What is the future of mathematics, what remains to ...

I'm not really an expert, but I know there's a lot to be discovered: the P vs. NP problem, the Navier-Strokes equations, and there are more (I actually took these from the TOC of this book).

But from what I remember, by exploring one problem in mathematics the mathematicians are finding more fields that are required to solve the original problem, and often these are very interesting themselves.

Today, the world of mathematics has become very theoretical. there are only a few people in the world who can understand the research that's being done at the cutting edge.

I think besides working on creating mathematical tools that can help solve problems in new ways (sometimes it's not the problem being solved but the way you solve it), thanks to the world of computers kicking in, there are many mathematical challenges today. The world is becoming more and more interdisciplinary and the world of mathematics will find itself intertwined with adjacent scientific fields. This new reality will bring fourth exciting new innovations.