Can you read the word above? Could a computer?
Manuel Blum won his Turing Award in 1995 for his work in computational complexity and its applications to cryptography. The theory of much of modern-day cryptography uses the assumption that certain problems are not easily computable to create unbreakable codes and protocols.
These days Blum is working on another project that also uses the assumption that some problems are hard computationally. The idea is to use problems that humans can solve easier than computers to prevent automated registration, voting, etc. Check out the CAPTCHA project web site.