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

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Discussion Overview

The discussion revolves around the question of what constitutes the most difficult and advanced level of mathematics. Participants explore various aspects of mathematical complexity, including specific proofs and classifications that are considered challenging.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant expresses curiosity about the most complex mathematics, noting their own challenges with math comprehension.
  • Another participant suggests that the question is meaningless, as different areas of mathematics present varying levels of difficulty to different individuals.
  • A third participant mentions specific advanced mathematical concepts, such as the classification of all simple groups and the proof of Fermat's Last Theorem, highlighting their complexity and the time required to understand them.
  • A later reply challenges the assertion about the limited number of people who understand Fermat's Last Theorem, suggesting that resources exist to help more individuals grasp the proof and that many graduate students might be capable of understanding it.

Areas of Agreement / Disagreement

Participants do not reach a consensus on what the most difficult mathematics is, with multiple competing views on the nature of mathematical difficulty and understanding.

Contextual Notes

The discussion reflects varying perspectives on mathematical difficulty and comprehension, with no clear definitions or criteria established for measuring complexity.

FishmanGeertz
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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?
 
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The level nobody has reached yet.

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

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