Poincare famously said:
The art of mathematics is to give the same name to different things.
I confess to loving Ancient Indian mythology. Here is my maximally inverse statement:
The art of mythology is to give different names to the same thing.
Evidently I am not the first person to have said something like this. From Rig Veda 1.164.46:
The wise speak of what is One in many ways.
The Ancient Greeks promoted a “divide and conquer” mindset and studied bite-sized pieces (of the larger puzzle) in isolation. As such, much of modern mathematics and physics is rectifying this fallacious framework – short term thinking — by abstracting and searching for unity.
The Ancient Indians, by stark contrast, axiomatically presumed unity.
To make such abstraction accessible to the masses, and to children, they created mnemonics in the form of rhyming mantras and shlokas and developed elaborate stories with mythological beings as visual aids to communicate core principles, both for practical living as well as to speculate about one’s place in the Universe, and so, in my retelling – Sridhara Aranyaka 😏 – they constructed:
Mythology in Service of Mathematics.
For instance, in Satapatha Brahmana, ostensibly to aid in Vedic rituals (for which they needed precise astronomical calculations), and design optimal temple spaces – as if mathematics was serving religion when in fact it was the maximally inverse! – they developed geometry, and approximations for Pi, having, among other things, recognized that the earth is circular and that it revolves around the sun. This is around 700 BCE. Indeed, the observational astronomy mentioned matches with Babylonian Tablets, that record independent observations, indicating that they were also aware of what we now incorrectly credit Copernicus for discovering, the heliocentric framework.
Copernicus is not the only person who is improperly credited with an important discovery.
Indeed, as Manjul Bhargava (2014 Fields Medal) has said about Pythagoras:
One is the one that originates in 2,500 BC in Egypt. There’s no statement of the theorem anywhere, but there is some knowledge that seems to be indicated of it because there are (Pythagorean) triples (when the length of the three sides are whole numbers, such as 34, and 5). The first systematic systems of listing happens in the Plimpton tablets, which happen in about 1,800 BC (in Mesopotamia, or the modern-day Arab world). That shows a systematic understanding of producing solutions to that equation. That shows much more likelihood of knowledge of the Pythagorean theorem in a more general framework. But again there’s no written statement of the theorem.
In that sense, if you want hard scientific evidence, it’s accurate to say that the Pythagorean theorem was first (recorded) in India in about 800 BC.
One can go further than that — which is the standard that mathematicians often use — that while it’s nice to have the explicit statement but if there’s no proof well, then, maybe they (the ancient culture being studied) didn’t know it. The Shuba Sutras do contain proofs in some special cases and contain numerical proofs in general, but the first actual rigorous proof of the Pythagorean theorem that’s on record originates in China — after the Shuba Sutra. So in China in school textbooks they often call it the Gougu theorem. And that was first given in a Chinese manuscript some years later.
The Pythagoras theorem is clearly the wrong name; that’s clear. He (Pythagoras) clearly stated it way after it was stated in India. It is not clear that he proved it at all. From neither perspective — the statement or the proof — is the ‘Pythagorean theorem’ a correct name.
It should either be an Egyptian theorem if you look at the standard of just having an idea about it, an Indian theorem if you’re looking for a complete statement of it, or a Chinese theorem if you’re looking for the proof of it.
This crediting to Pythagoras and Copernicus of known ancient results has created a:
Modern Mythology of Mathematics.
Cultural appropriation? White-washing?
Stop the Steal. 🤷🏽♂️
I read this a while ago “Ancient Babylonian Tablet May Hold Earliest Examples of Trigonometry”, Smithsonian (August 2017) (1800 B.C.E.). Cheers, Kathy