I've seen several citations of a letter from Weierstrass, talking about his dispute with Kronecker, in which he refers to Christoffel as a 'whimsical eccentric' (presumably the German original is even more flavorful). In what respect was he whimsical or eccentric?


One reference is Barrow, 'Pi in the Sky,' page 200, quoting the letter from Weierstrass. Was Christoffel generally nutty, or was Weierstrass just citing his support for Kronecker?


The Google translation of the German helpfully supplied by Suvrit is:



> 
> When a strange fellow as Christoffel says that in 20-30 years the
>  current function theory is carried to the grave and the whole analysis
>  to be worked out in the theory of forms, so you answered that with a
>  shrug.
> 
> 
> 


Subquestion: what does he mean here by 'die Theorie der Formen' here?



How was Christoffel a 'whimsical eccentric'?
(a) "Kauz" is literally a "brown (or tawny) owl," colloquially a "queer (or strange, familiarly a 'rum') fellow" (Muret-Sanders German-English Dictionary); certainly a more pungent expression than "whimsical eccentric," but not as dismissive as "crank" or "crackpot"; a rather precise English colloquial equivalent is "an odd duck."


(b) To illustrate that this is an apt characterization of Christoffel, cf. the opening sentence of a paper of his of 1888, "Lehrsätze über arithmetische Eigenschaften der Irrationalzahlen" (see his *Gesammelte mathematische Abhandlungen,* vol. 2, p. 216): "Da die Irrationalzahlen demnächst abgeschafft werden sollen, scheint es mir nicht unbillig, doch noch einmal zu erwägen, ob das, was bis auf heutigen Tag über diesen Zahlen ans Tageslicht gekommen ist, wirklich von solcher Art is, dass ihnen nunmehr die Existenzberechtigung aberkannt werden muss." ("Since the irrational numbers are about to be got rid of, it seems to me not unreasonable to consider yet once again whether what has come to the light of day up to now about these numbers is really of such a kind that from now on the right to exist must be denied them.")


(c) Although Christoffel doesn't name names in this statement, it seems rather clear that his reference is to Kronecker.


(d) To underscore his character as an odd duck: the aim of this paper is to present what Christoffel regards as the *first ever* account--the first ever discovery--of "genuinely arithmetical" properties of the irrational numbers; and by doing this, to establish that they *have* the right, not merely to exist, but to be regarded as *genuine numbers.*


(e) From this I conclude further that the remark Weierstrass ascribes to Christoffel was most probably made by the latter sarcastically (although Weiserstrass may not have recognized this); the "forms" C. refers to had, I should think, nothing to do with the Christoffel symbols in Riemannian geometry, but with the *algebraic* forms that play a central role in Kronecker's theory of algebraic numbers: Christoffel does not think Kronecker's algebraic methods will succeed in eliminating the real numbers.


