Shreya Mogrotu was born curious. As a high school student in New Jersey, she developed an interest in mathematics and theoretical computer science (TCS). Her curiosity led her to want to learn more, so she turned to online resources from MIT Open Learning and completed the MITx Online Paradox and Infinity course.
“Coming from a background in mathematics and TCS, the idea of pushing the limits of assumptions is really exciting to me,” said Mogrotou, now a third-year student at MIT. “I mean, who doesn’t want to know more about infinity?”
The class, taught by Agustin Rayo, professor of philosophy and current dean of the School of Humanities, Arts, and Social Sciences, and David Barcaras, a former philosophy lecturer and member of Open Learning’s Digital Learning Lab, explores the relationship between mathematics and philosophy, challenging students to think about paradoxes, unsolved problems, the limits of theorizing, and the limitations of standard mathematical tools.
“We talked about taking normal assumptions about numbers and objects and pushing them to their extremes,” Mogrotou said. “What contradictions arise when we talk about infinite sets, like the infinite exponent paradox, for example?”
The infinite hats paradox, also known as Bacon’s puzzle, involves an infinite line of people wearing two hats, one of each color. In this puzzle, each person can only see the hat of the person in front of them and must guess the color of their own hat. The puzzle asks students to determine if there is a strategy that can guarantee the fewest number of wrong answers and to consider how strategies change when there are limited numbers. Mogrotu is excited to have this class, even though she is not yet affiliated with MIT.
” My experience with MITx was one of the reasons I came to MIT,” she says. “I really enjoyed the course, and I’m glad it’s being shared with people like me who never studied at school. I think a place like that where you can be encouraged by people outside of school is a great place to study.”
Reflecting on the course, Balkaras says, “Shreya is perhaps the most impressive student in our online community of about 3,900 students and 100 verified students. No one else has achieved as much as she has.”
Mogrotu’s outstanding performance led to him being invited to submit his work for the 2021 MITx Philosophy Prize , which he won. In fact, Barcaras recalled that both of the papers he wrote in the course won prizes. He said they showed “unusual precision, formal insight, and philosophical sophistication for high school students.”
Completing the course and winning the prize was a reward, Mogrotu said, and it motivated her to keep exploring new things, both as a high school student and then as a freshman at MIT.
She went to college thinking she would major in math or computer science, but after considering what subjects interested her most, she realized she should major in physics.
She enjoyed her major, especially STS.042J/8.225J (Einstein, Oppenheimer, Feynman: 20th Century Physics) taught by Germeshausen Professor of the History of Science and Professor of Physics David Kaiser. She took the course on campus, but it is also available on Open Learning through MIT OpenCourseWare. As a student, she continues to use MIT Open Learning resources to take courses, explore curriculum, and plan her coursework.
In the summer of 2024, Mogrotou will be working on gravitational wave detection at PIER, a partnership between the DESY research center and the University of Hamburg in Hamburg, Germany. She hopes to complete a PhD in physics to continue her research, broaden her horizons, and satisfy the curiosity that broughther to MITx in the first place . She encourages all learners to feel comfortable and confident in trying something completely new.
“I went into Paradox and Infinity thinking, ‘Yeah, math is cool, computer science is cool,'” she says, “but it’s really amazing to take courses and learn things you didn’t even know existed. It makes you more curious and it’s incredibly rewarding to work on something and realize how much you can learn and grow.”
