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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.

Mathematics and art are generally viewed as very different disciplines – one devoted to abstract thought, the other to feeling. But sometimes the parallels between the two are uncanny. From Islamic tiling to the chaotic patterns of Jackson Pollock, we can see remarkable similarities between art and the mathematical research that follows it. The two modes of thinking are not exactly the same, but, in interesting ways, often one seems to foreshadow the other. Does art sometimes spur mathematical discovery? There’s no simple answer to this question, but in some instances it seems very likely.

in the very worst manifestation it was actually kind of a weaponized mathematical algorithm. I was working in online advertising. Most of the people working online advertising represented it as a way of giving people opportunities. That’s true for most technologists, most educated people, most white people. On the other side of the spectrum you have poor people, who are being preyed upon, by the same kinds algorithms.

people need to stop trusting mathematics and they need to stop trusting black box algorithms. They need to start thinking to themselves. You know: Who owns this algorithm? What is their goal and is it aligned with mine? If they’re trying to profit off of me, probably the answer is no.

EVERYONE by nature desires to know,” wrote Aristotle more than 2,000 years ago. But are there limits to what human beings can know? This is the question that Marcus du Sautoy, the British mathematician who succeeeded Richard Dawkins as the Simonyi professor for the public understanding of science at Oxford University, explores in “What We Cannot Know”, his fascinating book on the limits of scientific knowledge.

Eventually, he turns to his own field of mathematics. If people cannot know everything about the physical world, then perhaps they can at least rely on mathematical truth? But even here there are limits.

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.

And with the Islamic State’s prolific use of social media, terrorism experts and government agencies continually search for clues in posts and Twitter messages that appear to promote the militants’ cause.A physicist may not seem like an obvious person to study such activity. But for months, Neil Johnson, a physicist at the University of Miami, led a team that created a mathematical model to sift order from the chaotic pro-terrorism online universe.