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Mathematics in India

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32 pointsdedalus11 comments

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.)

They're short for different phrases.

"How many times does 2 go into 20" is 20/2, which is shortened to "2 into 20".

"20 divided by 2" is also 20/2, which is shortened to "20 by 2".

I'm not sure how either term is used in the case of multiplication however but I'm pretty sure that's how the division side of it works.

>I'm not sure how either term is used in the case of multiplication

(I grew up in India.) I imagine it was just "multiply 2 into 10" that got shortened into "2 into 10", and then "2 into 10" by itself became a noun that represents the product, so "What is 2 into 10? 2 into 10 is 20."

This discussion [1] seems to point to similar usage by British sources in the 1600s and 1700s.

1. https://english.stackexchange.com/questions/515089/saying-in...

Grew up in India. As the sibling commenter notes, this is likely an older British expression that has survived in Indian English.

It's hard to remember now, but I think the way I thought about it when I was taught is that "3 × 4" is combining 3 and 4 into a larger number 12. The "3 ÷ 4" was not special, and "by" there was just an abbreviation of "divided by" like you say.

For what it's worth, I think times usually should work in Indian English as well, as in "3 times 4" for 3 × 4.

We usually say "three fours are twelve"

Instead of "three times four is twelve"

Yep, that's true — but I think an oral question would be phrased as "What is three times four?", correct?

Yes, it could be phrased like the above, but from what I have experienced in day to day school life, people usually ask "What's three into four?" or even more likely an incomplete fill in the blank question "Three fours are?"

It's a British anachronism and also a translation thing.

"Teen ko Char se divide khar do"

Divide 3 by 4

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.

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