INITIAL ENTRIES INTO FOUNDATIONAL STUDIES
Mathematics occupied a controversial place in Cambridge in the late nineteenth-century: the Tripos was being roundly criticised as a mere set of skills, and yet it must have helped the university to gain a high reputation in applied mathematics. Alfred North Whitehead (1861–1947) started off in this branch after graduating from Trinity in 1884, being quickly elected to a college Fellowship with a dissertation on Maxwell's theory of electromagnetism. Further work drew him to the algebraic methods of the German mathematician Hermann Grassmann, which he popularised in a large book called A Treatise on Universal Algebra, with Applications (1898). The title was a misnomer, in that no one algebra was presented but instead a range of them, including also George Boole's algebra of logic.
Pure mathematics at Cambridge was rather boring, with excessive emphasis laid upon linear algebras due to Professor Arthur Cayley, and rather routine treatments of the calculus and analysis. Bertrand Russell (1872–1970) took the Mathematics Tripos from 1890 to 1893 (with Whitehead as one of his tutors), but then abandoned the subject in disgust and moved over to philosophy. He united these two trainings in an attempt to find a foundations for mathematics, starting with a Trinity Fellowship dissertation in 1895 which he revised into the book An Essay on the Foundations of Geometry (1897). His philosophical training lay in the neo-Hegelian tradition then dominant, which he exercised with skill; but the results for mathematics were not satisfactory.