It seems like the focus always tends to be on the achievement of Greek math (which strikes of eurocentrism a little bit) while civilizations like the Egyptians and Babylonians are overlooked
why do we overlook their mathematical contributions?
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2$\begingroup$ For an overview of "ancient" mathematics, the books of Otto Neugebauer are a good starting point, although there are more recent sources. What seems to be new with Hellenistic culture (of course the geographical scope is somewhat broader than what is modern Greece; much of "Greek" mathematics was written in North Africa; Alexandria is in Egypt after all) is the systematization of methods and conceptual frameworks, and committing them to paper. $\endgroup$– Dan FoxCommented Oct 31, 2017 at 6:09
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1$\begingroup$ As @DanFox says: Greek mathematics largely happened in Egypt. $\endgroup$– Francois ZieglerCommented Oct 31, 2017 at 8:18
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1$\begingroup$ Greek axiomatic approach was totally new. $\endgroup$– Mauro ALLEGRANZACommented Oct 31, 2017 at 8:34
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$\begingroup$ Its more than likely that we're asking the wrong questions when it comes to ancient mathematics; for example, I came across a short article on the history of the development of measuring systems in ancient Sumeria & Babylonia which I found fascinating. $\endgroup$– Mozibur UllahCommented Nov 3, 2017 at 5:17
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2 Answers
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The achievements of Babylonian mathematics are on a par with the Greek ones. Actually a rather significant part of Greek mathematics is a rewriting in a more modern style of Babylonian material. In contrast, Egypt which received even earlier a similar input, did not find interesting developments.
Much new material and ideas have been presented by Jöran Friberg in the two volumes of solid work (published unfortunately with bombastic titles):
Unexpected Links Between Egyptian and Babylonian Mathematics, Singapore: World Scientific (2005), Amazing Traces of a Babylonian Origin in Greek Mathematics, 2007, World Scientific
The Clay tablets Plimpton 322 and YBC 7289 are famous and offer indubitable evidence of sophistication, e.g. pythagorean triples larger than 10000 and srt(2) with six digits. The crux of the history, of course, is the discovery of incommensurables by the Greeks, that is the failing of the old programme "Everything is a Number"; no satisfactory solution being available, a new programme was launched with the moto "Geometry is Real". However in astronomy, during Hellenistic times, the Greeks were still using Babylonian computational techniques (see e.g. A Jones work).
The accessible sources are not equivalent: there are no traces what arguments or ideas did the Babylonian use, but what they have left are not the results of guesswork. In contrast the text known under the name of Euclides is obviously focused on method.
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$\begingroup$ so essentially the Babylonians were equal to the Greeks...The Egyptians not as much? $\endgroup$– user4281Commented Oct 31, 2017 at 17:22
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1$\begingroup$ Any mathematician or historian of mathematics will strongly disagree that Greek and Babylonian mathematics were "on par", or even remotely comparable. $\endgroup$ Commented Oct 31, 2017 at 19:17
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$\begingroup$ If you have ever studied mathematics in school or university, you studied mathematics of Euclid and Archimedes, not Plimpton 322 mathematics. $\endgroup$ Commented Oct 31, 2017 at 19:47
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$\begingroup$ And neither Euclid nor Archimedes had access to Plimpton 322. $\endgroup$ Commented Oct 31, 2017 at 19:48
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3$\begingroup$ The reapraisal of Babylonian mathematics is fairly recent; reviewing E. Robson's Mathematics in Ancien Iraq (2008) AJones notes: not one page of this book could have been written a generation ago. (@ Ermenko) Outdated opinions should not inconditionally trump recent resarch. $\endgroup$– sand1Commented Nov 1, 2017 at 13:26
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It was incomparable to Greek mathematics. So much that many historians who studied the subject claimed that mathematics was invented by the Greeks. Neither Egyptian nor Babylonian mathematics had a notion of proof. And real mathematics begins only with invention of proof (Of course this depends on how we define "mathematics", but proof is what makes mathematics different from all other sciences). In any case there is no trace of mathematical proofs in any culture but Greek. In this exact sense the Greeks invented mathematics. See
B. L. van der Waerden, Science Awakening.
O. Neugebauer, Exact sciences in antiquity.
L. Russo, Forgotten revolution.
Remark. Interestingly, Greek historians themselves claimed that the sources of Greek mathematics lie in Egypt. Modern research does not confirm this legend. These Greek historians did not understand what they were writing about. For example, they tell us that Thales traveled to Egypt, presumably to study. And they also tell us how he surprised Egyptian priests by measuring the height of a pyramid. So the modern historians are puzzled: If he surprised them with such a minor thing, what could they possibly teach him in Egypt?
EDIT. On "eurocentrism" mentioned in a comment. Nowadays mathematics is cultivated in many places, and great contribution to it comes from places outside Europe, for example from China and Japan and other places. However, WHAT do they study in schools, universities, and what they develop? Greek mathematics, not Mesopotamian, not indigenous Chinese, not indigenous Japanese etc.
answered Oct 31, 2017 at 13:36
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$\begingroup$ so its not just a case of "eurocentrism" that scholars focused on greek mathematics mostly? $\endgroup$– user4281Commented Oct 31, 2017 at 14:18
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1$\begingroup$ @user4281: No it is not "eurocentrism", just a statement of facts. (Unless you count mathematics itself as a "european activity"). By the way some most significant Greek mathematicians (Euclides, Apollonius, Diophantes) worked in Alexandria (which is in Africa). $\endgroup$ Commented Oct 31, 2017 at 19:13