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The introduction of numbers as coordinates ... is an act of violence...
-- H. Weyl, Philosophy of Mathematics and Natural Science
1949
The statement sometimes made, that there exist only analytic functions
in nature, is in my opinion absurd.
-- F. Klein, Lectures on Mathematics, 1893
Mandelbrot made quite good computer pictures, which seemed to show
a number of isolated "islands" (in the Mandelbrot set M).
Therefore, he conjectured that the set M has many distinct connected
components.
(The editors of the journal thought that his islands were specks of
dirt, and carefully removed them from the pictures).
-- John Milnor, in Dynamics in one complex variable, 1991