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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.

Would mathematics exist if people didn't? Did we create mathematical concepts to help us understand the world around us, or is math the native language of the universe itself? Jeff Dekofsky traces some famous arguments in this ancient and hotly debated question.

HERE’S an apparent paradox: Most Americans have taken high school mathematics, including geometry and algebra, yet a national survey found that 82 percent of adults could not compute the cost of a carpet when told its dimensions and square-yard price.

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.

The magnitude of false positives for medical tests—a positive test for a condition that a patient does not actually have—is something that is not well understood, even by members of the medical community. We should remember this, as the United States prepares to lock away potential scores of individuals who test positive for Ebola. Many observers do not realize just how many people may spend some time in quarantine when they do not have the dreaded disease.

The cognitive psychologist Max Gigerenzer once asked 24 physicians the following hypothetical question, and only two got it right: A test for breast cancer is 90% accurate in identifying patients who actually have breast cancer, and 93% accurate in producing negative results for patients without breast cancer. The incidence of breast cancer in the population is 0.8%. What is the probability that a person who tests positive for breast cancer actually has the disease? Think you know the answer? Many of the physicians in Gigerenzer’s study said there was a 90% probability that a now-terrified patient flagged for breast cancer is an actual victim of the disease. However, the correct probability is less than 10%.