The Dustbin of History, or How the Infinity Symbol Came Into Existence
John Wallis (1616-1703) possessed no knowledge of the mathematical arts at the age of fifteen, yet he later went on to become the Savilian professor of Geometry at Oxford, the friend and teacher of Isaac Newton (he was the first to charge that Leibnitz had stolen his ideas for the calculus), and a charter member of the Royal Society. Yet his place in the history of mathematical thought is, perhaps not unjustly, obscure (and oftentimes, simply, ignored). A list of his major formulations would serve, merely, as an esoteric series of footnotes to the said compilation, which would interest, it should be stated, rather few.
For example, Wallis discovered that, in all such operations, it was mass times velocity (mv) that was conserved and not, as it was widely held, merely velocity (v). However, he fell short of unsecreting the laws of motion (which Newton would later publish). He also, at one time, theorized “that for the purposes of calculation, the earth and moon can be treated as a single body, concentrated at their center of gravity …” but stopped short far short of formulating the basis for the Laws of Universal Gravitation.
It can also be noted that Newton borrowed his system of fluxional notation (in which the fluent of was represented by , and the fluent by and so on) yet this, too, was swept into the dustbin of history when it was later replaced by that system developed by Leibnitz. His significant work still owed a heavy debt to the Greeks and the most notable of these was Arithmatica Infinitorum sive Nova Methodus Inquirendi in Curvilineorum Quadraturam aliague difficilora Matheseosos Problemata (1673), which is more often recalled for its title rather than for the fact that it introduced to mathematics the idea of ‘limit’.
It is often opined that a man might fulfill the secret purpose of his existence in the doing of a seemingly trivial deed such as a word said in passing or, perhaps, an action not acted upon (the significance of which, more often than not, is forever hidden from the from the doer). In the case of John Wallis it can be said that he, quite possibly, achieved his destiny with the few simple strokes of his quill with which he, in 1656, modified a Roman variation for 1000.
This was to serve him simply as the notation for a very small quantity, but, in centuries to come, was to serve the world as the symbol (and signature) of INFINITY: