But the thing with "pure" math, is that it can unexpectedly get adulterated by debased concerns such as enabling cryptography for the world economy.
But even then your argument breaks down when you consider more complicated cryptographic structures.
Well, programmers couldn't devise such a method either. You seem to assume that mathematicians are better than them at finding efficient algorithms, which isn't very plausible.
> But even then your argument breaks down when you consider more complicated cryptographic structures.
Even if help of mathematics is needed there, applied — rather than pure — math might still be sufficient.