"Nothing is easier... than to fit a deceptively smooth curve to the discontinuities of mathematical invention. Everything then appears as an orderly progression... with Cavalieri, for instance, indistinguishable from Newton in the neighborhood of the calculus, or Lagrange from Fourier in that of trigonometric series, or Bhaskara from Lagrange in the region of Fermat's equation. Professional historians may sometimes be inclined to overemphasize the smoothness of the curve; professional mathematicians, mindful of the dominant part played in geometry by the singularities of curves, attend to the discontinuities. ...That such differences should exist is no disaster. Dissent is good for the souls of all concerned."

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Added on April 10, 2026
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Original Language: English