Technology
Leslie Lamport wrote a paper describing the Paxos algorithm in plain English. This is an algorithm that guarantees that a distributed system reaches consensus on the value of an attribute. Lamport claims that the algorithm can be derived from the problem statement, which would imply that it is the only algorithm that can achieve these results. Indeed, many of the distributed systems that we use today are based at least in part on Paxos. Linq not only introduced the ability to query a database directly from C#. It also introduced a set of language features that were useful in their own right. Lambda expressions did not exist in C# prior to 3.0, but now they are preferred to their predecessor, anonymous delegates. Extension methods were added to the language specifically to make Linq work, but nevertheless provide an entirely new form of expressiveness. Linq works because its parts were designed to compose. This is not quite so true of language features that came later, like async and primary constructors. Fermat was quite fond of writing little theorems and not providing their proofs. One such instance, known as "Fermat's Little Theorem", turns out to be fairly easy to prove, but provides the basis for much of cryptography. It states that a base raised to one less than a prime in the prime's modulus will always be equal to 1. This is useful in generating a good trap door function, where we can easily compute the discrete exponent of a number, but not the discrete logarithm.