My maths teacher always keeps telling me about this 'cutting edge maths' that is going on in the world, amazing maths research, etc.

A lot of the google searches I've done for 'Cutting Edge Mathematics' hasn't returned much useful information, so I've taken to mathematics stack exchange.

What kind of cutting edge maths research is going on in the world at the moment?

Don't we already know everything there is to know about numbers?

Considering maths is just numbers, I thought that we could apply maths to other subjects like physics and that was why maths was useful. However... I never realised that there could be more to find out about the numbers themselves...