What is Algebra?

Abstract

What is algebra? Is it a branch of mathematics, a method or a frame of mind? Such questions do not of course admit either short or unambiguous answers. One can attempt a description of the place occupied by algebra in mathematics by drawing attention to the process for which Hermann Weyl coined the unpronounceable word ‘coordinatisation’ (see [H. Weyl 109 (1939), Chap. I, § 4]). An individual might find his way about the world relying exclusively on his sense organs, sight, feeling, on his experience of manipulating objects in the world outside and on the intuition resulting from this. However, there is another possible approach: by means of measurements, subjective impressions can be transformed into objective marks, into numbers, which are then capable of being preserved indefinitely, of being communicated to other individuals who have not experienced the same impressions, and most importantly, which can be operated on to provide new information concerning the objects of the measurement.