Mathematical Theories
The term theory is used informally within mathematics to mean a self-consistent body of definitions, axioms, theorems, examples, and so on. (Examples include group theory, Galois theory, control theory, and K-theory.) In particular there is no connotation of hypothetical. Thus the term unifying theory is more like a sociological term used to study the actions of mathematicians. It may assume nothing conjectural that would be analogous to an undiscovered scientific link. There is really no cognate within mathematics to such concepts as Proto-World in linguistics or the Gaia hypothesis.
Nonetheless there have been several episodes within the history of mathematics in which sets of individual theorems were found to be special cases of a single unifying result, or in which a single perspective about how to proceed when developing an area of mathematics could be applied fruitfully to multiple branches of the subject.
Read more about this topic: Unifying Theories In Mathematics
Famous quotes containing the words mathematical and/or theories:
“The most distinct and beautiful statement of any truth must take at last the mathematical form.”
—Henry David Thoreau (1817–1862)
“It takes twenty or so years before a mother can know with any certainty how effective her theories have been—and even then there are surprises. The daily newspapers raise the most frightening questions of all for a mother of sons: Could my once sweet babes ever become violent men? Are my sons really who I think they are?”
—Mary Kay Blakely (20th century)