Some numerological flights of fancy inolving the number 137, compiled by Gary Adamson

The mathematical developments we have charted in this chapter show how a great divide came between old nexus of zero, nothingness and the void. Once, these ideas were part of a single intuition. The rigorous mathematical games that could be played with the Indian zero symbol had given credibility to the philosophical search for a meaningful concept of how nothing could be something. But in the end mathematics was too great an empire to remain intimately linked to physical reality. At first, mathematicians took their ideas of counting and geometry largely from the world around them. They believed there to be a single geometry and a single logic. In the nineteenth century they began to see further. These simple systems of mathematics they had abstracted from the natural world provided models from which now abstract structures defined solely by the rules for combining their symbols, could be created. Mathematics was potentially infinite. The subset of mathematics which described parts of the physical universe was smaller, perhaps even finite. Each mathematical structure was logically independent of the others. Many contained ‘zeros’ or ‘identity’ elements. Yet, even though they might share the name of zero, they were quite distinct, having an existence only within the mathematical structure in which they were defined and logically underwritten by the rules they were assumed to obey. Their power lay in their generality, their generality in their lack of specificity. Bertrand Russell, writing in 1901, captured its new spirit better than anyone:

“Pure mathematics consists entirely of such asseverations as that, if such and such a proposition is true of ‘anything’, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is of which it is supposed to be true… If our hypothesis is about ‘anything’ and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.”

Pure mathematics became the first of the ancient subjects to free itself of metaphysical shackles. Pure mathematics became free mathematics. It could invent ideas without recourse to correspondence with anything in the worlds of science, philosophy or theology. Ironically, this renaissance emerged most forcefully not with the plurality of zeros that it spawned, but with the plethora of infinities that George Cantor en.wikipedia.org/wiki/Georg_Cantor unleashed upon the unsuspecting community of mathematicians. The ancient prejudice that there could potential infinities, but never actual infinities, was ignored. Cantor introduced infinities without end in the face of howls of protest by conservative elements in the world of mathematics. Cantor was eventually driven into deep depression that overshadowed the end of his life, yet he vigorously maintained the freedom of mathematicians to invent what they will:

“Because of this extraordinary position which distinguished mathematics from all other sciences, and which produces an explanation for the relatively free and easy way of pursuing it, it especially deserves the name of ‘free mathematics,’ a designation which I, if I had the choice, would prefer to the customary ‘pure’ mathematics.”

These free-spirited developments in mathematics marked the beginning of the end for metaphysical influences on the direction of the mathematical imagination. Nothingness was unshackled from zero, leaving the vagueness of the void and the vacuum behind. But there were more surprises to come. The exotic mathematical structures emerging from the world of pure mathematics may have been conceived free from application to Nature, but something wonderful and mysterious was about to happen. Some of those same flights of mathematical fancy, picked out for their symmetry, their neatness, or merely to satisfy some rationalist urge to generalize, were about to make an unscheduled appearance on the stage of science. The vacuum was about to discover what the application of the new mathematics had in store for time and space and all that’s gone before. ~ Pages 165-166