In the 1930s the logician Kurt Gödel showed that if you set out proper rules for mathematics, you lose the ability to decide whether certain statements are true or false. This is rather shocking and you may wonder why Gödel's result hasn't wiped out mathematics once and for all. The answer is that, initially at least, the unprovable statements logicians came up with were quite contrived. But are they about to enter mainstream mathematics?
Many people like mathematics because it gives definite answers. Things are either true or false, and true things seem true in a very fundamental way. But it's not quite like that. You can actually build different versions of maths in which statements are true or false depending on your preference. So is maths just a game in which we choose the rules to suit our purpose? Or is there a "correct" set of rules to use? We find out with the mathematician Hugh Woodin.
That geometry should be relevant to physics is no surprise — after all, space is the arena in which physics happens. What is surprising, though, is the extent to which the geometry of space actually determines physics and just how exotic the geometric structure of our Universe appears to be. Plus met up with mathematician Shing-Tung Yau to find out more.
Quantum mechanics is usually associated with weird and counterintuitve phenomena we can't observe in real life. But it turns out that quantum processes can occur in living organisms, too, and with very concrete consequences. Some species of birds use quantum mechanics to navigate. And as Plus found out at a recent conference, studying these little creatures' quantum compass may help us achieve the holy grail of computer science: building a quantum computer.
On March 14 2010 a mathematician and a magician teamed up to perform what they believed to be the world's largest live magic trick. The trick involved a thousand volunteers from the around the world who, using free choice, each came up with a number that was only known to themselves. And although the volunteer might be on the other side of the globe, the mathematician and the magician were able to read their mind and tell them which number they had chosen.
