Last week, I had the pleasure of having my first article in Quanta come out, one of the science journalism outlets that I have admired the most over the last several years. In my article, I told the story of a remarkable discovery made by three elite mathematicians in 2019 and late 2020.
The question they investigated initially seemed to me to be technical, esoteric. But once I managed to shake off my hangups, my compulsive cataloging of every caveat, I came to realize their objective as incredibly elegant, and quintessentially mathematical, illuminating a concept that seems totally general but also completely specific, at the same time. Their question was this: Given any shape, how much must you roughen its surface before it can collapse?
We’re all familiar with shapes like the accordion, which are crushable *only* thanks to the fact that they are made up out of repeating ridges. Those ridges mean that the surface is rough, and you can quantify that roughness if you study it. But as it turns out, a shape need not be so rough as an accordion’s for it to be compatible with being crushed. It can actually be rather smooth.
Core to these ideas were the seminal results proved by John Nash, the brilliant mathematician made famous by the movie “A Beautiful Mind,” based off Sylvia Nassar’s book. Nash showed that you can crush something like a piece of paper into a ball not by creasing it, but rather, by bending it, corrugating it, reshaping it all over its surface with springs. These springy, corrugated surfaces invented by Nash are less rough than an accordion’s, but nor are they totally smooth.
Later, other mathematicians showed that you could make a surface a little bit smoother than Nash’s, and *still* crumple it. On the other hand, it had earlier been discovered that at a certain point, as you restrict yourself to bending a surface more and more gently, covering it with fewer and fewer corrugations, it becomes rigid. In other words, force a shape to stay smooth enough and it will no longer give way.
With a few important caveats, mathematicians have now discovered *exactly* when you get to the point where a shape is rough enough that it becomes floppy and flexible. There is still much for mathematicians to prove, but a large part of their epic work on the question is now done.
Writing this story was a trip for me as a writer … It required me to go through a serious writing growth spurt, with all the excruciating pain that that entails. It has never been more clear to me how having expertise in a subject makes it harder to tell a story to those who have none. The writing process was an emotional battle which I am undoubtedly still recovering from.
In any case, it’s all done now, and I’m on to what’s next, while I can. If you wind up reading, then I hope you’ll enjoy—or at least find the journey a little less painful than mine was. 🙂