The Babylonians used Pythagorean ideas long before Pythagoras

https://www.economist.com/science-and-technology/the-babylonians-used-pythagorean-ideas-long-before-pythagoras/21803301

154 74 5 years ago

Expounded in modern publication since at least Weisheit und Wissenschajt: Studien zu Pythagoras, Philolaos, und Platon (1962)

hdjjhhvvhga2• 5 years ago

Previous discussion: https://news.ycombinator.com/item?id=28062020

dang• 5 years ago

Thanks! Macroexpanded:

Australian mathematician discovers applied geometry on 3,700-year-old tablet - https://news.ycombinator.com/item?id=28062020 - Aug 2021 (11 comments)

ArtWomb• 5 years ago

Next up: the shocking discovery of a Vedic interpretation of quantum chromodynamics ;)

https://www.sanskritimagazine.com/vedic_science/quantum-mech...

rishikeshs• 5 years ago

hdjjhhvvhga2• 5 years ago

I believe sites like these do a disservice to the ancient knowledge of Hindu people. There were many important discoveries, some unknown to the West for centuries, and still not having enough exposure (when you read math books, they start with Greeks, then maybe they gloss a bit over al-Khwarizmi and then jump right into the 17th century to all big names, as if nothing was happening for over a thousand years - well, a lot was going on, just not in Europe).

However, some people exaggerate in the other direction, I'm not sure if this is just a Hindu thing or a more global phenomenon, but there is a limit of what you can explain using Vedas, at least as far as science is concerned. (Metaphysics is something different, but this a completely different discussion.)

Xplune132• 5 years ago

I agree. As an Indian it is just sad that there are people that do this. The effect of such articles is actually the loss of faith in the real findings of those ancient people caused by exaggerated claims presented in these articles.

There are so many actual great things and findings written in those texts, but it seems like people are either in the ship of "Everything is in Vedas" or "All this isn't worth researching". The lack of interest in researching these ancient texts caused by these 2 extreme sides is disheartening.

Falandafa2021• 5 years ago

Peter kingsley talks about this in both reality and a story that will pierce where you dive deep into the hidden connection between Pythagoreans and mystical traditions leading back to the mountains of Tibet.

The teachings of Falan Dafa also discusses this claiming that the earth and human civilizations has gone through cycles of destruction and renewal with the last period occuring in the time of the ice age where a small surviving group of mystics in Tibetan mountains managed to survive which matches up with the flood stories across cultures and recent scientific discoveries outlined by people like Graham Handcock.

throw135795• 5 years ago

A lot of math theorems might have been stolen / 'appropriated' from here: https://en.wikipedia.org/wiki/Kerala_school_of_astronomy_and...

8note• 5 years ago

The last sentence reads like a joke about how his equation was improved by Dirac to consider the speed of light

codekilla• 5 years ago

Yes, but the point is the approach to proof (proving this for all cases) that represented a paradigm shift in mathematics, largely attributed to Thales.

sn41• 5 years ago

The earliest known proof of Pythagorean theorem is due to Euclid. It is strange at all that any credit is attributed to Pythagoras, since Babylonians, Egyptians, Indians and Chinese all had discovered this [1]. And Pythagoras did not prove his theorem, to the best of our knowledge.

[1] https://en.wikipedia.org/wiki/Pythagorean_theorem#History

ttyprintk7• 5 years ago

Also weird that (more generally) Euclid is only rarely mentioned by name, and more often nearly anonymously as the author of Elements. Yet, Pythagoras is named early and often.

jules2• 5 years ago

How would one discover the Pythagorean theorem without having a proof?

ttyprintk7• 5 years ago

I think this is the most important point modern readers need to make.

If we discover a proof earlier than Thales, regardless of whether it’s Greek, we might revise the discovery of trig. But this is about certain triples being used practically in Babylon (who recorded everything) without any recorded interest in the relationship between triples.

Because Greeks first recorded the important part —- the proof —- I think it’s factual and not at all offensive to refer to Ancient Greek culture as influential in that recorded innovation in geometry.

I’ve seen a movement to broadly give credit to other cultures for Pythagoras, but knowing about triples is just not enough to say that they promoted innovation leading to trig.

babesh4• 5 years ago

I think that there are several ideas that are both powerful and that people muddle when they talk about mathematics. Also the talk is often tinged with cultural pride.

The ideas are conceptualization, generalization, and rigor.

The Pythagorean triples are a conceptualization that for certain right triangles, the squares of the three sides obey a relationship.

The Pythagorean theorem is both 1. a generalization that that would be the case for all right triangles and 2. rigorously proved it. Furthermore, at least for the proof in The Elements, it was axiomatic rigor, proving this via a chain of logic starting from base concepts.

Now to the cultural pride aspect. Many cultures came up with concepts in mathematics. Many cultures generalized. Many cultures were rigorous.

The argument is/should really be that the Pythagorean theorem is on the far end of the rigorous, generalization axis. The better argument actually is that The Elements is.

My personal take is that the Pythagorean theorem isn't, at least in the long span of mathematics history, an exemplar of conceptualization.

And yes, there is some overlap and ambiguity with these ideas and you can argue about where the boundaries lie but I don't think we gain that much from that.

If people don't think that other cultures conceptualized, generalized, and were rigorous, just look at The Art of War, Bhagavad Gita, etc...

thaumasiotes4• 5 years ago

this is about certain triples being used practically in Babylon (who recorded everything)

The difference isn't that Mesopotamia generated more records than other cultures. It's that Mesopotamian records become practically indestructible when burned.

(This didn't help much in Babylon itself, which didn't burn.)

throw135795• 5 years ago

The Hindu mathematicians Baudhāyana certainly discovered the theorem before Pythagoras [1] and Bhāskarāchārya independenly proved the theorem [2] (though the latter seems it was after Pythagoras).

It is also possible to discover mathematical truths without providing a formal proof. Indian mathematician Srinivasa Ramanujan "independently compiled nearly 3,900 results (mostly identities and equations). Many were completely novel; his original and highly unconventional results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and inspired a vast amount of further research. Of his thousands of results, all but a dozen or two have now been proven correct." [3]

The mathematical statement versus rigorous proof was also a cultural difference: "Their collaboration was a clash of different cultures, beliefs, and working styles. In the previous few decades the foundations of mathematics had come into question and the need for mathematically rigorous proofs recognised. Hardy was an atheist and an apostle of proof and mathematical rigour, whereas Ramanujan was a deeply religious man who relied very strongly on his intuition and insights." [3]

To the highly-material Western mind, Hindus can be a little weird sometimes: "A deeply religious Hindu, Ramanujan credited his substantial mathematical capacities to divinity, and said the mathematical knowledge he displayed was revealed to him by his family goddess Namagiri Thayar. He once said, "An equation for me has no meaning unless it expresses a thought of God."" [3]

[1] https://en.wikipedia.org/wiki/Baudhayana_sutras#Pythagorean_... [2] http://jwilson.coe.uga.edu/EMT668/EMT668.Student.Folders/Hea... [3] https://en.wikipedia.org/wiki/Srinivasa_Ramanujan

echopurity• 5 years ago

The great man theory almost always fails. The life of Pythagoras is largely myth. This theorem was most likely known and proven well before him. This is old news.

https://link.springer.com/article/10.1057/jt.2009.16

h2odragon• 5 years ago

Tomorrow, the newly formed "Estate of Pythagoras" corporation will begin selling shares in its upcoming lawsuits against "everybody who has ever used math" for IP infringement as appropriate in their many jurisdictions.

No one will really bet big on it until Disney takes them over.

Koshkin• 5 years ago

This is yet another evidence in favor of the idea that mathematics is not invented but discovered.

oblak• 5 years ago

During a heated argument, a person I know argued that humanity advanced as fast as it did during the 19th century after aliens invented(!) electricity and gave it to us.

Took me a while to process

mojuba• 5 years ago

The aliens lost patience, I can understand them.

ganzuul• 5 years ago

https://archive.is/DUZat

kgeist• 5 years ago

Did Pythagoras/Pythagoreans ever claim they invented all the things they discussed?

contradistinct• 5 years ago

Nothing is ever invented by the person it's named after [1].

[1] https://taylor.gl/blog/11

etothepii2• 5 years ago

I don't know if it's true but we were always taught in the History of Maths course at Cambridge[1] that Pythagoras did not exist, or at least there was no evidence of a specific person called Pythagoras. Further if you followed the footnotes in most any research on the subject (especially claims that the Egyptians or Babylonians knew the theorem) you almost always end up at a loose end.

[1] https://www.ice.cam.ac.uk/about-us/staff-profiles/tutor/pier...

tim3332• 5 years ago

For what it's worth Wikipedia has him as a real person living 570 – c. 495 BC, son of Mnesarchus, a gem-engraver on the island of Samos, who travelled to Croton about 530 BC and set up some kind of school there.

spoonjim• 5 years ago

It might be the mathematical equivalent of Winston Churchill... a person who definitely existed, but who didn’t say 90% of the famous bon mots attributed to him. It might have been that if you wanted your ideas to spread you had to attribute them to “Pythagoras.”

grae_QED• 5 years ago

Maybe its because I'm on mobile, but your link brings me to a faculty page and nothing there suggests Pythagoras wasn't a person.

I even went through the syllabus of the most closely related of their past lectures (a quick history of ancient mathematics and mathematical ideas) and I quickly realized that I don't even know which book to read to try find anything related to Pythagoras' existence.

Is there a specific piece of text I could read that would verify your claim?

ummonk3• 5 years ago

So Pythagoras likely didn't even formulate the theorem - he was more into numerology and only cared about sum of squares triplets, not the results about right triangles.

On the other hand, we have strong evidence that the Babylonians understood and applied the "Pythagorean" theorem long before Pythagoras lived.

Additionally, the first recorded explicit statement of the theorem is actually by the Indian writer Baudhayan, over a century before Pythagoras.

The oldest extant proof of the theorem comes from Euclid. The proof commonly attributed to Pythagoras actually first shows up in the Chinese Zhoubi Suanjing, several centuries after Pythagoras.

Quite simply, "Pythagorean theorem" is a major misnomer.

Natsu• 5 years ago

Things get named after the person who popularized something, not generally after the first to discover it.

It's called the Pythagorean theorem because that's where western people who called it that learned it from, the other things being unknown to them.

yhoneycomb• 5 years ago

Whatever. Still a misnomer in my book. With that said, you are free to invent your definition of misnomer if you so desire.

ummonk3• 5 years ago

Explaining why a misnomer came about isn't an argument for why we should continue to perpetuate it.

jdkfglkjh34• 5 years ago

https://en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy

throw135795• 5 years ago

Colonized Indians need to take control of their history like the Chinese did. Otherwise the appropriators will continue to have a field day.

estaseuropano3• 5 years ago

This is a 2000-year-precolonial issue though.

pushpen992• 5 years ago

copied/stolen from India/Hindus

estaseuropano3• 5 years ago

There is a huge swath of Indian comments here, claiming vaguely that all these are Indian ideas without any evidence to back this up. Would be curious to see some actual evidence.

Not to forget that things can also be invented/discovered more than once independently.

pushpen992• 5 years ago

Pythagoras had visited India as reported by Diogenes Laertiu. Pythagoras theorem is actually Baudhayana Sutra and was widely used by Brahmins in India to build vedic hawan kunds.

Mikeb85• 5 years ago

So who's the Babylonian guy who we can name it after?

Also, this has been well known for awhile.

joemaller1• 5 years ago

An uncomfortably large percentage of our population doesn’t understand the theorem, no matter what it’s called. But sure, let’s quibble about the name.

gremloni• 5 years ago

It’s important because otherwise you keep getting the “white people made everything” argument.

senorsmile• 5 years ago

This makes me want to learn Akkadian and it's descendants even more now.

The Babylonians used Pythagorean ideas long before Pythagoras

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