But it is not the separate signs (e.g., χ, π, ς) serving to express the functions _but the function itself as unit_, as element, the variable relation no longer capable of being optically defined, that constitutes the new number; and this new number should have demanded a new notation built up with entire disregard of Classical influences. Consider the difference between two equations (if the same word can be used of two such dissimilar things) such as 3^x + 4^x = 5^x and x^n + y^n = z^n (the equation of Fermat’s theorem). The first consists of several Classical numbers—i.e., magnitudes—but the second is _one number_ of a different sort, veiled by being written down according to Euclidean-Archimedean tradition in the identical form of the first. In the first case, the sign = establishes a rigid connexion between definite and tangible magnitudes, but in the second it states that within a domain of variable images there exists a relation such that from certain alterations certain other alterations necessarily follow. The first equation has as its aim the specification by measurement of a concrete magnitude, viz., a “result,” while the second has, in general, no result but is simply the picture and sign of a relation which for n>2 (this is the famous Fermat problem[66]) _can probably be shown to_ exclude integers. A Greek mathematician would have found it quite impossible to understand the purport of an operation like this, which was not meant to be “worked out.” As applied to the letters in Fermat’s equation, the notion of the unknown is completely misleading. In the first equation _x_ is a magnitude, defined and measurable, which it is our business to compute. In the second, the word “defined” has no meaning at all for _x_, _y_, _z_, _n_, and consequently we do not attempt to compute their “values.” Hence they are not numbers at all in the plastic sense but signs representing a connexion that is destitute of the hallmarks of magnitude, shape and unique meaning, an infinity of possible positions of like character, an ensemble unified and so attaining existence as a _number_. The whole equation, though written in our unfortunate notation as a plurality of terms, is actually _one single_ number, _x_, _y_, _z_ being no more numbers than + and = are.