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.

 

[CellCoree]

I can understand your curiosity about the most advanced level of mathematics that exists. However, it is important to note that there is no single answer to this question as mathematics is a vast and constantly evolving field. There are several branches of mathematics, each with its own complex and advanced concepts.

Some may argue that the most difficult level of mathematics is found in theoretical branches such as abstract algebra, topology, and number theory. These areas deal with highly abstract concepts and require a deep understanding of mathematical structures and relationships.

On the other hand, some may argue that the most advanced level of mathematics is found in applied branches such as differential equations, mathematical modeling, and computational mathematics. These areas involve using mathematical tools to solve real-world problems and require a strong foundation in calculus and other advanced mathematical techniques.

It is also worth mentioning that the difficulty of mathematics is subjective and can vary from person to person. Some individuals may find certain concepts more challenging than others, and it is important to acknowledge and respect these differences.

In conclusion, the most difficult and advanced level of mathematics is a subjective and constantly evolving concept. It is a reflection of the vastness and complexity of the field and the various branches and applications of mathematics.