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According to the Wikipedia article on the Abacus, Ettore Carruccio stated in Mathematics and Logic In History and In Contemporary Thought that the Old Babylonians:

may have used the abacus for the operations of addition and subtraction; however, this primitive device proved difficult to use for more complex calculations

translated by Isabel Quigly

The Old Babylonians, however, performed more complex mathematics than basic arithmetic. In the well referenced Wikipedia article on Babylonian mathematics it is stated that there is evidence they solved equations algebraically. Analysis of the Plimpton 322 tablet even seems to indicate they calculated a list of Pythagorean triples "too many and too large to have been obtained by brute force".

What methods then did the Old Babylonians use for solving equations? Were other devices aside from the abacus employed, or were these mostly manual methods on tablets? How did their manual methods differ from those we use today?

I'm not sure how much information we have on their mathematics. If there is a lot available, then this may be a little broad--in that case a summary of the state of research with links to good starting places to read about the research would make a useful answer.

Referenced Wikipedia articles:


Note: I have discovered papers such as this, but I am unable to ascertain whether the paper is reputable (I'm unfamiliar with the scholars in this field) or whether it contains much in the way of an answer to my question. It would be nice to know that before purchasing access to a paper at random. In this case, the paper seems to be freely accessible and at a glance appears scholarly, yet I still cannot verify if it represents the current state of research.

  • This might be better on the math & science history forum. – Tyler Durden May 12 '16 at 19:26
  • Also, you are asking a lot of different questions here. – Tyler Durden May 12 '16 at 19:27
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    @TylerDurden There is truly one question. The rest is peripheral. The question is what methods they used for equation solving (whether device-assisted or manual). – called2voyage May 12 '16 at 19:28
  • @called2voyage Both articles have decent lists of literature in their footnotes. Have you had a look whether you can hunt any of them down? – Marakai May 12 '16 at 20:45
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    @Marakai It's really a good amount of information for an encyclopedia. It just doesn't answer my particular question. – called2voyage May 12 '16 at 21:40
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You can see some general survey, like: Victor Katz, A History of Mathematics: An Introduction (3rd edition, 2008), Ch.1.2 MESOPOTAMIA, page 10-on.

There are references to "modern classics":

More recent and "technical":

  • The validation of Høyrup, at least, is helpful. Thanks! I'll need some time to analyze the rest to see if it answers my question. – called2voyage Jun 21 '16 at 15:23

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