Descartes... complained that Greek geometry was so much tied to figures "that is can exercise the understanding only on condition of greatly fatiguin… - 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.

The historical associations of the word algebra almost substantiate the sordid character of the subject. The word comes from the title of a book written by... Al Khowarizmi. In this title, al-jebr w' almuqabala, the word al-jebr meant transposing a quantity from one side of an equation to another and muqabala meant simplification of the resulting expressions. Figuratively, al-jebr meant restoring the balance of an equation... When the Moors reached Spain... algebrista... came to mean a bonesetter... and signs reading Algebrista y Sangrador (bonesetter and bloodletter) were found over Spanish barber shops. Thus it might be said that there is a good historical basis for the fact that the word algebra stirs up disagreeable thoughts.

The Greeks failed to comprehend the infinitely large, the infinitely small, and infinite processes. They "shrank before the silence of the infinite spaces."