Fermat applied his method of tangents to many difficult problems. The method has the form of the now-standard method of differential calculus, though… - Morris Kline

As for negative numbers... most mathematicians of the sixteenth and seventeenth centuries did not accept them... In the fifteenth century and, in the sixteenth, Stifel both spoke of negative numbers as absurd numbers. ...Descartes accepted them, in part. ...he had shown that, given an equation, one can obtain another whose roots are larger than the original one by any given quantity. Thus an equation with negative roots could be transformed into one with positive roots. Since we can turn false roots into real roots, Descartes was willing to accept negative numbers. Pascal regarded the subtraction of 4 from zero as utter nonsense.

The Pythagoreans associated good and evil with the limited and unlimited, respectively.

The history of arithmetic and algebra illustrates one of the striking and curious features of the history of mathematics. Ideas that seem remarkably simple once explained were thousands of years in the making.