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 perspective, historical and/or perspective:
“Reason, progress, unselfishness, a wide historical perspective, expansiveness, generosity, enlightened self-interest. I had heard it all my life, and it filled me with despair.”
—Katherine Tait (b. 1923)
“Some of us still get all weepy when we think about the Gaia Hypothesis, the idea that earth is a big furry goddess-creature who resembles everybody’s mom in that she knows what’s best for us. But if you look at the historical record—Krakatoa, Mt. Vesuvius, Hurricane Charley, poison ivy, and so forth down the ages—you have to ask yourself: Whose side is she on, anyway?”
—Barbara Ehrenreich (b. 1941)
“All things being equal, I would choose a woman over a man in order to even the balance of power, to insinuate a different perspective into the process, to give young women something to shoot for and someone to look up to. But all things are rarely equal.”
—Anna Quindlen (b. 1952)