her attachment with math, as the female students were given the attention that is normally given to boys in math classes. Growing up, Dr. Catepillán was also especially interested in her native ancestry. These two factors, math and native ancestry, combined to grow her fascination with the systems of pre-Columbian math.
Later, when Dr. Catepillán was studying math at the Pontifical Catholic University of Valparaiso, a Peace Corps math professor arrived at the school. He took a small group of students to the capital, Santiago. Dr. Catepillán almost immediately became interested in this professor, amazed that he could travel the world for conferences and teach at any time of the day, which she credits as the moment she realized that she wanted to be a math professor.
Her first teaching job was at the University of Chile in Osorno. From there, she transferred to the University of Magallanes, the southernmost university in the world at the time. After ten years, she moved to the United States for her Ph.D. and began teaching at Millersville University, near Lancaster, Pennsylvania, in 1991.
Two years after she arrived, the African American Studies Minor was created at the university. Since Dr. Catepillán was one of two minorities in the math department, the university asked her to make a math course for the minor. It was then that she created Millersville University’s Mathematics in Non-European Cultures course, a class on ethnomathematics. Ethnomathematics is the study of the relationship between culture and mathematics. It interested the students so much that the class would fill up within hours of registration opening and be offered every semester. Non-math and science students, no matter what their major or minor was, flooded in to take the class.
The popularity of the course led Dr. Catepillán to make an ethnomathematics seminar for freshman students who had not decided on a major. In the seminar, she focused on the Math of the Pre-Columbian Americas, which had always been a particular passion of hers. This seminar was immensely popular as well. Dr. Catepillán went on to co-author a textbook for the course, Mathematics in a Sample of Cultures, now in its second edition. Dr. Catepillán’s dream of displaying the diversity of mathematics was coming true.
As if that wasn’t impressive enough, Dr. Catepillán began to travel overseas during her summers to research historical mathematics with teams of archaeologists and mathematicians. On Easter Island, she worked with a team with drones and studied the elliptical bases of some of the ancient indigenous houses. Another summer, she traveled a week on the Rio Negro, visiting indigenous communities to document their mathematical systems. In Peru, she studied Incan architecture and how it aligned with the position of the Sun at different times of the year in addition to visiting indigenous schools. Dr. Catepillán already has plans to bring her research to Cambodia, where her team will continue studying the zenith passage in the structures at Angkor Wat. Dr. Catepillán is interested in visiting the site with the oldest Khmer inscription of the number zero, that dates from 605, in Sambor, Cambodia.
From 2006 onward, Dr. Catepillán would bring her students on overseas trips as part of the class, often to the Yucatan Peninsula. They would learn about Mayan culture alongside volunteering at local schools.
Dr. Catepillán retired in 2020, but she continues to expand the ethnomathematics course and travel for research. She has even continued to teach. After she retired, Dr. Catepillán taught a graduate ethnomathematics course back in Santiago, so she translated all of the course material and has taught the course in Spanish. She hopes that in the future more courses on ethnomathematics will be made accessible in Chile and around the world in a similar manner. Thanks to these contributions and all of the inspiring work she has done, Dr. Catepillán was elected the Chair of the History of Mathematics Special Interest Group of the Mathematical Association of America (HOM-SIGMAA). Through all of these efforts, Dr. Catepillán continues to grow her impressive mathematical career.
Dr. Catepillán’s advice to students considering a career in mathematics is to simply enjoy it and push forward. She would especially like to “see more girls pursuing mathematics” because girls are often discouraged by the extra attention paid to male students. As a result, they are not often able to prove that they are just as capable, which Dr. Catepillán wants to change in the future. In her own words, “Anybody can do this, just put enough effort in,” and it is this principle of effort that is woven throughout Dr. Catepillán’s career. Dr. Catepillán has devoted decades of tireless work to pursue her passion, crossing mountains and even continents in the process, always providing invaluable access to the lesser-known corners of mathematics’ rich history.
 Catepillán, X., Szymanski, W., and Cardwell, A. Mathematics in a Sample of Cultures. Kendall Hunt, 2021.