I once read that Hilbert and Hurwitz (I think it was them) once discussed the theorem about unique factorization of ideals/divisors in algebraic number fields in one of their walks. They, the story went, considered both Dedekind's proof of this and Kronecker's proof of this, and concluded they were both ugly.
Does anyone know where I might have read this? Is there an actual source confirming it?
Otto Blumenthal, "Lebensgeschichte." In: David Hilbert Gesammelte Abhandlungen, Vol. 3, Berlin: Springer 1935, pp. 388-429. On p. 397:
Auf den Spaziergängen mit Hurwitz wurden Kroneckers und Dedekinds Arbeiten eingehend besprochen. Hilbert erzählte später drastisch: „Einer nahm den Kroneckerschen Beweis für die eindeutige Zerlegung in Primideale vor, der andere den Dedekindschen, und beide fanden wir scheußlich“.
[Google translation with my modifications]: During the walks with Hurwitz, Kronecker's and Dedekind's works were discussed in detail. Hilbert later said dramatically: "One of us presented Kronecker's proof of the unique decomposition into prime ideals, the other presented Dedekind's, and we found both of them hideous."
