Well this post is "related" two math but I found the chat room to be the most appropriate place for this.

Now I found a lecture series on youtube by a mathematician N J Wildberger.

He claims that the "Foundations of mathematics" are flawed. The area of mathematics he claims need to be revised thoroughly are:

1)Calculus/Analysis (Including the definition of real numbers- be it infinite decimals or dedekind's cuts or others)

2)Geometry/Topology

3)Algebraic Geometry

etc

Here is a link to lecture 94 where he claims that the cauchy sequence definition of reals is not quite correct.

http://www.youtube.com/watch?v=kcirw...feature=relmfu

He starts challenging the foundations of mathematics from lecture 87 onwards.

Guess you guys will find it interesting.