Analytical philosophy refers as much to a method as to a body of philosophical doctrine. It is extremely difficult to give a unifying characterization of analytical philosophy that picks out what is common to all its instances. Analysis is a process which aims to elucidate complexes by reducing them to their simpler elements and the relations between those elements. This can apply to complex concepts, entities, or philosophical problems. The origins of analytical philosophy lie in work done in the latter half of the nineteenth century and the beginning of the twentieth century on logic and the foundations of mathematics. Bertrand Russell saw the new logic as an ideal language which in philosophy could sometimes replace the vagaries of ordinary language. Ludwig Wittgenstein saw the new logic as revealing the essential structure of ordinary language itself, ordinary language was in logical order, needed to be shown through logical analysis.