Duncan F. Gregory and Robert Leslie Ellis: second-generation reformers of British mathematics

The paper discusses some of the contributions of Duncan Farquharson Gregory and Robert Leslie Ellis to symbolical algebra and their views on the philosophy of mathematics with the aim of revisiting the accepted characterisation of the second generation of reformers of British mathematics found in Crosbie Smith and Norton Wise’s seminal Energy and Empire. It is argued that at least some of the features brought to the fore in their treatment of the work of Gregory and Ellis – namely “geometrical methods” in mathematics and “anti-metaphysical”, “non-hypothetical” and “practical” knowledge – cannot be straightforwardly upheld. On the one hand, Gregory’s generalisation of George Peacock’s symbolical algebra was connected to several natural philosophical considerations underlying the Scottish Newtonians’ “abstractionism” and “geometrical fluxional analysis”. On the other hand, Ellis’s idealist philosophy of mathematics and science insisted that the a priori necessary truths of mathematics could inform the “hypothetical part of scientific induction”. A more nuanced understanding of the place of the second generation of reformers within the analytical revolution in Victorian Britain should thus take into account the eclectic foundational position that arises from the work of Gregory and Ellis.