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)
“The two most far-reaching critical theories at the beginning of the latest phase of industrial society were those of Marx and Freud. Marx showed the moving powers and the conflicts in the social-historical process. Freud aimed at the critical uncovering of the inner conflicts. Both worked for the liberation of man, even though Marx’s concept was more comprehensive and less time-bound than Freud’s.”
—Erich Fromm (1900–1980)