There is no such thing as abstractly proving something

Of course there is. A proof of a mathematical proposition is just as much itself a mathematical object as the proposition being proved; it exists just as independently of physics. The proof as written down is a physical object standing in the same relation to the real proof as the digit 2 before your eyes here bears to the real number 2.

But perhaps in the context Deutsch isn't making that confusion. What scope and limitations on mathematical knowledge, conditioned by the laws of nature, does he draw out from these considerations?