From the outset, keeping the journal up and running was to prove a challenging task.

It was edited under the new title by James Joseph Sylvester and Norman Macleod Ferrers, assisted by George G. Stokes and Arthur Cayley, with Charles Hermite as corresponding editor in Paris, an arrangement that remained stable for the first fifteen volumes.

Thus, by the twenty-eighth volume in 1896, Glaisher, who had edited Messenger of Mathematics single-handedly since its inception in May, 1870, was also left as the sole editor of the Quarterly.

It came to be felt that these periodicals had become so identified with Glaisher that it would be awkward to attempt to continue them after his death (in 1928).

In the mid-1920s, this led G. H. Hardy to push for two new titles, the Journal of the London Mathematical Society and The Quarterly Journal (Oxford Series); Hardy was then secretary of the London Mathematical Society and Savilian Professor of Geometry at the University of Oxford.