At the age of 92, Joan Birman, a retired professor of mathematics from Columbia University, found herself reinvigorated by an unexpected request from a high school student eager to explore mathematics beyond the classroom. In the summer of 2019, after receiving an email from a teenager expressing interest in understanding genuine mathematical proofs, Dr. Birman reconsidered her initial reluctance to take on what she had long viewed as routine mentoring.
The student, Vasudha Bharathram, had recently turned 15 and was a rising sophomore at Riverdale Country School in the Bronx. Having moved from India two years earlier, Bharathram lived just blocks from Birman’s Manhattan apartment on Riverside Drive. Their proximity allowed for in-person meetings that began in the lobby of Birman’s co-op building, where the two mathematicians would discuss foundational topics and work through challenging problems.
Birman, whose expertise lies in topology—a branch of mathematics focused on properties of space that are preserved under continuous deformations—introduced Bharathram to the concept of braids, a central object in her field. She assigned chapters from I.N. Herstein’s “Topics in Algebra,” a text known for its rigor and complexity, often reserved for graduate students.
To Birman’s surprise, Bharathram responded promptly with detailed photographic submissions of her handwritten solutions. Although the teenager’s notes were cursory and at times difficult to read, they revealed an unusual depth of insight and originality in problem-solving. Birman noted the adolescent’s willingness to explore unconventional approaches to proofs, which impressed the seasoned mathematician.
Their continued collaboration evolved beyond textbook exercises as Birman identified a long-standing problem in topology that had eluded her for decades and began working through it with Bharathram. The partnership highlights the potential for intergenerational mentorship in mathematics, demonstrating that rigorous academic inquiry can flourish outside traditional institutional settings.
Following the passing of her husband Joseph Birman in 2017, Joan Birman moved from New Rochelle back to Manhattan to remain close to Columbia and the mathematical community. This proximity—and a renewed enthusiasm sparked by Bharathram’s earnest appeal—enabled her to continue contributing to mathematical research well into her ninth decade.
The relationship between Birman and Bharathram underscores how early encouragement and access to advanced mathematical concepts can inspire young talent. It also illustrates the enduring role of experienced mathematicians in nurturing the next generation, offering guidance that extends from classical algebra to the frontiers of topology.