The RSA algorithm for public-key encryption is used practically whenever a secure connection must be established. The A in RSA is Leonard Adleman. He recieved the Turing Award for this work. He is also doing lots of rather theoretical stuff with DNA.
His reply to the Hamming question is:
Your question is a good one and to give a complete answer would require more time than I currently have; so I will just provide a brief remark:
- NP≟P (or some varient of it) is the most important open problem in CS. It is also on the short list of most important open problems in mathematic (see the Cole prize).
- I don’t work on it for 2 reasons. First, I did work on it for a few years as a youth, I had a few ideas worth (I thought) writing down (see “Time Space and Randomness” by moi), but ultimately I came to the conclusion that the problem was not “ripe” – ready to be solved. A few more decades (at least) of research would be required. It is for this reason that I changed my research to work on Fermat’s Last Theorem instead. My intuition suggested that, after 3 centuries, the problem was ripe. When Andrew Wiles proved FLT a few years ago, my consolation prize was to know that at least my intuition was correct.
Adleman is the first to respond with the P=NP problem. Is the P≟NP problem more a prestige problem than a theoretical one? Whether the result is useful depends on the answer. So we don’t know how important it is.
I feel that a result settling P ?= NP will be useful whatever the answer is. This is also a deep theoretical problem. However, many theoreticians don’t actively work on it because they need to publish in order to get PhD’s/get tenure/etc. Focusing solely on such a hard problem is the luxury of ppl with secure positions in academia.