Aging Excerpt

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The World Is a Room With a Piano Waiting to Be Played by Roger Rosenblatt
Mr. Rosenblatt is the author of a new book, “More Rules for Aging.”

The older I get, the more I appreciate the wonders around me. I’m not just talking about nature’s extravagances — zebras, cuttlefish, dragon flies, octopuses, though they do still amaze — but rather the wonder attached to the everyday things a younger me might have not paid much notice to, the happy social interactions, coincidences and surprises that counteract all the sorrows and horrors, and say by their existence, we too are life, maybe most of it.

Perhaps the mundane becomes more wondrous as we age partly because we move slower. We are more careful. Each step we take becomes fascinating, an object of exquisite study, not only because the stability of your body rides on it, but also because it takes on a disembodied life of its own.

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Mathematical artistry excerpt

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The 92-Year-Old Mathematician and the Teenage Apprentice by  Gregory Barber

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It 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 Dr. Birman could show her what she was missing.

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There was a knock on the door, and Ms. Bharathram walked in. The child who first visited this apartment seven years ago was gone, replaced by (as Dr. Birman had proudly put it, out of her earshot) “a tall, elegant woman” starting her first year of graduate school. She was headed to Philadelphia for the International Congress of Mathematicians, and she had only a few hours to spare before her train. Dr. Birman would be going too, she said, if she weren’t still figuring out the wheelchair.

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The paper [a proposed solution by the teacher, student, and another professor] 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.