I skimmed most of this because I can’t handle quote-dumps. I wanted to comment similarly on some of your earlier maths quote-dumps but since you said there that you were just trying to organise your thoughts, I assumed that you would convert more of the quotes into prose.
I’ve wondered what to do about this. I like the idea of quoting really good people verbatim at length because (a) they have more credibility than I do and (b) I feel a little squeamish about paraphrasing them for fear of skewing the truth.
Would appreciate more detailed suggestions here if you have any to offer.
On the post itself: The ‘beaver’ part kind of appears out of nowhere, I suggest putting more foreshadowing/summarising at the beginning.
Okay, right.
I’m also not sure I understand what a beaver does that’s different to the other groups. Frogs and birds seem to straightforwardly correspond to bottom-up and top-down thinking, or Sensing versus Intuitive in Myers-Briggs jargon. Beavering seems quite top-down to me.
As I said to ThomasR, my subjective impression is that there are examples both of bird/beaver hybrids and frog/beaver hybrids. Maybe there’s a bird vs. frog axis and an independent axis measuring beaver-likeness. There is something real that I’m trying to get at here, but I’ll have to think more about what it is.
Felix Klein may be seen as a “bird/beaver” hybrid, in view of the calculational view on complex multiplication and class fields in the 19th century, leading to modular equations etc. Klein’s “icosahedron” and Weber’s 3 vol. “Algebra” (the best until v.d. Waerden’s book and E. Noether’s school). link A more modern example may be this, but I know only a part of the story.
I’ve wondered what to do about this. I like the idea of quoting really good people verbatim at length because (a) they have more credibility than I do and (b) I feel a little squeamish about paraphrasing them for fear of skewing the truth.
Would appreciate more detailed suggestions here if you have any to offer.
Okay, right.
As I said to ThomasR, my subjective impression is that there are examples both of bird/beaver hybrids and frog/beaver hybrids. Maybe there’s a bird vs. frog axis and an independent axis measuring beaver-likeness. There is something real that I’m trying to get at here, but I’ll have to think more about what it is.
Felix Klein may be seen as a “bird/beaver” hybrid, in view of the calculational view on complex multiplication and class fields in the 19th century, leading to modular equations etc. Klein’s “icosahedron” and Weber’s 3 vol. “Algebra” (the best until v.d. Waerden’s book and E. Noether’s school). link A more modern example may be this, but I know only a part of the story.
Right, makes sense.
I just remember a very nice online docu on the Chudnovsky brothers, an old NY’er article , the “one mathematician in two brains”.