"God made the integers; all the rest is the work of Man." ~ Leopold Kronecker, when criticizing Cantor's work [0]. See also Stephen Hawking's Anthology by a similar name. [1]
Rational numbers are pretty easy to understand. There are easy to understand proofs that at least some irrational numbers (famously square root of 2) exist. That is, the square root of 2 cannot be represented as a rational number. I'm sure there are other such proofs.
My take is that Kronecker and Hawking were either making an ironic statement or just expressing irony or exasperation.
> I'm sure there are other such proofs. The reals are uncountable.