For anyone who might be misled, here are some links that people can use to judge for themselves how "crank" someone is:

Professor Norman Wildberger's homepage:

http://web.maths.unsw.edu.au/~norman/

...a paper by Wildberger tackling some of the issues in this thread:

Set Theory: Should You Believe?

http://web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf

Some interesting works by Gregory Chaitin

Meta Math! The Quest for Omega

https://arxiv.org/abs/math/0404335

Exploring Randomness

https://www.cs.auckland.ac.nz/~chaitin/ait/

How Real are Real Numbers?

https://arxiv.org/abs/math/0411418

People who are interested in ultrafinitism would also want to check out Doron Zeilberger

http://www.math.rutgers.edu/~zeilberg/

and

Edward Nelson

https://web.math.princeton.edu/~nelson/