W. R. Hamilton

founding of algebra as a science in intuition of pure time

Abstract

Hamilton has been recognized for the risk of his proposal, apparently very metaphysical, but also clearly against the reforms developed since 1820. His principles led him in the opposite sense of the reformists who advocated the need of a Symbolical Algebra. Therefore, he surprises when he substitutes “order in progression” for “magnitude”, having pointed out the evidence of the relation between the time and the progress of algebra. He builds a mathematical Science of Pure Time. This science exists, it is naturally comparable to algebra (as a Science), it coincides with it, and, finally, it is Algebra itself. The algebra then is left out of problems and becomes a branch of the Philosophy of the Mind. The discovery of the quaternion will be considered, from the very first “opponents” of the English Algebraic School, like an overture to the liberty of “creation” in mathematics.