Poincaré Conjecture - Numberphile

The Poincare's Conjecture is what I'd like to talk about and it is one of

seven kind of maths

questions, maths problems which were picked by the clay institute in well in the year 2000 as kind of the the

biggest outstanding problems in maths the kind of Real Massive unanswered questions.

And they they picked a list of seven things and for each one. There is a million-dollar prize

That they literally have that money waiting for people and of these seven problems only one of them so far has been solved.

And it was the poincare conjecture

So the poincare conjecture which was put up by poincare and

I forget around the turn of the last century around 1900 was a particular

conjecture as a guess and we were and he claimed that there were these certain relationships between

Geometry and Topology so I can try and explain a little bit about what the poincare conjecture is

It's from an area of math called Topology which is to do with kind of shape and how things fit together in space.

And but it's essentially about

Spheres, so a common idea in topology is the idea of deforming things, so I've got here a cube.

Which is made out of dough and in topology we can sort of

kind of move things around a little bit.

It's sometimes called rubber sheet geometry so I could take this Cube.

And I could kind of mess around with it.

And I could round it off like that using my hands and I can get a sphere

pretty much near enough.

So that's that the sphere the theory is that you're allowed to squash things stretch things

And all that kind of thing

But you're not allowed to punch holes in things you're not allowed to make a hole and you're not allowed to close up a hole