212 RELATIVITY, THE GENERAL THEORYat that time that Riemann had studied the foundations of geometry in an even
more profound way. I suddenly remembered that Gauss's theory was contained
in the geometry course given by Geiser when I was a student. ... I realized that
the foundations of geometry have physical significance. My dear friend the math-
ematician Grossmann was there when I returned from Prague to Zurich. From
him I learned for the first time about Ricci and later about Riemann. So / asked
my friend whether my problem could be solved by Riemann's theory [my italics],
namely, whether the invariants of the line element could completely determine the
quantities I had been looking for' [II].
Regarding the role of Carl Friedrich Geiser,* it is known that Einstein attended
at least some of Geiser's lectures [K2]. Toward the end of his life, he recalled his
fascination with Geiser's course [S5] on 'Infinitesimalgeometrie' [E19]. Gross-
mann's notebooks (preserved at the ETH) show that Geiser taught the Gaussian
theory of surfaces.
I believe that this first encounter with differential geometry played a secondary
role in Einstein's thinking in 1912. During long conversations with Einstein in
Prague, the mathematician Georg Pick expressed the conjecture that the needed
mathematical instruments for the further development of Einstein's ideas might
be found in the papers by Ricci and Levi-Civita [Fl]. I doubt that this remark
made any impression on Einstein at that time. He certainly did not go to the
trouble of consulting these important papers during his Prague days.
Einstein's second statement on the July-August period was made in 1923: 'I
had the decisive idea of the analogy between the mathematical problem of the
theory [of general relativity] and the Gaussian theory of surfaces only in 1912,
however, after my return to Zurich, without being aware at that time of the work
of Riemann, Ricci, and Levi-Civita. This [work] was first brought to my attention
by my friend Grossmann when I posed to him the problem of looking for generally
covariant tensors whose components depend only on derivatives of the coefficients
-Sra,} of the quadratic fundamental invariant [g^dx^dx']' (my italics) [E20].
We learn from these two statements that even during his last weeks in Prague
Einstein already knew that he needed the theory of invariants and covariants
associated with the differential line element
'Geiser was a competent and influential mathematician who did much to raise the level of the math-
ematics faculty at the ETH [Kl]. His successor was Hermann Weyl.in which the ten quantities g^, are to be considered as dynamic fields which in
some way describe gravitation. Immediately upon his arrival in Zurich, he must
have told Grossmann of the problems he was struggling with. It must have been
at that time that he said, 'Grossmann, Du musst mir helfen, sonst werd' ich ver-
riickt!' [K2], G., you must help me or else I'll go crazy! With Grossmann's help,