"The introduction of numbers as coordinates is an act of violence." - Hermann Weyl.
A lot of people like this quote, apparently. They also seem to associate it to the manifold context in the obvious way: they interpret the quote as saying that focusing on coordinate charts is insightless, or at least dry. Although I aggree with this, I feel like the way the quote is phrased is not inclined to that interpretation. If not by the fact that Weyl is connected to geometry (and that this quote is in Bredon), I would interpret this phrase as saying that "Representing numbers by a given basis is insightless and can lead to mistakes, like thinking that divisibility is dependent of the number basis you are using." I think the words numbers and coordinates are strangely placed.
Therefore, my question is: What was the precise context on which this quote arose and, if possible, can we pinpoint exactly what did Weyl mean?