  Einstein identified singularities in spacetimes, such as at the Schwarzschild
radius, where later relativists only find a coordinate system assigning
multiple values to a single spacetime event. These differing judgments derive
from differences in mathematical methods. Later relativists employ geometrical
structures to correct anomalies in the coordinate systems used in analytic
expressions. Einstein took the analytic expressions to be primary and the
geometrical structures as mere heuristics that could be overruled if physical
assumptions required it. Einstein's non-geometric methods had a firm base in
the history of mathematical methods. They continued the non-geometric
orientation of Christoffel, Ricci and LeviCivita. Einstein's insistence that
singularities must be eliminated marked a departure from earlier tolerance of
singularities. It was founded upon his longterm project of eliminating
arbitrariness from fundamental physical theories. However, Einstein was willing
to theorize with singularities only temporarily if they were the least
arbitrary approach then available.
