  The 19th century opened in England with mathematics in the doldrums. The English mathematicians had feuded with the continental mathematicians over the issues of priority in the development of the calculus, resulting in the English following Newton’s notation, and those on the continent following that of Leibniz. One of the obstacles to overcome in updating English mathematics was the fact that the great developments of algebra and analysis had been built on dubious foundations, and there were English mathematicians who were quite vocal about these shortcomings. In ordinary algebra, it was the use of negative numbers and imaginary numbers that caused concern.  