You are indignant at me since I had written that “analysis relates to the universe, reveals the glory of the Lord, and implies equality and smoothness” in a transcript of a talk at a mathematical conference. So some explanations are in order in regard to the thought presented and the form of presentation.
1: The intentions of Newton and Leibniz were similar in that both tried to explain the world before them mathematically. Both were religious, both were Christians, and both believed in what the Bible had narrated.
Since the creation of the universe had been finished in a week and resumed never after, the present-day state of mechanical machinery of the world seemed to be determined from the initial conditions in a unique fashion. Equality was the idea of uniformity and uniqueness before the Lord, and so on. Newton's views reflected these ideas in his Philosophiæ Naturalis Principia Mathematica.
Leibniz wrote about the best of all possible worlds. For him the universe had been done once and so the problem was to find the principles of the divine choice. His second idea was the presence of the Creator in every instance of the universe. This led him to reconsideration of the idea of monad he had known from Euclid. Mathematics of Hellas distinguished the two kinds of atoms—points and monads. Leibniz was monistic and he combined the different definitions of Euclid into the sole notion and extended the concept of monad beyond mathematics in his La Monadologie.
These were the ideas of the Age of Enlightenment. In fact, the Enlightenment was a Christian attempt to find a mathematical wording of God's plot.
Euclid was not especially interested in unique existence. The prevalence of this idea has started with the Enlightenment. Nonsmooth analysis appeared in the twentieth century, in the Age of Freedom. The choices became human rather than divine. In mathematics freedom paved way to nonunicity, stochasticity, optimization, etc.
2: My short digression on the origins of nonsmooth analysis was inspired by the book The Best of All Possible Worlds of Ivar Ekeland, one of the leading figures in mechanics and optimization. There are different styles of writing and speaking about mathematics. The succinct style of Euclid makes mathematics immortal per se. The human style of the famous talk of Hilbert makes mathematics a challenge and inspiration for the present generations.
Mathematics is a human enterprise, and so there is nothing bad in making a mathematical talk more human.
October 2, 2012
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