Gregory BarberSep 10, 2026 – 5.00amIt was a kind of note that Joan Birman had received many times: a plea from a high school student, asking for help learning mathematics.After enjoying freshman geometry class, the student wrote, she had recently read her first real mathematical proof. It made her think there might be something more to math than what she was learning in school. Perhaps Birman could show her what she was missing.Subscribe to gift this articleGift 5 articles to anyone you choose each month when you subscribe.Subscribe nowAlready a subscriber? Fetching latest articles
The 92-year-old mathematician and the teenage apprentice
The unlikely pairing spent years working toward a proof, an arduous task that defined a knotty problem.
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