In 1957, a few years after Francis Crick co-discovered the DNA double helix and a few years before he co-won a Nobel Prize for doing so, he published a paper on the genetic provenance of amino acids, the organic compounds that make proteins, and therefore life, possible. It was already known that the four chemical bases of DNA coded for the twenty standard amino acids. What wasn’t yet known was whether DNA had the equivalent of punctuation—points along its strands that demarcated where one bit of code ended and another began. Crick’s belief was that each amino acid could arise only from a unique triplet of bases, making such punctuation unnecessary. In the paper, which he titled “Codes Without Commas,” Crick noted that his theory correctly predicted the “magic number” of twenty. As he wrote in his memoir, almost thirty years later, the idea had “seemed so pretty, almost elegant,” at the time. It also happened to be entirely wrong. (Different sequences can, in fact, code for the same amino acid.) From this experience, Crick concluded that it is “very rash to use simplicity and elegance as a guide in biological research.”

Despite Crick’s injunction, scientists have continued to seek elegance in their work. But what, exactly, is it? A list of elegant things, like a list of obscene things, includes no single trait in common across its members. The parasitic wasp T. elegans, the roundworm C. elegans, the feather-tailed dinosaur J. elegans, John Singer Sargent’s “Madame X,” Crick’s “Codes Without Commas”—what unites them? When I asked the Stanford neuroscientist Robert Sapolsky for a definition of elegant science, he said, “You know it when you see it.” Edward Witten, a physicist at the Institute for Advanced Study, in Princeton, was similarly cagey. “After you define music for me, I will try to define elegance,” he said. Alyssa Goodman, of the Harvard-Smithsonian Center for Astrophysics, answered more forthrightly: “There is something about the way things fit together, a kind of fluidity. If it is done right, and elegantly, you do not see all the individual parts, because they all fit together in a way that looks like a whole.” She was talking, unfortunately, about tennis.

The edges of some linguistic categories, like the edges of clouds, seem to disappear as you get closer. In these cases, it can be helpful to consider what something is not. (To fly, as the British writer Douglas Adams defined it, is to throw oneself at the ground and miss.) William Newsome, the co-chair of President Obama’s recent BRAIN Initiative, defined elegance by its inverse: “Baroque.” Likewise the statistician Edward Tufte, the author of books on data display and visual design: “Poshlust—the Nabokov spelling—a kind of banal pretentiousness.” Jonathan Corum, the science-graphics editor at the Times, offered “clunky”; Alexander Nemerov, a Stanford art critic, said “abject”; a thousand people on Amazon’s Mechanical Turk, whom I polled in hopes that the opposite of elegance could, like the weight of an ox, be determined in aggregate, responded with “trashy,” “crude,” “clumsy,” “awkward,” “cumbersome,” and “uncoördinated.”

According to a 2010 paper in the journal Nature Nanotechnology, “When a theory or a model explains a phenomenon clearly, directly and economically, we say it is elegant: one idea, easy to understand, can account for a large amount of data and answer many questions.” This definition—simplicity plus capaciousness—seems right. Goodman told me that, to her, Newton’s second law of motion, F = ma, which relates force with mass and acceleration, is one of the most elegant findings in science. “Once you understand the math behind how to apply that law, you can explain the motion of almost anything,” she said. Tufte’s candidate was the second law of thermodynamics, which states that the amount of disorder in the universe will always increase. “If we see alien science someday, they will have the equivalent equation,” Tufte said. “That’s real elegance.” (Tom Stoppard, in his play “Arcadia,” summarized this law as “You cannot stir things apart.”)

Witten, who has been instrumental in advancing string theory—a framework alternately praised and derided for its elegance—noted that elegance can be a kind of guide toward what is reasonable and plausible. “To work successfully in physics or mathematics, one is helped by a sort of sixth sense that lets one guess what a good approach might be,” he told me. “One could describe this sixth sense, roughly, as a sense of elegance.” But, as Crick learned, the same isn’t necessarily true of all scientific pursuits. “In biology, it’s possible to be elegant and be wrong,” Newsome, who began his career in physics but now studies the neuroscience of vision, told me. Nature doesn’t always find the most elegant solution. “Evolution just seizes on certain convenient solutions that present themselves,” he said. “They get frozen in place, reproduced, and used again and again.” Newsome cited the example of the retina. “Vertebrates have exactly the wrong solution,” he said. In vertebrates, the light-sensitive cells are in the back of the eye and must compensate, at a cost, for light scattering through the lens and other nearby cells. “Any human engineer would have placed the light-absorbing cells closest to the light source,” he said. (Which, in fact, is how many invertebrates are built.)

Last year, neuroscientists in the United Kingdom put expert mathematicians in an fMRI and tested whether their brains responded to equations the way that other people’s brains respond to, say, a beautiful painting or piece of music. They found that some equations—often simple, powerful ones like Euler’s identity, ei^π ^+_ _1 = 0, which joins together five mathematical constants—caused “activity in the same part of the emotional brain, namely field A1 of the medial orbito-frontal cortex (mOFC), as the experience of beauty derived from other sources.” Things are not always clear in the brain, though; it is impossible to say for certain whether activity in the mOFC is a response or a precursor to an emotion, or whether it’s the emotion itself. Likely, any full description will be messy, turbulent. But within that turbulence will be, finally, an explanation for what it means to know something when one sees it, or for what the “great liquid whip” of Roger Federer’s forehand and the “whip-like thrashing” of the roundworm tell us about string theory, or for how it came to be that three pounds of inelegance thought up such a concept as elegance in the first place.