1898. It was commenced in January, 1891. The ideas in it were largely founded on Hermann Grassmann’s two books, the Ausdehnungslehre of 1844, and the Ausdehnungslehre of 1862. The earlier of the two books is by far the most fundamental. Unfortunately when it was published no one understood it; he was a century ahead of his time. Also Sir William Rowan Hamilton’s Quaternions of 1853, and a preliminary paper in 1844, and Boole’s Symbolic Logic of 1859, were almost equally influential on my thoughts. My whole subsequent work on Mathematical Logic is derived from these sources. Grassmann was an original genius, never sufficiently recognized. Leibniz, Saccheri, and Grassmann wrote on these topics before people could understand them, or grasp their importance. Indeed poor Saccheri himself failed to grasp what he had achieved, and Leibniz did not publish his work on this subject.
My knowledge of Leibniz’s investigations was entirely based on L. Couturat’s book, La Logique de Leibniz, published in 1901.
This mention of Couturat suggests the insertion of two other experiences connected with France. Elie Halévy, the historian of England in the early nineteenth century, frequently visited Cambridge, and we greatly enjoyed out friendship with him and his wife.
The other experience is that of a Congress on Mathematical Logic held in Paris in March, 1914. Couturat was there, and Xavier Léon, and (I think) Halévy. It was crammed with Italians, Germans, and a few English including Bertrand Russell and ourselves. The Congress was lavishly enter- tained by various notables, including a reception by the President of the Republic. At the end of the last session, the President of the Congress congratulated us warmly on its success and concluded with the hope that we should return to our homes carrying happy memories of “La Douce France.” In less than five months the First World War broke out. It was the end of an epoch, but we did not know it.
The Treatise on Universal Algebra led to my election to the Royal Society in 1903. Nearly thirty years later (in 1931) came the fellowship of the British Academy as the result of work on philosophy, commencing about 1918. Meanwhile between 1898 and 1903, my second volume of Universal Algebra was in preparation. It was never published.
In 1903 Bertrand Russell published The Principles of Mathematics. This was also a “first volume.” We then discovered that our projected second volumes were practically on identical topics, so we coalesced to produce a joint work. We hoped that a short period of one year or so would complete the job. Then our horizon extended and, in the course of eight or nine years, Principia Mathematica was produced. It lies outside the scope of this sketch to discuss this work. Russell had entered the University at the beginning of the eighteen nineties. Like the rest of the world, we enjoyed his brilliance, first as my pupil and then as a colleague and friend. He was a great factor in our lives, during our Cambridge period. But our
