Vladimir Arnold is known, among other things, for offering a scathing critique of Bourbaki:


[The Arnold – Serre debate](https://mathoverflow.net/questions/153604/the-arnold-serre-debate)


Recently I've been reading some Nietzsche, and he chides some Germans in the wake of the Franco-Prussian War for triumphantly proclaiming that the English and French might have civilization, but we have culture.


Inspired by reading this, I'm wondering if there are any critiques by 20th century German mathematicians of Bourbaki out there?



Reference request: any 20th century German critiques of Bourbaki?
It seems to me that German-(speaking) mathematics at the advent of Bourbaki was primed to be, by and large, comfortable with trends towards axiomatization, abstraction, and structure theory in the footsteps of Hilbert and with the successes of abstract algebra in the Goettingen school around Emmy Noether and van der Waerden. See Alten et al "[4000 Jahre Algebra" Springer](https://www.springer.com/gb/book/9783540855514), 2003 (in German).


There was some engagement around the question of reforming pre-university eduation in the late 60s and 70s. In his 1965 book "[Mathematik als Bildungsgrundlage](https://www.amazon.de/Mathematik-Bildungsgrundlage-German-Herbert-Meschkowski/dp/3663033694)" (Mathematics as foundation of education"), Meschkowski dedicates a chapter titled "Bourbaki in der Schule?" (Bourbaki in schools?) to the question of ideas of Bourbaki (here primarily the advocacy of Dieudonne) making it into highschool education. While there is some critique (particularly the idea of replacing Euclidean geometry with vector spaces), it is nuanced and overall quite positive.


Carl Ludwig Siegel has been mentioned. As an addition to what has been said, I'd warn against reading his rejection of abstraction in algebra as a reaction against French mathematics. Siegel's 1959 letter to Weil give more context:



> 
> It is entirely clear to me what circumstances have led to the inexorable decline of mathematics from a very high level, within about 100 years, to its present nadir. The evil began with the ideas of Riemann, Dedekind and Cantor, through which the well-grounded spirit of Euler, Lagrange and Gauss was slowly eroded. Next the textbooks in the style of Hasse, Schreier, and van der Waerden, had further a detrimental effect upon the next generation of scholars. And finally the works of Bourbaki here provided the last fatal shove.
> 
> 
> 


Notice how the mentioned drivers of Siegel's perceived "decline", namely Hasse, Schreier and van der Waerden as well as Riemann, Dedekind and Cantor are all German or German-speaking. (See Grauert's "Wie Gauß die alte Göttinger Mathematik schuf" in "[Proceedings of the 2nd Gauss Symposium, 1993](https://www.degruyter.com/viewbooktoc/product/144060)". Relevant quote is also cited in these more [accessible German](https://books.google.com/books?id=EEWLoVnoUMsC&pg=PA26&lpg=PA26&dq=Hasse,%20Schreier%20and%20van%20der%20Waerden&source=bl&ots=IzNT1Piz3Q&sig=ACfU3U0FqE8zMOxsECnPB1zz-2YGNQbnpw&hl=en&sa=X&ved=2ahUKEwilv_3EnojkAhUCXawKHQt3DnkQ6AEwAXoECAkQAQ#v=onepage&q=Hasse%2C%20Schreier%20and%20van%20der%20Waerden&f=false) and [English translated](https://books.google.com/books?id=3UBZDwAAQBAJ&pg=PA190&lpg=PA190&dq=van%20der%20Waerden%20schreier%20hasse%20siegel&source=bl&ots=9GJAtFAqCU&sig=ACfU3U1vQuqD2pZJtBIDktYPzpSwLnkHxQ&hl=en&sa=X&ved=2ahUKEwinyY2ZoojkAhUGd6wKHQLoApgQ6AEwC3oECAkQAQ#v=onepage&q=van%20der%20Waerden%20schreier%20hasse%20siegel&f=false) sources.) Grauert incidentally, citing this very letter to Weil, advocates for a nuanced view of Siegel in the letter to the editor linked by ThiKu. I encourage reading the letter (which isn't that long) in full.


