Indeed! For instance, Wikipedia presents a couple of proofs of the irrationality of √2 (including a geometric one). None of these require knowledge of its digit

Indeed! For instance, Wikipedia presents a couple of proofs of the irrationality of √2 (including a geometric one). None of these require knowledge of its digits. https://en.wikipedia.org/wiki/Square_root_of_2 https://en.wikipedia.org/wiki/Square_root_of_2