It’s taking me all day to read this thread. Lockhart’s Lament is interesting, but it lambasts the traditional math curriculum in favor of dreamy ideals. Not exactly the touchy feely approach, maybe, but it could be taken that way. His blast at Geometry is particularly disconcerting. I guess he’s just trying to make a point.
I did learn of Gauss’s “notions vs. notations” quote and tracked it down to an online edition of the Disquisitiones Arithmeticae ( linked by Wikipedia. ) I wondered what the Latin might be. Well, it’s “notionibus” and “notationibus”. I believe this is the “ablative of means” applied to “notio” and “notatio”. So that was interesting.
OMG
Ablative has reached the data of FR!