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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / j. Complex numbers

[numbers built from square root of -1]

2 ideas

14439	A complex number is simply an ordered couple of real numbers [Russell]
	Full Idea: A complex number may be regarded and defined as simply an ordered couple of real numbers
	From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], VII)

12425	Complex numbers were only accepted when a geometrical model for them was found [Kitcher]
	Full Idea: An important episode in the acceptance of complex numbers was the development by Wessel, Argand, and Gauss, of a geometrical model of the numbers.
	From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5)
	A reaction: The model was in terms of vectors and rotation. New types of number are spurned until they can be shown to integrate into a range of mathematical practice, at which point mathematicians change the meaning of 'number' (without consulting us).