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Single Idea 12425

[from 'The Nature of Mathematical Knowledge' by Philip Kitcher, in 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / j. Complex numbers ]

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.

Gist of Idea

Complex numbers were only accepted when a geometrical model for them was found

Source

Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5)

Book Reference

Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.176


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).