# In Stephen Hawking's book "The Grand Design" he states that "Pythagoras probably did not discover this - he also did not discover the theorem that bears his name" ... if not Pythagoras then who?

from page 19 “The Grand Design”

... what else are we taught that isn’t really true? Who discovered “The Pythagoras Theorem?”

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According to wikipedia there is some evidence that the Babalonyians knew about it before the big P.

@Lightlyseared

It is also possible for Pythagoras to have independently come up with the same theorem, but I have no idea if he did or not.

The Pythagorean theorem was one of the earliest theorems known in ancient civilizations. There is evidence that it was known at least 1000 years before Pythagoras. In other words, the theorem was known by 1600 BC, and it was quite possibly used even earlier. However, we do not have any records of its discovery. Every ancient text we have that uses the theorem assumes that it is already known.

I believe the theorem is attributed to Pythagoras for several reasons:

**A.** While the Chinese *Zhoubi suanjing* demonstrates that a right triangle with legs of 3 and 4 units has an hypotenuse of 5 units, it did not generalize the concept. The Pythagoreans were the first to produce a general proof of the theorem. (Even at this, Pythagoras may not have been the one to prove the theorem. The Pythagoreans were largely a secret society, so it is often impossible to determine which of them to credit for any particular work.)

**B.** This theorem led the Pythagoreans to discover the existence of irrational numbers. One of the central tenets of Pythagorean philosophy was that a number was just a combination of indivisible units. They believed that everything in reality could be reduced to numbers, which implied that lengths could always be counted. They found that for any given unit, if the sides of a square were divided perfectly into those units, the diagonal could not be divided into a perfect number of the same units. They were forced to abandon their philosophy that everything in the universe was composed of numbers (what we would now call natural numbers). This led them to prove the existence of irrational numbers. If I recall correctly, they considered a right triangle with legs that had a length of one unit. Using the Pythagorean theorem, they proved that the square root of two was a legitimate length, and later proved that it was irrational. Naturally, the discovery of irrational numbers opened the door for many more discoveries and mathematical advancements.

**C.** Any theorem this significant is usually given a name. Given what I’ve said above about the work of the Pythagoreans with this theorem, and given that we don’t know who initially discovered it, it makes sense to credit the Pythagoreans with it.

main source

other source

Some of this came from my own memory of previous studies. Obviously, I cannot directly attribute any source for that.

@Faiblesse We don’t know who first discovered the theorem. Unfortunately, we have lost huge quantities of historical information, in large part due to wars and the burning of libraries. Who first discovered the Pythagorean theorem is one of many things we will likely never know.

Oh, don’t mind me, I’m just making obscure internet jokes.

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Likewise Euclid did not come up with all those geometric theorems. The great thinkers of antiquity are probably remembered because they compiled and organized a hodge-podge of known facts into a unified written work.

@bobbinhood The proof that square root of two (the measure of the hypotenuse of a unit isosceles right triangle) is elementary—takes just a few lines of *reductio ad absurdum*. The legend is that this discovery (of the proof) so upset the Pythagoreans—a mystical, quasi-religious sect—that they murdered its discoverer by throwing him off a boat.

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Another interesting question that will probably never be answered is who created the first formal proof. The Greeks attributed this to Thales, but historians dismiss this idea.

Even if Pythagoras was not the first to come up with the equation named for him, he is of interest from a philosophic point of view. He believed that numbers were the ultimate reality, specifically whole numbers and their ratios, which is why he got so upset about the irrationality of the square root of 2. There are some modern philosophers of science who have also considered the possibility of numbers being the ultimate reality. I wonder if they include complex numbers. I could just imagine what Pythagoras would have thought of imaginary numbers.

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