Complex Numbers (Sunday Reflection)

"…there is never a need to go beyond the complex numbers. No further numbers are needed. They suffice and so they bring to completion the very long effort at construction that over thousands of years yielded first the natural numbers, then the fractions, then zero and the negative numbers, and after that the real numbers. The complex numbers complete the arch.
"Beyond the theory of complex numbers, there is the much greater and grander theory of the functions of a complex variable, as when the complex plane is mapped to the complex plane, complex numbers linking themselves to other complex numbers. It is here that complex differentiation and integration are defined. Every mathematician in his education studies this theory and surrenders to it completely. The experience is like first love.
"I once mentioned the beauty of complex analysis to my great friend, the mathematician M.P. Schutzenberger. We were riding in a decrepit taxi, bouncing over the streets of Paris.
" 'Perhaps too beautiful,' he said at last.
"When I mentioned Schutzenberger's remarks to Rene' Thom, he shrugged his peasant shoulders sympathetically.
"This is one of the charms of the theory of complex numbers and their functions. It has broken men's hearts."

-- David Berlinski from "Infinite Ascent"


[…If you have a favorite math-related passage that might make a nice Sunday morning reflection here let me know (SheckyR@gmail.com). If I use one submitted by a reader, I'll cite the contributor.]