Machines can already write music and beat us at games like chess and Go. But the rise of artificial intelligence should inspire hope as well as fear, says Marcus du Sautoy

As Marcus du Sautoy greets me at the entrance to New College, Oxford, his appearance is a quiet riot of colour. His clothes rather suggest someone who ran into White Stuff or Fat Face and frantically grabbed anything he could find – in this case, a salmon zip-up top, multihued check trousers and shoes that are a headache-inducing shade of turquoise. When we settle down to talk in a nearby meeting room, he repeatedly glances at a notepad – whose pages, just to add to all the garishness, are a bold shade of yellow.

They are full of what look like scrawled equations, mixed with odd-looking shapes: the raw material, he explains, of a project involving very complicated geometry. “There’s an infinite symmetrical structure that I’m looking at,” he says, “and I think the top bit of it will tell me everything that’s going on inside it. It’s almost like an infinite lake, and I should be able to know everything that’s happening in it by looking at the first centimetre.”

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