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.

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

Guess you guys will find it interesting.