At 92, a mathematician found an apprentice and a problem to solve

At 92, Joan Birman had little interest in becoming a high-school student’s babysitter. But when Vasudha Bharathram wrote asking for help with mathematics, Birman sensed that the teenager genuinely wanted to learn.

The emails were familiar. Birman had received similar messages throughout her career, including after retiring from Columbia University in 2004. This one arrived in the summer of 2019, when she was living alone in New Rochelle after the death of her husband, Joseph, two years earlier. She had decided to move back to New York, choosing an apartment on Riverside Drive so she would remain close to the Columbia office she still kept and to mathematical conversation.

Bharathram’s message stood out. She had enjoyed her first-year geometry class and had recently read her first real mathematical proof. It made her wonder whether mathematics offered more than what she encountered at school. After thinking it over, Birman agreed to meet her and told her to find a copy of I. N. Herstein’s Topics in Algebra, a famously punishing text for aspiring graduate students.

Bharathram arrived that July at Birman’s postwar cooperative on Manhattan’s Upper West Side. She had just turned 15 and was about to begin her second year at Riverdale Country School in the Bronx. Her family also lived nearby, only ten blocks away. Birman asked about her move from India two years earlier and what she liked about school geometry.

Birman explained that her field was topology, which also studies shapes but treats them as fluid and elastic rather than fixed by rigid coordinates. She drew a braid with a pencil, twisting like the hairstyle, and sent the student home with a chapter to read.

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She still hadn’t had her growth spurt.