What is the most difficult and advanced level of math that exists?

[FishmanGeertz]

I have a learning disability solely in math comprehension, much of the advanced math was omitted throughout my high school career. I was able to graduate without any very difficult math.

But I'm curious, what is the most complex, difficult, and advanced level of mathematics that exists?

 

[fss]

The level nobody has reached yet.

Honestly your question is pretty meaningless. Different areas of math are difficult to different people.

 

[micromass]

Well, the most difficult math doesn't exist. But there certainly are some mathematical things that are very advanced and very difficult, for example:

- the classification of all simple groups: it's a staggering 10000 pages long and it would take a professional mathematician many years to fully understand the proof.

- the proof of Fermat's last theorem: it would surprise me if there were more than 100 people in this world who understand it

 

[fourier jr]

- the proof of Fermat's last theorem: it would surprise me if there were more than 100 people in this world who understand it

I don't know about that, here are a couple books that explain it, & with plenty of references to build up the background:
http://books.google.ca/books?id=W1Nso5E6G3YC
http://books.google.ca/books?id=Va-quzVwtMsC
If there are still so few people who understand it, it's only because so few bother to try. I bet a lot of grad students could understand it at this point.