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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.

Entertaining the idea of a peculiar long number such as pi puts me in mind of its cousins twice removed, prime numbers, which have so many strange properties. Prime numbers are those numbers, such as 3, 5, 7, 11, and so on, that can be cleanly divided only by one and themselves. Primes and pi suggest a benign infinity, a pleasing order—pi because of its endlessness and its relation to the circle, and primes because no matter how far you travel on the number line you will always encounter a prime, as Euclid proved in 300 B.C. Recently, Yitang Zhang solved a problem involving prime numbers called bounded gaps that had been open for more than a hundred years. Zhang proved that no matter how far you go on the number line, even to the range where the numbers would fill many books, there will, on an infinite number of occasions, be two prime numbers within seventy million places of each other. (Other mathematicians have reduced this gap to two hundred and forty six.) Before, it had not been known whether any such range applied to prime numbers, which seem to behave, especially as they get larger, as if they appear at random.

Decades after foot-binding was outlawed in China, a British photographer has met some of the last women subjected to the practice. It was with a sense of pride that Su Xi Rong revealed her feet to British photographer Jo Farrell. Her feet, bound from the age of seven, were so small that she had been renowned for their beauty. The 75-year-old is among the last remaining women in China to bear the effects of foot-binding, a practice first banned in 1912. Farrell met more than 50 of them over an eight-year period, and says she was surprised to find stories of pride and empowerment. Her book about the women is being launched at the British Council in Hong Kong on Monday. Foot-binding was believed to create a more beautiful foot and promote obedience.

An exhibition at the British Library in London reveals the importance that visualising data has had on the scientific process – from 19th Century ship logs that still influence climate science, to models used to forecast the 2009 influenza pandemic.These images not only aid scientific progress, but also help to change the world.

What is the sky worth? This sounds like a philosophical question, but it might become a more concrete one. A report released last week by the National Research Council called for research into reversing climate change through a process called albedo modification: reflecting sunlight away from earth by, for instance, spraying aerosols into the atmosphere. Such a process could, some say, change the appearance of the sky — and that in turn could affect everything from our physical health to the way we see ourselves. If albedo modification were actually implemented, Alan Robock, a professor of environmental sciences at Rutgers, told Joel Achenbach at The Washington Post: “You’d get whiter skies. People wouldn’t have blue skies anymore.” And, he added, “astronomers wouldn’t be happy, because you’d have a cloud up there permanently. It’d be hard to see the Milky Way anymore.”

When the artist Peggy Weil first learned about the National Ice Core Laboratory, a few years ago, she was captivated. She contacted Geoffrey Hargreaves, the lab’s curator, and soon found herself inside a giant freezer, bundled in an Arctic-ready parka. (The temperature was minus thirty-eight degrees Fahrenheit.) With the help of lab assistants, she loaded up a cart with cannisters made of thick cardboard, each containing a small segment of a two-mile-long core from the Greenland ice sheet. Weil trundled her specimens to a cylindrical scanner and photographed them in high resolution. Eventually, she strung together eighty-eight scans, top to bottom. Then she animated them and added an accompanying score, creating a four-and-a-half-hour video, designed to be projected onto a wall.

Neuroscience is a fast growing and popular field, but despite advances, when an area of the brain 'lights up" it does not tell us as much as we'd like about the inner workings of the mind. Many of us have seen the pictures and read the stories. A beautiful picture of the brain where an area is highlighted and found to be fundamental for processes like fear, disgust or impaired social ability. There are so many stories it can be easy to be swayed into thinking that much more of the brain's mystery has been solved than is the case.

There's no transit map in North America as polarizing as the one Massimo Vignelli made more than 40 years ago for New York City. MTA riders say it was confusing. Designers say it may have just been too beautiful for this world. 

But now experts say a reliance on sat-navs and smartphone map apps is undermining map-reading skills. So here are five reasons why you should love maps and resist the easy attraction of the sat-nav.

“English is not a language in India,” a friend once told me. “It is a class.” This friend, an aspiring Bollywood actor, knew firsthand what it meant to be from the wrong class. Absurd as it must sound, he was frequently denied work in the Hindi film industry for not knowing English. “They want you to walk in the door speaking English. Then if you switch to Hindi, they like it. Otherwise they say, ‘the look doesn’t fit.’ ” My friend, who comes from a small town in the Hindi-speaking north, knew very well why his look didn’t fit. He knew, too, from the example of dozens of upper-middle class, English-speaking actors, that the industry would rather teach someone with no Hindi the language from scratch than hire someone like him.

Shakespeare has not lost his place in this new world, just as, despite the grim jeremiads of the cultural pessimists, he has not lost his place in colleges and universities. On the contrary, his works (and even his image) turn up everywhere, and students continue to flock to courses that teach him, even when those courses are not required. But as I have discovered in my teaching, it is a different Shakespeare from the one with whom I first fell in love. Many of my students may have less verbal acuity than in years past, but they often possess highly developed visual, musical and performative skills. They intuitively grasp, in a way I came to understand only slowly, the pervasiveness of songs in Shakespeare’s plays, the strange ways that his scenes flow one into another or the cunning alternation of close-ups and long views. When I ask them to write a 10-page paper analyzing a particular web of metaphors, exploring a complex theme or amassing evidence to support an argument, the results are often wooden; when I ask them to analyze a film clip, perform a scene or make a video, I stand a better chance of receiving something extraordinary. A student with a beautiful voice performed Brahms’s Ophelia songs, with a piano accompaniment by another gifted musician. Students with a knack for creative writing have composed monologues in the voice of the villainous Iago, short stories depicting an awkward reunion of Shylock and his daughter, Jessica, or even additional scenes in Shakespearean verse.