I really liked Hermann Weyl's mathematical books and would like to get accustomed to general relativity from his perspective, but wonder if it's still relevant after almost 100 (!) years?
Can this book be used to actually learn something useful about GR or should it be read only as investigation of historical perspective? Won't it cause any misconceptions?

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    $\begingroup$ This briefly annotated list of books may be of interest. Weyl's book is mentioned, but probably too briefly to be of any use for your actual question. William O. Straub's web pages about Weyl's work might also be of interest. Finally, you might try contacting John Baez with a short email having a very specific and non-spam looking subject. $\endgroup$ Oct 12, 2020 at 12:37
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    $\begingroup$ @DaveLRenfro thank you for the small research ^^ ! Well, William O. Straub's page pretty much convinced me this book is definitely worth reading and shouldn't have any misleading concepts. It even has notion of some modern *gauge invariance principle"! $\endgroup$
    – Slaus
    Oct 12, 2020 at 21:54
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    $\begingroup$ A co-lateral remark: I warmly recommend the 2 bilingual volumes (German+its French translation by Audureau and Bernard) "Mathematische Analyse des Raumproblems / L'analyse mathématique du problème de l'espace" (Presses Universitaires de Provence, 2015) which is a transcription of lecture notes of conferences given by Hermann Weyl in Barcelona in 1922, i.e., a year before. It's crystal clear.... $\endgroup$ Nov 1, 2020 at 22:32

1 Answer 1


It's not a book of physics per se, but a book on metaphysics, that is meta-physics, where the term means on or about physics. It's a general disquisition on the most general notions that physics contemplates: space, time and matter.

In fact, Aristotle had a similar division in his book on metaphysics. Having looked at both, I would say that Aristotle is the easier read. But then again, Weyl was not noted for his literary style, whereas Aristotle was: how one writes is important if one is to be understood by both the few and the many.

If you want to read a more upto date work on similar material and with a similar slant, try Space, Time & Matter, ed. Majid with contributions from Polkinghorne and Connes and others.


@slaus: Try reading my answer again to understand what I'm saying ...

@slaus: It's strange that you say that Weyl's book mentions gauge, since, although Weyl was in part responsible for it; it's not mentioned in the book - which perhaps is not entirely surprising since it took around 50 years for the notion to be understood fully and Weyls book was first published in 1921.

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    $\begingroup$ Hm, I don't think I grappled the notion of Aristotle in terms of this book. I'm 'quarter'-through this book and Weyl defines vectors, tensors, gauges, etc. to describe space curvature which redefines objects homomorphisms compared to flat euclidean space. I didn't yet notice much philosophy in it. Aristotle, on the other hand, states that everything is either fire/earth/water/air; planets(+moon+sun) are perfect spheres; resistance to motion; and basically wasn't aware of most of his days mathematics. Are we sure we talk about the same book here? ^^ $\endgroup$
    – Slaus
    Nov 13, 2020 at 11:32

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