The study and use of dual mathematical programs.

Although the concept of duality goes back to the last century, it has only been the last few years that it string theories were seen to possess a duality structure. Simply put, two theories are said to be dual to each other if they describe the same physics using different language. Because we usually only have perturbation theory to investigate a theory with, two theories may appear completely different. However it is now believed that the non-perturbative regime (i.e. where the perturbative expansion does not provide a reliable approximation) of one string theory is actually described by the perturbative regime of another string theory. In this way it is thought that all the string theories are in fact different aspects of one underlying theory, M theory. Duality is thus a very powerful tool in understanding the full physics of a theory.

(physics) the property of matter and electromagnetic radiation that is characterized by the fact that some properties can be explained best by wave theory and others by particle theory

A correspondence between apparently different theories that lead to the same physical results.

In the mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by Pop. This dual order Pop is defined to be the set with the inverse order, i.e. x ≤ y holds in Pop iff y ≤ x holds in P. It is easy to see that this construction, which can be depicted by flipping the Hasse diagram for P upside down, will indeed yield a partially ordered set.