In June this year five mathematicians turned into millionaires when they were awarded the Breakthrough Prize set up by Facebook founder Mark Zuckerberg and internet entrepreneur Yuri Milner. Simon Donaldson, Maxim Kontsevich, Jacob Lurie, Terry Tao and Richard Taylor each received £1.8m. That's more than the £930,000 that's awarded for the Nobel prize and should make up for the fact neither of the five is likely to ever to receive a Nobel: there isn't one for mathematics.

Back in November the five winners gave a lectures at the Breakthrough Prize Symposium, which have been filmed for you to watch. We especially recommend Terence Tao's talk on collaboration in maths (mathematicians seem to be getting more sociable):

Richard Taylor's talk about some beautiful number theory (does get a little technical later but starts very accessibly):

And Jacob Lurie's talk on analogy and abstractions in maths, involving some impossible shapes:

Simon Donaldson and Maxim Kontsevich's talks are a little more technical, but still worth a look if you're a bit more advanced in maths. Just click on the links!