tions of cryptography upon which today’s electronic transactions are based. It could give us efficient ways to solve intractable problems (such as the traveling salesman problem and the subgraph isomorphism problem) that arise in mathematics, as well as in every other science and engineering discipline. A proof in the negative (P ≠ NP) would have profound theoretical consequences for computer science and mathematics, perhaps by discovering a brand-new proof technique.

In order to answer what is computable, we must consider the underlying machine (abstract or physical) that is the computer. Consider the Internet as a computer. What is a universal machine model for the