Thats a tough one.
We cant point to how it was discovered, but it was kinda around ever since humany began, we just didnt have a name for it, or an explanation.
The earliest known mention of a multiplication table was about 2000 BC, when a Babylon tutor got tired of explaining the shit, and started making clay tablets of multiplication tables.
Now, they used a base 60 system, so their math was kinda weird compared to ours today.
Aound 300 BC, a chinese tutor wrote down a base 10 multiplication table, the system we use today. Thats the first real example of our modern math we have.
It was invented, more recognized. If i have 2 apples, and 3 other people have 2 apples, our community has 6 apples to share. It predates any form of writting we have, and it wasnt until we transitioned from hunter-gathering to an agricultural society that people started to think, discover, and advance beyond basic survival
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