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Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

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Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#21

Post by geraneum »

saithound wrote: post #5

Every group who ever managed to build a building with a rectangular foundation figured out the relation between the side lengths and the diagonal. The Egyptians used Pythagorean triples to measure right angles way before the birth of Pythagoras. But that's not a theorem, just an observation. It becomes a theorem when you prove (i.e. explain why) this relationship always holds, based on more evident things. The Babylo…

From the article:

> Pythagoras is immortally linked to the discovery and proof of a theorem that bears his name – even though there is no evidence of his discovering and/or proving the theorem.

Simply quoting. It seems like

> Greek definitely did

is not a universally held belief.

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#22

Post by mauvia »

loganc2342 wrote: post #18

> The Pythagorean Theorem is arguably the most famous statement in mathematics, and the fourth most beautiful equation. Just out of curiosity, which equations are considered the top three “most beautiful?”

I know the top one is generally considered to be Euler's Equation.

e^(i * pi) + 1 = 0

It's considered incredibly elegant because it manages to combine multiple fundamental mathematical concepts into a single equation.

1 is the multiplicative identity, 0 is the additive identity, pi is the circle constant, e is euler's number, i is the square root of -1, the basic building block of complex numbers.

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#23

Post by fsckboy »

saithound wrote: post #5

Every group who ever managed to build a building with a rectangular foundation figured out the relation between the side lengths and the diagonal. The Egyptians used Pythagorean triples to measure right angles way before the birth of Pythagoras. But that's not a theorem, just an observation. It becomes a theorem when you prove (i.e. explain why) this relationship always holds, based on more evident things. The Babylo…

> Pythagorean triples to measure right angles ... But that's not a theorem, just an observation. It becomes a theorem when you prove (i.e. explain why) this relationship always holds, based on more evident things. The Babylonian tablet mentioned in the article doesn't seem to do anything like that

according to the article, this Babylonian tablet does come closer to theorem than you are suggesting. They weren't using Pythagorean triples, rather they figured out that the diagonal of a unit square is the square root of 2, and knew how to calculate that:

1 + 24/60 + 51/602 + 10/603 = 1.414213

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#24

Post by zabzonk »

loganc2342 wrote: post #18

> The Pythagorean Theorem is arguably the most famous statement in mathematics, and the fourth most beautiful equation. Just out of curiosity, which equations are considered the top three “most beautiful?”

not sure if you include physics, but newton, the gas laws, and einstien?

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#25

Post by zeroonetwothree »

loganc2342 wrote: post #18

> The Pythagorean Theorem is arguably the most famous statement in mathematics, and the fourth most beautiful equation. Just out of curiosity, which equations are considered the top three “most beautiful?”

Ask ten people you will get ten different answers.

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#26

Post by saithound »

geraneum wrote: post #21
saithound wrote: post #5

Every group who ever managed to build a building with a rectangular foundation figured out the relation between the side lengths and the diagonal. The Egyptians used Pythagorean triples to measure right angles way before the birth of Pythagoras. But that's not a theorem, just an observation. It becomes a theorem when you prove (i.e. explain why) this relationship always holds, based on more evident things. The Babylo…

From the article: > Pythagoras is immortally linked to the discovery and proof of a theorem that bears his name – even though there is no evidence of his discovering and/or proving the theorem. Simply quoting. It seems like > Greek definitely did is not a universally held belief.

Your quote from the article does not suggest what you seem to think it suggests.

The Greeks definitely were able to prove the Pythagorean theorem, and the Greeks definitely though Pythagoras specifically knew how to prove it: e.g. Proclus II states this in writing explicitly, as does Euclid 300 years later, and numerous ancient sources inbetween. It would be hard for this not to be the consensus. We can't know if Pythagoras really did, simply because we have no surviving writings directly from Pythagoras - as I stated explicitly in my previous post.

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#27

Post by saithound »

sn41 wrote: post #17
saithound wrote: post #5

Every group who ever managed to build a building with a rectangular foundation figured out the relation between the side lengths and the diagonal. The Egyptians used Pythagorean triples to measure right angles way before the birth of Pythagoras. But that's not a theorem, just an observation. It becomes a theorem when you prove (i.e. explain why) this relationship always holds, based on more evident things. The Babylo…

Proofs are of course the gold standard. But even if others discovered the rule, their contribution should not be held to be trivial. A modern analogy: today, people are very happy to use LLMs and Transformers without anyone "proving" that they work. Right now, philosophically, they are at the level of empirical observations (perhaps not even that). Does that mean that today's AI researchers should get no credit when…

Yes, when people in the 4000s write clickbait holonet articles about how the Master Theorem of Neural Network Scaling was not actually invented by the Muskovites of Mars, but was found written on an Ancient American tablet containing the works of Hoffmann et al., I hope somebody will offer substantial corrections.

That's not in any sense a value judgment of the empirical work done at DeepMind. Nor does it stop anybody from writing a better article which explains that the Babylonians (and many others) used the empirical observations underlying the theorem, while explaining that this did not constitute mathematical proof.

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#28

Post by hyperthesis »

fsckboy wrote: post #23
saithound wrote: post #5

Every group who ever managed to build a building with a rectangular foundation figured out the relation between the side lengths and the diagonal. The Egyptians used Pythagorean triples to measure right angles way before the birth of Pythagoras. But that's not a theorem, just an observation. It becomes a theorem when you prove (i.e. explain why) this relationship always holds, based on more evident things. The Babylo…

> Pythagorean triples to measure right angles ... But that's not a theorem, just an observation. It becomes a theorem when you prove (i.e. explain why) this relationship always holds, based on more evident things. The Babylonian tablet mentioned in the article doesn't seem to do anything like that according to the article, this Babylonian tablet does come closer to theorem than you are suggesting. They weren't using…

Agree it's closer but still an instance.

Re: Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

#30

Post by tapotatonumber9 »

loganc2342 wrote: post #18

> The Pythagorean Theorem is arguably the most famous statement in mathematics, and the fourth most beautiful equation. Just out of curiosity, which equations are considered the top three “most beautiful?”

The most delicious is:

“(-1)^0.5 2^3 Σ π.”

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