Two ways to look at it: 1. Return on investment. Every hour spent on applied math generates a lot more applications (not to mention elegant mathematics) than t

Two ways to look at it: 1. Return on investment. Every hour spent on applied math generates a lot more applications (not to mention elegant mathematics) than the same spent on theoretical math. Theoretical math has about as much value as knitting and crochet. Does someone occasionally come up with something of value? Sure. Does it have more value than any other hobby? Not really. 2. With encryption in particular, Diffie-Hellmen is simple enough that public key would have been created regardless of research in theoretical math. Furthermore, most of the people developing such (including Diffie, Hellmen, Merkle, Rivest, Shamir, Adleman, etc.) have applied backgrounds. Indeed, most are computer scientists, rather than mathematicians. The same goes for cryptographic protocols, doubly so. Symmetric encryption, in contrast, does build a little bit on theoretical math, but it's also just an arms race. More knowledge about number theory helps both cryptography and cryptanalysis about equally. There's no reason to believe that more number theory makes us in any way more secure. Cryptography itself would exist without number theory (indeed, history is a bit fuzzy as to whether something like the scytale or number theory came first, and regardless, there is no reason to believe one fed the other).