Early in his new book, physics historian Graham Farmelo quotes Nima Arkani-Hamed, a theoretical physicist at the Institute for Advanced Study (IAS) in Princeton, N.J.: “We can eavesdrop on nature not only by paying attention to experiments but also by trying to understand how their results can be explained with the deepest mathematics. You could say that the universe speaks to us in numbers.” Relax, he doesn't mean numerology.
That quote provides the book's title: The Universe Speaks in Numbers. Of course, there's a subtitle, too: How Modern Math Reveals Nature's Deepest Secrets. The book also deals with the thorny question of whether the revelations of math truly are nature's deepest secrets or whether they're merely some secrets that we can glimpse via math. That discussion can lead to physics conference fistfights.
The IAS hosted a symposium on Farmelo's subject on May 29. In brief opening remarks, IAS director Robbert Dijkgraaf said, “There are many anecdotes about the relationship between physics and mathematics.” He then quoted Richard Feynman—“not known as a lover of abstract mathematics”—as having said, “‘If all mathematics disappeared today, physics would be set back exactly one week.’” After the laughs (possibly from only the physicists and not the mathematicians in the audience) subsided, Dijkgraaf continued: “Sir Michael Atiyah actually gave me the perfect riposte, which was, ‘That was the week that God created the world.’”
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Atiyah, who died in January at the age of 89, was described in his New York Times obituary as a “British mathematician who united mathematics and physics during the 1960s in a way not seen since the days of Isaac Newton.” So he was probably one of the few people on the planet who could outfox Feynman.
Atiyah helped to end a period of estrangement between physics and math, which Freeman Dyson (who at 95 is safely referred to as a living legend) talked about at the symposium. Dyson had noticed the falling-out when he joined Einstein (among other luminaries) on the IAS faculty: “When I became a professor, [which] just coincided with the time when [Robert] Oppenheimer [former head of the Manhattan Project] became director..., there was a divorce—largely occasioned by the fact Oppenheimer had no use for pure mathematics, and the pure mathematicians had no use for bombs.”
When asked what the most important questions were still to be addressed by physics and math, Dyson said, “The question of what's important is entirely a matter of taste. I like to think of going to the zoo … you can either admire the architecture of the zoo or you can admire the animals. And so, at the present time, mathematicians are very busy admiring the architecture. The physicists are admiring the animals. Which is actually more important isn't to me the interesting question. The interesting question is, Why do they fit so well?”
Mathematician Karen Uhlenbeck, professor emeritus at the University of Texas at Austin, had a different take: “There's this picture [that] there's a perfect world out there, and it has laws, and we're going to discover these laws. [But we're] just a bunch of human beings muddling along in a world that's very hard to understand. I mean, it's deceptive that the world looks so clear and beautiful and well put together. Because the minute you look at it with a different wavelength, it looks completely different. So our picture of the world as completely made and perfect—and all we need to do is find the rules for it—doesn't fit with my feeling. It's a kind of a muddle-y place, and you look at a piece of it, and we try to straighten it out, and we put together ideas in our mind, and we somehow make rules and order, and we create mathematics as a language in response to external stimuli.”
Dyson immediately attempted a reconciliation: “I don't disagree with you. We're exploring a universe which is full of mysteries … what to me is still amazing is that we understand so much.”
These conversations always remind of the very short Robert Frost poem: “We dance round in a ring and suppose,/But the Secret sits in the middle and knows.” I would have loved to ask Frost how he knew the secret was sitting.