Gift link:

https://www.nytimes.com/2026/09/06/science/92-year-old-mathe...

This is a really cool story. Joan Birman is 99 now and her apprentice Vasudha Bharathram, a 15 y/o high school student at the time, is now a graduate student at Princeton, originally accepted on a recommendation letter from Birman. And it all started with an email sent by Bharathram on a whim and Birman's unusual decision to reply.

> Ms. Bharathram sat down, tapping her silver rings on the oak table. Looking back, she’s not sure if the girl who sent that email could have articulated why she did it. She just did it. It is easy to imagine a version of herself, she said, who had never found math. Perhaps if Dr. Birman had not responded, or even if they had not turned out to be neighbors. She hadn’t felt any nerves that first day in the lobby, because there were no stakes that she was aware of.

The just publisher paper ("The Burau representation of the braid group is faithful for n = 4"):

https://arxiv.org/abs/2607.05283

https://archive.ph/T372h

> The paper was “remarkable in many ways,” said Emmanuel Breuillard, a mathematician at the University of Oxford, with a method that built on old theories (some dating to Dr. Birman’s Ph.D) but with new ideas. Dr. Breuillard had been leading an effort to solve the question with the help of an A.I. chatbot. That humans appear to have sorted it out first — and these three particular humans — “almost feels like a blessing,” he said.

Well worth reading!