I was flabbergasted when I first read Augustus De Morgan’s writings about negative numbers1. For example, in the Penny Cyclopedia of 1843, to which he contributed many articles, he wrote in the article Negative and Impossible Quantities:Wallis and Newton had fully accepted negative numbers by 1685.It is not our intention to follow the earlier algebraists through their different uses of negative numbers. These creations of algebra retained their existence, in the face of the obvious deficiency of rational explanation which characterized every attempt at their theory.In fact, he spent much of his life, first showing how equations with these meaningless negative numbers could be reworked so as to assert honest facts involving only positive numbers and, later, working slowly towards a definition of abstract rings and fields, the ideas which he felt were the only way to build a fully satisfactory theory of negative numbers. On the other hand, every school child today is taught in fourth and fifth grade about negative numbers and how to do arithm
Closely related is the discovery of zero.
It is repeated everywhere that the Indians invented zero and place notation and that the Arabs learned it from them and later transmitted this to Europe. It’s bizarre that such a misunderstanding should be widespread but in fact, the Babylonians invented place notation (albeit using base 60) and their arithmetic was used by many Greeks, e.g. Ptolemy. I hope I have made the case that the most substantial arithmetic discovery of the Indians – and independently the Chinese – was not merely that of zero but the discovery of negative numbers. Sadly this discovery was not absorbed in any but a superficial way by the Arabs.His essay has examples of famous mathematicians being leery about negative numbers. Also imaginary numbers, infinities, and other constructs.
I am not sure how well these are accepted today, outside of Mathematics. If you read the business section of the newspaper, a company's loss is just a negative profit, but the articles hardly every express it that way.