4 ms·

I'm not sure you've got that right. We know almost nothing about the historical Pythagoras and none of his actual writings survived. We only know of him throug

I'm not sure you've got that right. We know almost nothing about the historical Pythagoras and none of his actual writings survived. We only know of him through the Pythagorean brotherhood and other people (eg Plato) who he influenced. While the Pythagoreans did come up with many things (eg the first rigorously documented scientific experiments) my understanding was that it is known for certain that they definitely were not responsible for Pythagoras’ theorem (or this rationality corolary you're talking about), and that the earliest formulation of it that is currently known is from Babylon where it's documented to do with sizing of farm plots[1] about a thousand years before Pythagoras. The proof of the irrationality of the square root of two was so terrifying to the Pythagoreans that the legend has it they threw the dude who produced it off a boat into the sea to drown because it was such a heresy (although I believe that is also known not to be true and the pythagoreans knew that root 2 was irrational). In that sense it's like Euler's number (first documented by Napier), Lambert's W function (Invented by Euler to solve a family of equations Lambert couldn't solve), Lagrange's notation for calculus (used by Lagrange yes but first also invented by Euler) etc etc. [1] https://www.researchgate.net/publication/222892801_Methods_and_traditions_of_Babylonian_mathematics_Plimpton_322_Pythagorean_Triples_and_the_Babylonian_Triangle_Parameter_Equations https://www.researchgate.net/publication/222892801_Methods_a...

lordnacho 2y ago
Stigler's Law of Eponymy
- pfdietz 2y ago
  Let me guess: Stigler didn't invent that.
  - lordnacho 2y ago
    Correct! He heard it from a friend and decided it needed his name on it, that way it is an example of the law itself.
bandrami 2y ago
The documentatary evidence is fragmentary but there is significant evidence that a 5th-century BC Greek mathematician proved the incommensurability of the side of a square with its diagonal (it was apparently trivially known a century later since it appears in Plato's "Meno"). Whether that person was named Pythagoras or Hippasus or something else is really neither here nor there since he was pretty clearly part of the Pythagorean tradition that got associated with one name. The point in any case is that incommensurability as a concept was not widely accepted at the beginning of the 5th century BC and was widely accepted at the end, and the name "Pythagoras" gets attached to the mathematicians who discovered that. But like for that matter Plato's name wasn't "Plato"; that was a nickname his wrestling coach gave him.
- dr_dshiv 2y ago
  Speaking of Plato’s wrestling coach… Pythagoras was also a successful wrestling coach. In fact, he coached the most winningest Olympic athlete of all time: Milo of Croton. Milo won 5 consecutive Olympics over a 20 year period. Pythagoras himself was thrown out of the boys Olympics at age 16 for being too effeminate (long hair), but then entered the men’s Olympics and won. Supposedly, he introduced some new kind of martial arts technique. This is documented in Thibodeau, 2019 “The Chronology of the Early Greek Natural Philosophers.” Happy to share the refs. Ok, back to maths…
  - javier_e06 2y ago
    Thank you so much! Like my teacher always says: "If at the end of the class, you haven't learned something new, come see me"
  - n4r9 2y ago
    There is a PDF of your citation available at https://www.researchgate.net/publication/335965217_THE_CHRONOLOGY_OF_THE_EARLY_GREEK_NATURAL_PHILOSOPHERS https://www.researchgate.net/publication/335965217_THE_CHRON... I searched for "long hair" and found only this: >The man with long hair at Samos’: They say there was a Samian boxer with long hair who went to Olympia and won after being mocked by his opponents for looking like a woman; he became proverbial. Eratosthenes says that Pythagoras of Samos won with long hair during the 48 th Olympiad; Duris represents this as Pythagoras being excluded, challenging the men, and beating many of them. Like many stories concerning Pythagoras, I wonder if this was some local fable onto which his name later became plastered.
ants_everywhere 2y ago
I haven't read the paper you posted yet, but just to clear up a common confusion, Pythagorean triples are not the Pythagorean theorem. The theorem is a logical statement about all right triangles, and it has a proof that the statement holds. Pythagorean triples are specific instantiations of the relation for some known triangles and probably would have served as evidence that the statement was even provable. Historically we probably had triples long before we had a proof of the theorem, just like many of the theorems proved by Euclid were probably already known as rules of thumb. Compare with an open problem today, like the Riemann hypothesis.
- bandrami 2y ago
  I mean, it's correct that Pythagorean triples are not the same thing as the Pythagorean theorem, but "Pythagoras" (or at least the Pythagorean school) proved things about modular arithmetic with the triples. The geometric interpretation was they were the measures of the sides of right triangles and that no other right triangles were "measurable" (that is, they could not be expressed as having 3 rational side lengths).
EGreg 2y ago
This is exactly right! Oh, how I wish there was a book on the history of science and math. Like how they went from the Four Humours or Phlogiston and Spontaneous Generation and Luminferous Ether theories to what they had later. Like how scientists all thought the earth was 100 million years old for a couple centuries until the discovery of radioactivity. I want a book that would speak about how people made fun of Ignaz Semmelweis for washing hands in hospitals, until Pasteur in France and John Snow in England showed evidence for the germ theory of disease. How people used leeches and bloodletting, and when / why they stopped. (And maybe anecdotes like How Washington Roebling building the Brooklyn Bridge died from a gangrene because he thought pouring water over his wound was enough, and his son finished it) I want a book that would explain the experiments that led to the theories, like Michelson-Morley that challenged the Lumeniferous Ether model. Or how people first discovered X-rays and didn’t know what to make of them. How, indeed, did people prove to others that atoms existed? I don’t mean Democritus’ theories 2500 years ago, I mean what made people convinced the world was made from atoms? And then the experiments that led to the standard model, how was it developed? The word Quark, where it came from, the reactions of scientists to Quantum theory etc. Our science comes shrinkwrapped, showing only the end result, not the history of thought and the places where (eg Andalusia in the 1100s or China in 20 AD). To me it is very interesting when people weren’t sure yet but got the right result based on circumstantial reasoning, didn’t have high-powered electron microscopes and still somehow realized about atoms and molecules (Gregor Mendel etc). Or how Darwin and Mendeleev developed theories genetics, why they so thoroughly discounted Lamarckian evolution and were they correct etc. I want a book that discusses the history including the ERRONEOUS theories, the time frames, the experiments that challenged prevailing theories, the controversies, and what made people find the correct theories. And maybe the people (eg Newton avoided women, and studied Hebrew to reconstruct Biblical history, Michael Faraday was a devout Christian etc.) Is there such a book? Can you guys recommend ??
- jtimdwyer 2y ago
  I may be falling into a trap here by answering this, but you might enjoy The Structure of Scientific Revolutions by Thomas Kuhn.
- generuso 2y ago

lordnacho 2y ago

Stigler's Law of Eponymy

pfdietz 2y ago
Let me guess: Stigler didn't invent that.
- lordnacho 2y ago
  Correct! He heard it from a friend and decided it needed his name on it, that way it is an example of the law itself.

bandrami 2y ago

The documentatary evidence is fragmentary but there is significant evidence that a 5th-century BC Greek mathematician proved the incommensurability of the side of a square with its diagonal (it was apparently trivially known a century later since it appears in Plato's "Meno"). Whether that person was named Pythagoras or Hippasus or something else is really neither here nor there since he was pretty clearly part of the Pythagorean tradition that got associated with one name. The point in any case is that incommensurability as a concept was not widely accepted at the beginning of the 5th century BC and was widely accepted at the end, and the name "Pythagoras" gets attached to the mathematicians who discovered that. But like for that matter Plato's name wasn't "Plato"; that was a nickname his wrestling coach gave him.

dr_dshiv 2y ago
Speaking of Plato’s wrestling coach… Pythagoras was also a successful wrestling coach. In fact, he coached the most winningest Olympic athlete of all time: Milo of Croton. Milo won 5 consecutive Olympics over a 20 year period. Pythagoras himself was thrown out of the boys Olympics at age 16 for being too effeminate (long hair), but then entered the men’s Olympics and won. Supposedly, he introduced some new kind of martial arts technique. This is documented in Thibodeau, 2019 “The Chronology of the Early Greek Natural Philosophers.” Happy to share the refs. Ok, back to maths…
- javier_e06 2y ago
  Thank you so much! Like my teacher always says: "If at the end of the class, you haven't learned something new, come see me"
- n4r9 2y ago
  There is a PDF of your citation available at https://www.researchgate.net/publication/335965217_THE_CHRONOLOGY_OF_THE_EARLY_GREEK_NATURAL_PHILOSOPHERS https://www.researchgate.net/publication/335965217_THE_CHRON... I searched for "long hair" and found only this: >The man with long hair at Samos’: They say there was a Samian boxer with long hair who went to Olympia and won after being mocked by his opponents for looking like a woman; he became proverbial. Eratosthenes says that Pythagoras of Samos won with long hair during the 48 th Olympiad; Duris represents this as Pythagoras being excluded, challenging the men, and beating many of them. Like many stories concerning Pythagoras, I wonder if this was some local fable onto which his name later became plastered.

ants_everywhere 2y ago

I haven't read the paper you posted yet, but just to clear up a common confusion, Pythagorean triples are not the Pythagorean theorem. The theorem is a logical statement about all right triangles, and it has a proof that the statement holds. Pythagorean triples are specific instantiations of the relation for some known triangles and probably would have served as evidence that the statement was even provable. Historically we probably had triples long before we had a proof of the theorem, just like many of the theorems proved by Euclid were probably already known as rules of thumb. Compare with an open problem today, like the Riemann hypothesis.

bandrami 2y ago
I mean, it's correct that Pythagorean triples are not the same thing as the Pythagorean theorem, but "Pythagoras" (or at least the Pythagorean school) proved things about modular arithmetic with the triples. The geometric interpretation was they were the measures of the sides of right triangles and that no other right triangles were "measurable" (that is, they could not be expressed as having 3 rational side lengths).

EGreg 2y ago

This is exactly right! Oh, how I wish there was a book on the history of science and math. Like how they went from the Four Humours or Phlogiston and Spontaneous Generation and Luminferous Ether theories to what they had later. Like how scientists all thought the earth was 100 million years old for a couple centuries until the discovery of radioactivity. I want a book that would speak about how people made fun of Ignaz Semmelweis for washing hands in hospitals, until Pasteur in France and John Snow in England showed evidence for the germ theory of disease. How people used leeches and bloodletting, and when / why they stopped. (And maybe anecdotes like How Washington Roebling building the Brooklyn Bridge died from a gangrene because he thought pouring water over his wound was enough, and his son finished it) I want a book that would explain the experiments that led to the theories, like Michelson-Morley that challenged the Lumeniferous Ether model. Or how people first discovered X-rays and didn’t know what to make of them. How, indeed, did people prove to others that atoms existed? I don’t mean Democritus’ theories 2500 years ago, I mean what made people convinced the world was made from atoms? And then the experiments that led to the standard model, how was it developed? The word Quark, where it came from, the reactions of scientists to Quantum theory etc. Our science comes shrinkwrapped, showing only the end result, not the history of thought and the places where (eg Andalusia in the 1100s or China in 20 AD). To me it is very interesting when people weren’t sure yet but got the right result based on circumstantial reasoning, didn’t have high-powered electron microscopes and still somehow realized about atoms and molecules (Gregor Mendel etc). Or how Darwin and Mendeleev developed theories genetics, why they so thoroughly discounted Lamarckian evolution and were they correct etc. I want a book that discusses the history including the ERRONEOUS theories, the time frames, the experiments that challenged prevailing theories, the controversies, and what made people find the correct theories. And maybe the people (eg Newton avoided women, and studied Hebrew to reconstruct Biblical history, Michael Faraday was a devout Christian etc.) Is there such a book? Can you guys recommend ??

jtimdwyer 2y ago
I may be falling into a trap here by answering this, but you might enjoy The Structure of Scientific Revolutions by Thomas Kuhn.
generuso 2y ago