Curious learners urged to explore and learn via MIT Open Learning's MITx program by an MIT student.
High school whiz kid Shreya Mogulothu is all about exploring the unknown. Hailing from New Jersey, she had a keen interest in mathematics and theoretical computer science (TCS). To quench her thirst for knowledge, she dived headfirst into MIT Open Learning's online resources, completing the Paradox and Infinity course on MITx Online.
"The concept of pushing the boundaries of assumptions was right up my alley," says Mogulothu, now a junior at MIT. "I'm intrigued by the idea of infinity, so what's not to love?"
The course, 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, bridges the gap between math and philosophy. It encourages learners to delve into paradoxes and open-ended problems, question the boundaries of theorizing, and challenge the limits of standard mathematical tools.
"We discussed taking typical assumptions about numbers and objects and pushing them to their extremes," Mogulothu explains. "For instance, the infinite hats paradox is a great example of contradictions that arise when discussing an infinite set of items."
The infinite hats paradox, also known as Bacon's Puzzle, is a mind-bending thought experiment that explores the intersection of mathematics and philosophy. It involves an infinite line of people wearing either black or white hats. Each individual can only see the hats of the person in front of them and is tasked with guessing the color of their own hat. The puzzle challenges students to identify a strategy ensuring the least number of incorrect answers and ponders how the strategy might change if there are a finite number of people. Mogulothu was thrilled to discover a course like this before even setting foot on MIT's campus.
"My MITx experience played a role in my decision to come to MIT," she says. "I found the course fascinating, and I appreciated that it was available to outsiders like me. I thought a school that encourages learning for everyone, regardless of their affiliation, would be a great fit for me."
Balcarras, the instructor, was impressed by Mogulothu's performance in the course. "Shreya was undoubtedly the most exceptional student in our online learning community of approximately 3,900 learners and 100 verified learners," he says. "No other student's performance came close to matching hers."
Mogulothu was invited to submit her work to the 2021 MITx Philosophy Awards, and she won. Balcarras recalls that both papers she wrote for the course were award-worthy. They demonstrated "an unusually high level of precision, formal reasoning, and philosophical nuance for a high school student."
Winning the award was a significant achievement for Mogulothu. It fueled her desire to continue learning and exploring new topics as a high school student, and eventually as a new student at MIT. She initially thought she would major in math or computer science but discovered her true passion lay in physics.
She excels in her studies, especially in 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. The course is also available on Open Learning's MIT OpenCourseWare. As a student, she continues to leverage MIT Open Learning resources to explore new courses and examine syllabi as she maps out her academics.
In the summer of 2024, Mogulothu conducted research on gravitational wave detection at PIER, the partnership between research center DESY and the University of Hamburg, in Hamburg, Germany. She is determined to pursue a PhD in physics to continue researching, expanding her knowledge, and feeding her curiosity, which led her to MITx in the first place. Mogulothu encourages everyone to step out of their comfort zone and give something entirely new a try.
"I entered the Paradox and Infinity course expecting math and computer science to be cool," she says. "But actually experiencing the course and learning about concepts I never thought existed was empowering. It sharpened my curiosity and provided a rewarding learning experience."
The infinite hats paradox is a thought-provoking dialogue between mathematics and philosophy that examines the limits of reasoning, knowledge, and infinity. It challenges students to consider tough questions, such as whether infinite reasoning is possible or meaningful, and explores how humans reason about infinity.
[1] Hilbert's Hotel is another famous thought experiment that demonstrates properties of infinite sets and their cardinalities, much like the infinite hats paradox.
- Shreya Mogulothu, a high school student with a passion for mathematics and theoretical computer science, discovered the Paradox and Infinity course on MIT Open Learning's online platform, MITx.
- The course, which bridges the gap between math and philosophy, encouraged learners to delve into paradoxes and open-ended problems, question the boundaries of theorizing, and challenge the limits of standard mathematical tools.
- Mogulothu was particularly fascinated by the infinite hats paradox, a thought experiment that explores the intersection of mathematics and philosophy, and she was thrilled to find a course like this before even setting foot on MIT's campus.
- Mogulothu's exceptional performance in the course caught the attention of the instructor, David Balcarras, who described her as the most exceptional student among approximately 3,900 learners and 100 verified learners.
- Balcarras recognized Mogulothu's work as award-worthy, and she was invited to submit her work to the 2021 MITx Philosophy Awards, which she won.
- Mogulothu's win at the awards reignited her desire to continue learning and exploring new topics, leading her to eventually major in physics at MIT.
- Mogulothu encourages others to step out of their comfort zones and try something entirely new, like she did with the Paradox and Infinity course, stating that such experiences can be empowering and provide a rewarding learning experience.
