For more than 3,000 years, questions concerning the nature of mathematics and mathematical entities have engaged the attention of countless philosophers. Nevertheless, in Britain the difficulties encountered in attempting to answer these questions never affected the general understanding of the value of mathematics, which in the nineteenth century remained very much as John Dee and John Wallis described in the sixteenth and seventeenth centuries – namely, as being essential for dealing with practical problems concerning multitude and magnitude, and for formulating theories concerning the natural world. Britain was therefore not well-placed to absorb a highly abstract, non-utilitarian view of pure mathematics that had arisen on the Continent. Attempts were made by its supporters to make this view acceptable, but they were unable to make much headway because a discipline having no practical value was competing with very successful science. It was only the arrival of the aesthetic tendency in the 1870s that gave pure mathematicians a persona that could become acceptable, for they were no longer competing with science, but had become creators and contemplators of the beautiful.