| Until a little over a year ago, I was an experimental physicist. I used math all the time, so you might expect that becoming a math journalist would be well within my comfort zone. In many ways that's true. But in others, my new intellectual home planet feels like an alien world.
In my former life, I studied physical objects and measurable phenomena. Math was a bag of tools that allowed me to do this. I used to laugh at my theorist friends who, instead of telling me what they'd been "working on" recently, would tell me what they'd been "thinking about." It conjured images of these friends reclining at their desk all day, head tilted back, eyes squinting at the ceiling, mind somewhere in the stratosphere. Now everyone I interview talks about their research in the same way.
The kind of math that mathematicians focus on is very different from the tool kit I used as a physicist. Their work is driven deeply by human notions of beauty and abstraction, and is all about pushing pure logic to its limit. Experiments and observations can help guide mathematicians' understanding, but ultimately, they don't accept something as mathematically true until they can craft a rigorous argument that proves it. As one mathematician recently assured me, "There's no rigorous proof that somebody cannot live more than a thousand years. It's only an empirical fact."
This emphasis on rigor sometimes leads to proofs of seemingly impossible phenomena. The Banach-Tarski paradox, for instance, says that you can break one ball into pieces and use it to create two balls that are identical to the original. To my physics brain, this sounds like creating matter from nothing, but it's mathematically true, beyond any doubt — and also beautiful.
I appreciate this rigorous way of thinking. One thing I don't miss about physics is the unsteady theoretical ground you're often standing on when trying to follow a lecture or a paper. Math is so sturdy, so devoid of hand-waving. In a way, mathematical truth is made of more solid stuff than the steel bolts on a vacuum flange I used to spend my days tightening.
Mathematical thinking might seem excessively demanding, but it's important. As both an art and a science, it showcases the power of human creativity while also unraveling the mysteries of the world around us. It even has all sorts of practical applications: Mathematical abstractions that were once seen as useless now play a crucial role in cryptography, chemistry, engineering, machine learning and more. But at its core, math is about exploration, discovery, beauty and understanding.
Here are some of Quanta's math stories from 2024 that helped me settle into this new world, often by challenging what I thought I knew math to be.
Stories That Changed How I Think About Math
A lot of my sense of what math is all about and how its practitioners think came from reading Quanta's explainers and Q&As. If you had asked me a year ago how to properly define the square root of 2, I would have been confused — it's the number that, when you multiply it by itself, equals 2! But after reading Jordana Cepelewicz's explainer, I see how mathematicians need to define everything, including numbers, concretely in terms of well-established axioms and theorems. Thus the square root of 2 required a more rigorous definition.
I've often heard Galileo's statement that the universe "is written in the language of mathematics," but I hadn't considered that distinct mathematical languages can describe the same universe until I read this Q&A with Claire Voisin. She explains how mathematicians are always working to translate between different mathematical languages — between, say, the language of algebra and the language of geometry — to gain new insights. Physicists often use different descriptions to try to understand the same fundamental reality, the idea being that no one description is more "real" than another. I never imagined the language of math could work the same way.
During my days as a physicist, I was usually stuck in three dimensions (not including time). Unbounded by the limitations of physical reality, mathematicians get to soar through higher planes filled with objects beyond even their own comprehension. They can only feel around the edges of these shapes, often by looking at simpler, lower-dimensional shapes embedded within them. This year, mathematicians found weirder and richer embeddings than they previously thought possible, showing that the 4D world is even stranger than they knew.
One 2024 math news story really captured my heart, partly because I'm an avid birder, but also because it shows how mathematics, like the other sciences, is full of accidental discoveries. Lyndie Chiou reported earlier this year on mysterious mathematical patterns called murmurations, named for how the patterns resemble the gorgeous wavelike ripples that form in flocks of soaring starlings. The pattern was discovered by an undergraduate student named Alexey Pozdnyakov when he used a public database of equations to plot a graph that would never occur to a veteran number theorist. The strange ripples he saw in this graph, far from being limited to these equations, have since proved ubiquitous in number theory and beyond. At a recent workshop I attended on the subject at Stony Brook University, the number theorist Andrew Sutherland of the Massachusetts Institute of Technology showed Pozdnyakov's plot and compared it to "when they found mold in the petri dish to discover penicillin."
Thanks to these stories, I've got my math legs (somewhat) steady below me, and I can't wait to see what new breakthroughs 2025 has in store. |
