Yitang Zhang: While working for  University of New Hampshire as a lecturer, Zhang submitted an article to the Annals of Mathematics in 2013 which established the first finite bound on the least gap between consecutive primes that is attained infinitely often

Occasionally, a major mathematical discovery comes from an individual working in isolation, and this gives rise to great surprise. Such an advance was(...)

Having these conversations with your children isn’t going to just teach them about pornography; they’re going to teach your children how to be mindful, critically engaged, empathetic, and self-aware. Photograph: Getty Images

Dear Roe, I’m the mother of two boys, ages 13 and 15. I’m constantly reading and hearing about how young men are exposed to pornography at a young ag(...)

A study by the Pew Research Centre found young people were significantly more likely to report positive experiences online than negative ones. Photograph: Istock

A recent article in these pages has questioned the advice of the special rapporteur for child protection that the so-called “digital age of consent” s(...)

Senator  Elizabeth Warren (left), New Hampshire governor Maggie Hassan and democratic presidential nominee  Hillary Clinton greet supporters during a campaign rally at Saint Anselm College this week   in Manchester, New Hampshire. Photograph: Justin Sullivan/Getty Images

On a brisk New Hampshire morning, Marc Tetrenault walks with friends on the campus of leafy St Anselm College in Manchester as Hillary Clinton’s play(...)

Hillary Clinton and Senator Elizabeth Warren at a rally Monday at St Anselm College in Manchester, New Hampshire. “I just want to be official here: I’m with her. Are you with her?” Warren asked the enthusiastic crowd. Photograph: Robyn Beck/AFP/Getty Images

In New Hampshire, the “Live Free or Die” state in the northeastern US, young Democrats have found a happy electoral compromise between freedom and de(...)

  Republican presidential candidate Jeb Bush addresses a crowd at a town hall event  in Portsmouth, New Hampshire.  Photograph:  Scott Eisen/Getty Images

Jeb Bush seems finally to have figured out what his campaign should be about. The problem for the former Florida governor and one-time presumed Republ(...)

US senator and Democratic presidential hopeful Bernie Sanders is surrounded by students following a town hall meeting at Dartmouth College in Hanover, New Hampshire. Photograph: CJ Gunther/EPA

The queue of people snakes its way around Dartmouth College’s Hopkins Center for the Arts. Hundreds of people, mostly university students and younge(...)

Democratic presidential candidate Hillary  Clinton  appears to be behaving like she might have something to lose in her race to win the Democratic nomination. Photograph: AP Photo/Charlie Neibergall

Hillary Clinton is approaching her presidential campaign with a new abandon. She is showing a more human side by lampooning Republicans on comedy TV a(...)

High hopes: millennials with an engineering degree may think they will be on a major project straight away. Photograph: Thinkstock

They are the last of the “millennials”, the generation born between the late 1970s and mid-1990s. They emerge from college with expectation, ho(...)

Hillary Clinton meets and greets supporters after a discussion at Whitney Brothers in Keene, New Hampshire, on Monday. New Hampshire will be the first to hold a presidential primary. Photograph: The New York Times

The event is beautifully staged: the owner of the business and six employees sit around as Hillary Rodham Clinton fields questions and shares her view(...)