For anyone interested, this 2-volume series is gold. The first volume deals with numerals and arithmetic, and the second with algebra, linear equations, quadratic forms, solutions to pell's equations, etc.
https://archive.org/details/historyofhindumathematicsbhibuti...
My grandfather used to tell me what was written was known for centuries prior but handed down by word of mouth, all memorised by sages. It was only written down at a later date which became the point used of discovery for historians.
Here’s something I’d like to figure out, when, how and why it happened.
India has got “by” and “into” back to front: that is, they say “by” means division and “into” multiplication, whereas places like Australia and the USA have “by” meaning multiplication and “into” division.
I’ve confirmed this inversion with current students and with a retired chemistry teacher in his late 70s in Hyderabad, and with a man in his 30s in West Bengal.
If you ask WolframAlpha “3 by 4”, you get: “Assuming "by" is Times | Use Divide instead”. Ask it “3 into 4”, and you get: “Assuming "3 into 4" is referring to arithmetic | Use as a math function instead” and it does division (and the math function offered is `QuotientRemainder[4, 3]` which returns `{1, 1}`).
(Not sure if there’s an intrinsic reason to prefer either assignation. Full forms are commonly expressed “divided by” and “multiplied by”, and if “by” is just an abbreviation, &c. &c. Then there’s “of” which feels more definitely context-dependent: “paint three of the four albino elephants” is division, “I want three of those asbestos-plated helberds” is multiplication.)