(no subject)

[sigmaleph]

Unrelated history-of-mathematics observation: Apparently for a pretty long time it was a fairly widespread view that 1 isn't a number (see this pdf about historical answers to the question of what the first prime number is, arguing that often the question of whether 1 is prime doesn't even come up, because the author in question doesn't even think 1 is a number). And by "a pretty long time" I mean up to the 16th century and among both European and Islamic mathematicians.

In some sense one can see the appeal (it's even preserved in idiomatic expressions! If I say something is true for "a number of reasons" I don't mean to include the possibility of the number being one) and ultimately it's a choice of definitions and presumably they wouldn't argue that the expression "2+1=3" is nonsense because I'm adding a non-number to a number. Still, it sounds so weird in a modern context. The obvious argument I'd make would be something about fractions, but presumably the relevant notion of 'number' is about natural numbers.

how people used to think about math is fascinating and kinda weird