Ever wondered as a kid, why 0.9999=1, and never really appreciated the school text-book proof? Did you always think that the school proofs for calculus theorems didnt "seem" correct? (Ed: In fact they are horrible and incorrect; see the link on 'What is a derivative' below.) Did you like math paradoxes and love infinity? If so here's a collection of math sub-topics, pages and proofs which I believe you might enjoy, written/maintained by experts who are able to explain the ideas in a much better way...

Building on Numbers

• Hyperreal Numbers - "A Very Brief History of Almost-Nothing and More-than-Everything!"
• Surreal Numbers - The Big Daddy of all Sets of Numbers
• P-adic Numbers - Ordinal numbers with a twist

Interesting and Serious (Sub) Topics in Math

• Chaitin's page for Algorithmic Information Theory.
• Pages on Kolmogorov Complexity.
• The Axiom of Choice.
• Constructivism Is Difficult.
• A plethora of (unsolved) Math problems
• Ultra Filter Theory - It exists!, but cannot be constructed..
• Collatz Problem aka. The 3n+1 problem - Snakes and Ladders, mathematician style ...

Books

• Godel's Theorem: An Incomplete Guide to its Use and Abuse: Torkel Franzen
• Roads to Infinity: John Stillwell
• Incompleteness and Computability: Open Logic Text
• Infinity and the Mind: Rudy Rucker.

Having fun with Math!

• Get a random Math Fun Fact
• Some Mathematical Paradoxes.
• Not all Math constants are created equal
• Hotel Infinity - A first date with Miss. Infinity
• Fractal of the Day
• Escher on the Web. (See the gallery of paintings)
• Fermat's last Theorem . ( BTW, the French have a way of venerating their greats! Here's the French statue of Fermat (in deep thought?) in Toulouse.

Insights into simple math questions

• Why is 0.99999 = 1? (amongst the simplest, clearest explanations of this fact that I have seen)
• Simple and Charming Mathematical proofs.
• Is &radic 2 ^{&radic 2} a rational number?
• What is a derivative? (Scroll down to an alternative proof for differentiation using hyperreal numbers)
• What is a closed form number? Frankly I dont understand much of the paper, but I like the question that the author tries to answer