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The golden ratio's aesthetic bona fides are an urban legend, a myth, a design unicorn. Many designers don't use it, and if they do, they vastly discount its importance. There's also no science to really back it up.

"Strictly speaking, it's impossible for anything in the real-world to fall into the golden ratio, because it's an irrational number," says Keith Devlin, a professor of mathematics at Stanford University.

You Don't Really Prefer The Golden Ratio In the real world, people don't necessarily prefer the golden ratio.

For anyone who has endured clichéd, condescending, uncomprehending, or otherwise aggravating depictions of classical music in American TV ads—the snobs at the symphony, the sopranos screaming under Valkyrie helmets, the badly edited bowdlerizations of the “Ode to Joy”—a new ad for the Apple iPad featuring the conductor and composer Esa-Pekka Salonen may come as a pleasant shock. It is, first of all, a cool, elegant piece of work—not surprising, given Apple’s distinguished history of television propaganda. Salonen is shown receiving inspiration for a passage in his Violin Concerto and trying it out in his iPad; then, after a montage of scenes in London and Finland, we see the violinist Leila Josefowicz and the Philharmonia Orchestra, of London, digging in to the score. More notably, it is musical: the concerto dictates the rhythm of the editing, and the correlation between notation and sound is made excitingly clear.

A 19th-century French impressionist artist who perished almost a century ago is the world’s leading aesthetic terrorist; you just don’t know it.Fortunately, the Renoir Sucks at Painting (RSAP) movement is here to change that.

t the core of RSAP’s serious political critiques are Eurocentric aesthetics and beauty standards and the domination of art museums by white men. “If the problems with Eurocentricity were personified in a man, Renoir would be the disgusting” embodiment, Geller insisted.Geller did not mince words: “Renoir is the most pulsating, puss-ridden boil which is the most blatant essence of the problem,” he added.“The fact that this utter charlatan can get by the watchmen defending the high altar of art is the proof positive that the system is broken, and that, for far too long, these decisions have been made by people who have access to fancy art educations and pursue them with an eye toward dictating taste,” Geller explained.

Mainly, I think, the restoration story gets people hooked because it raises ancient and endlessly fascinating philosophy-of-art questions. In this respect, the restored murals are really a new work, a work of conceptual art. To look at them is to have thoughts about the nature of art. When I was a student, I went to a class taught by the art historian Meyer Schapiro. There were lots of people in the room; I think it was supposed to be his last class. (This was at Columbia, where Schapiro had been, as a student and a professor, since 1920.) He devoted the entire opening lecture to forgeries. I couldn’t believe it. I wanted to hear him talk about paintings, not fakes. I didn’t go back.

Why are identical twins alike? In the late nineteen-seventies, a team of scientists in Minnesota set out to determine how much these similarities arose from genes, rather than environments—from “nature,” rather than “nurture.” Scouring thousands of adoption records and news clips, the researchers gleaned a rare cohort of fifty-six identical twins who had been separated at birth. Reared in different families and different cities, often in vastly dissimilar circumstances, these twins shared only their genomes. Yet on tests designed to measure personality, attitudes, temperaments, and anxieties, they converged astonishingly. Social and political attitudes were powerfully correlated: liberals clustered with liberals, and orthodoxy was twinned with orthodoxy. The same went for religiosity (or its absence), even for the ability to be transported by an aesthetic experience. Two brothers, separated by geographic and economic continents, might be brought to tears by the same Chopin nocturne, as if responding to some subtle, common chord struck by their genomes.

Contemplating such works, we can think in two modes at once, the aesthetic and the historical-political—generally a wise way to navigate the labyrinth of art. To debate whether politics is always present or always absent is to play a parlor game irrelevant to the complex, ever-shifting reality in which both artists and their audiences reside.

There is much in Wagner that has nothing to do with Hitler; there is much in Wagner that contradicts Hitler. That said, I would never dream of suggesting that Wagner’s operas should be detached absolutely and utterly from politics. It cannot be done; it can never be done.

From Amie I first heard about Yitang Zhang, a solitary, part-time calculus teacher at the University of New Hampshire who received several prizes, including a MacArthur award in September, for solving a problem that had been open for more than a hundred and fifty years. The problem that Zhang chose, in 2010, is from number theory, a branch of pure mathematics. Pure mathematics, as opposed to applied mathematics, is done with no practical purposes in mind. It is as close to art and philosophy as it is to engineering. “My result is useless for industry,” Zhang said. The British mathematician G. H. Hardy wrote in 1940 that mathematics is, of “all the arts and sciences, the most austere and the most remote.” Bertrand Russell called it a refuge from “the dreary exile of the actual world.” Hardy believed emphatically in the precise aesthetics of math. A mathematical proof, such as Zhang produced, “should resemble a simple and clear-cut constellation,” he wrote, “not a scattered cluster in the Milky Way.” Edward Frenkel, a math professor at the University of California, Berkeley, says Zhang’s proof has “a renaissance beauty,” meaning that though it is deeply complex, its outlines are easily apprehended. The pursuit of beauty in pure mathematics is a tenet. Last year, neuroscientists in Great Britain discovered that the same part of the brain that is activated by art and music was activated in the brains of mathematicians when they looked at math they regarded as beautiful.

After a law went into effect last summer banning obscenities in public performances, the playwright and director Ivan Vyrypaev excised the curse words from one of his plays, “The Drunks,” for its Russian debut at the prestigious Moscow Art Theater. Some actors played the new version straight, he said, while others winked to make clear what was cut.

At what point does a widely shared yen for aesthetic engagement alter the character of that engagement? We’ve reached that point on many days at the Museum of Modern Art, where the crowds experience mainly crowdedness, and the Picassos and Pollocks take on the glazed miens of traumatized warriors. MOMA’s own planned expansion bodes an architecture keyed to crowd management, which explains the logic behind even the cruel demolition of the intimate former American Museum of Folk Art.