The Year in Mathematics

Carlos Arrojo for Quanta Magazine At 17, Hannah Cairo Solved a Major Math Mystery At 17, Hannah Cairo Solved a Major Math Mystery Mathematics is, at its core, an art. Like painters, musicians or writers, mathematicians create and explore new worlds. They test, and then push past, the limits of their imagination. They engage with thousands of years of history, with concepts and tastes and fashions that are constantly in flux. This artistic pursuit of beauty, truth and meaning is what every Quanta math story is about, to some extent. This was on full display in one of my favorite articles of the year, an account by Kevin Hartnett of how a mathematician named Hannah Cairo solved an important problem in the field of harmonic analysis - at just 17 years old. Cairo grew up in the Bahamas, where she was homeschooled, learning math by watching Khan Academy videos and consuming everything else she could find online. She found the homeschooling experience overwhelmingly lonely and confining. “There was this inescapable sameness,” she told Hartnett. “No matter what I did, I was in the same place doing mostly the same things. I was very isolated, and nothing I could do could really change that.” Except studying math. Math gave her the escape she needed, an entire universe to roam - in Cairo’s words, a “world of ideas that I can explore on my own.” It’s impossible not to see math as art here: a way of experimenting with new ideas, of grappling with a world that doesn’t always make sense. And, crucially, of questioning assumptions. As a teenager, Cairo moved to California, where she took graduate-level classes at the University of California, Berkeley and encountered a 40-year-old conjecture about the behavior of functions. After several months of persistent work, she constructed a counterexample to the conjecture that more seasoned mathematicians had missed. Just as art is so frequently inextricable from the artist who makes it, Cairo was uniquely positioned to formulate a fresh perspective on the functions she was studying, which allowed her to show that they can behave in more counterintuitive ways than mathematicians had imagined. That’s often what success in math is all about. Wei-An Jin for Quanta Magazine ‘Ten Martini’ Proof Uses Number Theory To Explain Quantum Fractals ‘Ten Martini’ Proof Uses Number Theory To Explain Quantum Fractals Math is also beautiful and strange. I remember when I first heard about the solution to the “ten martini problem” - a result about how the energy levels of electrons can form a well-known fractal pattern called the Cantor set - I was floored. It brought to mind Eugene Wigner’s famous essay on the “ unreasonable effectiveness of mathematics ,” which examines how abstract math often mysteriously provides the perfect language for understanding the natural world. For the Cantor set to rear its head in solutions to Schrödinger’s equation in quantum physics, for it to be able to give insights into how electrons in a crystal behave when placed near...

Preview: ~500 words