numbers, the infinitesimal calculus, and the branches of geometry. Russell was
importing a German mathematical movement to Britain; his work followed up
Felix Klein’s Erlangen program to unify geometry, and Hilbert’s still broader
program of axiomatic unification. In the process, Russell independently created
much the same logic of sets as Frege. This is no surprise; both of them were
in the same faction in the mathematical foundations conflict, allied with
Cantor. The two branches of the movement toward axiomatization—the route
through rigorization of analysis and geometry on the Continent and the route
through elementary algebra in Britain—now converged.
Just as W. R. Hamilton had gotten credit for quaternions while Grassman
was relatively ignored in Germany, Russell reaped the initial fame while Frege
languished. This happened because algebra and elementary arithmetic were
much more central in British mathematical interests than they were on the
Continent, where the main action was in the more elaborately developed
“advanced” fields. Peirce, who paralleled Frege during the 1870s in developing
FIGURE 13.2. BRITISH PHILOSOPHERS AND MATHEMATICIANS,
1800–1935: UNIVERSITY REFORM, IDEALIST MOVEMENT,
TRINITY-BLOOMSBURY CIRCLE710 •^ Intellectual Communities: Western Paths