Historically, it was Euclidean geometry that, developed to a large extent as a votive offering to the God of Reason, opened men's eyes to the possibi… - Morris Kline

Henri Poincaré thought the theory of infinite sets a grave malady and pathologic. "Later generations," he said in 1908, "will regard set theory as a disease from which one has recovered.

By 1700 all of the familiar members of the [number] system... were known. However, opposition to the newer types of numbers was expressed throughout the century. Typical are the objections of... Baron Francis Masères... in 1759 his Dissertation on the Use of the Negative Sign in Algebra... shows how to avoid negative numbers... and especially negative roots, by carefully segregating the types of quadratic equations so that those with negative roots are considered separately; and... the negative roots are to be rejected.

The goal of deriving all the phenomena of nature from a few basic physical laws and the axioms of mathematics had been set by Galileo...
In studying curvilinear motions on the earth Galileo had found the parabola to be the basic curve. In the heavens... Kepler... had found the ellipse to be the basic curve. Why this difference? ...since parabola and ellipse are both conic sections there was the provocative suggestion that perhaps some physical law unified these related paths of motion. ...
It has often happened in the history of mathematics and science that major problems remained outstanding... great minds... succeeded only in revealing the true difficulties... and in generating an atmosphere of dispair... Then a genius appeared... with ideas that seemed remarkably simple once propounded, clarified the entire situation, dispelled the confusion, restored order, and produced a new synthesis that embraced far more even than the phenomena under consideration. The genius who... picked up the torch of science dropped by Galileo, was Isaac Newton.