For me, Bertrand Russel is more known for his teapot which is said to be orbiting the sun somewhere between our orbit and Mars.
While it ought to be obvious for any rational-thinking person that such a teapot does not exist, it is impossible to prove the claim false (and it will remain impossible for the foreseeable future).
Now, there are many other claims put forward that are impossible to prove - like, the existence of a god. For Russell, the existence of a Christian god was no more likely than the existence of such a teapot.
RE: A Gentle Introduction To Mathematics - Russel's Paradox