Shreya Mogulothu is naturally curious. As a high school student in New Jersey, she was interested in mathematics and theoretical computer science (TCS). So, when her curiosity compelled her to learn more, she turned to MIT Open Learning’s online resources and completed the Paradox and Infinity course on MITx Online.
“Coming from a math and TCS background, the idea of pushing against the limits of assumptions was really interesting,” says Mogulothu, now a junior at MIT. “I mean, who wouldn’t want to learn more about infinity?”
The class, taught by Agustín Rayo, professor of philosophy and the current dean of the School of Humanities, Arts, and Social Sciences, and David Balcarras, a former instructor in philosophy and fellow in the Digital Learning Lab at Open Learning, explores the intersection of math and philosophy and guides learners through thinking about paradoxes and open-ended problems, as well as the boundaries of theorizing and the limits of standard mathematical tools.
“We talked about taking regular assumptions about numbers and objects and pushing them to extremes,” Mogulothu says. “For example, what contradictions arise when you talk about an infinite set of things, like the infinite hats paradox?”
The infinite hats paradox, also known as Bacon’s Puzzle, involves an infinite line of people, each wearing one of two colors of hats. The puzzle posits that each individual can see only the hat of the person in front of them and must guess the color of their own hat. The puzzle challenges students to identify if there is a strategy that can ensure the least number of incorrect answers and to consider how strategy may change if there is a finite number of people. Mogulothu was thrilled that a class like this was available to her even though she wasn’t yet affiliated with MIT.
“My MITx experience was one of the reasons I came to MIT,” she says. “I really liked the course, and I was happy it was shared with people like me, who didn’t even go to the school. I thought that a place that encouraged even people outside of campus to learn like that would be a pretty good place to study.”
Looking back at the course, Balcarras says, “Shreya may have been the most impressive student in our online community of approximately 3,900 learners and 100 verified learners. I cannot single out another student whose performance rivaled hers.”
Because of her excellent performance, Mogulothu was invited to submit her work to the 2021 MITx Philosophy Awards. She won. In fact, Balcarras remembers, both papers she wrote for the course would have won. They demonstrated, he says, “an unusually high degree of precision, formal acumen, and philosophical subtlety for a high school student.”
Completing the course and winning the award was rewarding, Mogulothu says. It motivated her to keep exploring new things as a high school student, and then as a new student enrolled at MIT.
She came to college thinking she would declare a major in math or computer science. But when she looked at the courses she was most interested in, she realized she should pursue a physics major.
She has enjoyed the courses in her major, especially class STS.042J/8.225J (Einstein, Oppenheimer, Feynman: Physics in the 20th Century), taught by David Kaiser, the Germeshausen Professor of the History of Science and professor of physics. She took the course on campus, but it is also available on Open Learning’s MIT OpenCourseWare. As a student, she continues to use MIT Open Learning resources to check out courses and review syllabi as she plans her coursework.
In summer 2024, Mogulothu did research on gravitational wave detection at PIER, the partnership between research center DESY and the University of Hamburg, in Hamburg, Germany. She wants to pursue a PhD in physics to keep researching, expanding her mind, and indulging the curiosity that led her to MITx in the first place. She encourages all learners to feel comfortable and confident trying something entirely new.
“I went into the Paradox and Infinity course thinking, ‘yeah, math is cool, computer science is cool,’” she says. “But, actually taking the course and learning about things you don’t even expect to exist is really powerful. It increases your curiosity and is super rewarding to stick with something and realize how much you can learn and grow.”