Historical Perspective
The process of unification might be seen as helping to define what constitutes mathematics as a discipline.
For example, mechanics and mathematical analysis were commonly combined into one subject during the 18th century, united by the differential equation concept; while algebra and geometry were considered largely distinct. Now we consider analysis, algebra, and geometry, but not mechanics, as parts of mathematics because they are primarily deductive formal sciences, while mechanics like physics must proceed from observation. There is no major loss of content, with analytical mechanics in the old sense now expressed in terms of symplectic topology, based on the newer theory of manifolds.
Read more about this topic: Unifying Theories In Mathematics
Famous quotes containing the words historical and/or perspective:
“By contrast with history, evolution is an unconscious process. Another, and perhaps a better way of putting it would be to say that evolution is a natural process, history a human one.... Insofar as we treat man as a part of nature—for instance in a biological survey of evolution—we are precisely not treating him as a historical being. As a historically developing being, he is set over against nature, both as a knower and as a doer.”
—Owen Barfield (b. 1898)
“Egoism is the law of perspective as it applies to feelings, according to which what is closest to us appears to be large and weighty, while size and weight decrease with our distance from things.”
—Friedrich Nietzsche (1844–1900)