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While I was devouring books on Riemann, I learned that Weyl had reviewed on several of Riemann's papers (I can't remember exactly what book it was, but it was probably John Derbyshire's Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics), including his 1854 Habilitation, and I was very curious about this reviews and visited many sites for find it, but I kept failing to find it.

Therefore, I ask where I can find Weyl's reviews on Riemann's papers.

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  • $\begingroup$ Did you look for it in Weyl's Gesammelte Abhandlungen? $\endgroup$ Commented Nov 7 at 7:33
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    $\begingroup$ Derbyshire mentions Weyl only three times in the book and not once in connection with Riemann. I am not sure that "Weyl's reviews" exist as such, but he does review Riemann's ideas from On the Hypotheses Which Lie at the Foundations of Geometry (1854) in Space, Time, Matter, § 11, p.133ff. $\endgroup$
    – Conifold
    Commented Nov 7 at 8:08

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It's hard to know what exactly is sought here, but it is possible that the correct answer is Weyl's commentary of an edition of Riemann's Hypothesen with Springer in 1919, which he edited, which runs pp 24-47:

  • Riemann, B. (1919) Über die Hypothesen, welche der Geometrie zu Grunde liegen, (ed. Weyl, H.), Springer.

One can find some notes about revision of the commentary on p.60 of:

  • Scholz, E. (Ed.). (2001). Hermann Weyl’s Raum-Zeit-Materie and a general introduction to his scientific work. Springer.

This source incidentally contains interesting discussion of the possible roots of Weyl's perspective on Riemann coming from the influence of Klein.

Another worthwhile historical discussion of Weyl's work relating to Riemann can be found in (in German):

  • Frei, G., & Stammbach, U. (1992). Hermann Weyl und die Mathematik an der ETH Zürich, 1913–1930. Springer-Verlag.

There is no doubt that Weyl was deeply read into Riemann's work and in fact his first few books are all on the topic. There is a chance that by review even his whole first book could be meant:

Frei and Stammbach describe the book as follows:

Im Frühjahr 1913 hatte Weyl sein epochemachendes Buch Die Idee der Riemannschen Fläche abgeschlossen, in welchem diese Theorie erstmals "eine den modernen Anforderungen an Strenge genugende Behandlung" erfuhr.

Certainly an "epochmaking exposition to modern standards" could be viewed as a review of sorts.

(As a side note: A substantially more modern source for commentary on Riemann's Hypothesen is Jost's 2013 edited edition with Springer (English translation: Birkhäuser in 2016)., which includes very extensive commentary, substantially exceeding those of Weyl.)

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