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Michael J. Barany @MBarany
, 9 tweets, 2 min read Read on Twitter
The specific answer to this question is well beyond my expertise. However, I'd like to abuse the invitation and offer (yet) another little twitter thread about historical expertise and the history of mathematics.
A) historical expertise is a form of professional knowledge, which means often the answer to a question is "I know whom I'd ask if I really needed to know."
In this case, my first turn would be to Jens Hoyrup
A ctd.) Hoyrup knows the right range of primary and secondary sources to give one of
i) a specific answer (unlikely);
ii) an idea of where a specific answer might be found (more likely); or
iii) a good explanation of why it's a malformed question (most likely)
B) why is it most likely it's a malformed question? Because posing robust historical questions requires expertise. It's one of the main challenges one confronts as a history grad student, usually with lots of help from mentors.
In this respect, history and math are similar.
B ctd.) you don't expect amateur mathematicians or even beginning grad students to come up with well-posed research questions, and it's the same in history.
Corollary: questions with yes/no or number answers are often not well posed, in both math and history
B ctd.) That's because *having an answer* and *having a meaningful answer* are two very different things. A question should be something whose answer (or unresolved process of answering) tells us something significant.
C) one reason professional historians haven't spent a lot of time updating Cajori's antediluvian opus on math notation isn't because it's a rock solid reference (it's littered with errors); it's because "firsts" in math notation are rarely sources of historical insight.
C ctd.) rarely doesn't mean never. But the best studies of notations (including by Hoyrup and many others) always use them as a way of answering big questions about mathematical methods, contexts, and implications.
D) So we should ask (as some replying to @stevenstrogatz have asked already): what are the stakes of linking certain parts of certain alphabets to certain kinds of mathematical reasoning?
And that's where I'll have to leave it for today.
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