The unnaturalness of mathematical symbolism is attested to by history. The algebra of the Egyptians, the Babylonians, the Greeks, the Hindus, and the… - Morris Kline

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.

Galileo had provided the methodology for the analysis of motions on and near the earth and had applied it successfully. Copernicus and Kepler had previously obtained the laws of motion of the planets and their satellites. ...But Galileo had succeeded in deriving numerous laws from a few physical principles and... the axioms and theorems of mathematics. ...The Keplerian laws ...were not logically related to each other. Each was an independent inference from observations. ...They seemed to be suspended in the same vacuum in which the planets moved.
Galileo's laws had the additional advantage of supplying physical insight. The first law of motion and the law that the force of graviation gives... a downward acceleration of 32 ft/sec²... explain the vertrical rise and fall of bodies, motion on slopes, and projectile motion. Kepler's laws... had no physical basis. ...Kepler tried to introduce the idea of a magnetic force which the sun exerted... But he failed to related the behavior of the planets to the precise laws of planetary motion. ...
The new astronomical theory was completely isolated from the theory of motion on earth. ...it bothered mathematicians and scientists who believed that all the phenomena of the universe were governed by one master plan instituted by the master planner—God.

Aristotle had considered the question of whether space is infinite and gave six nonmathematical arguments to prove that it is finite; he foresaw that this question would be troublesome.