The big innovation that the Greek mathematicians (geometers and philosophers) came up with was to prove theorems logically, deductively -- they transformed mathematics from a bunch of empirical rules (some exact, some approximate) to the first modern science. If you read Euclid's Elements you will be struck at the sophistication of its contents and its thoroughly modern tone. (This text dates to two or three centuries before Christ.) This is what is interesting about Greek mathematics. Not its precision, a simple matter of arithmetic. (The Greeks, by the way, used the Babylonian system of arithmetic, which was base 60, from which we get our degrees-minutes-seconds. This was a completely modern form of arithmetic, only superceded by the Indian base 10 system in the middle ages. The arithmetic of the ancient Egyptians was a horror show by comparison. They did not use a base system, they used a system resembling Roman numerals, with pictograms representing numbers such as 1, 5, 10, 100, etc. This was tough to do arithmetic with. Worse, except for the fraction 2/3, they only allowed fraction with numerator 1. So they would allow 1/5 but they wouldn't allow 2/5, 3/5, etc. They needed complicated rules for adding fractions to achieve answers with only numerator 1, because strangely they did not allow repeated fractions of the same denominator.)
This is not to denigrate Egyptian mathematics, some of which was quite impressive for premodern times. But it wasn't the Egyptians who conceived of the notion of a rational number -- or who proved that the square root of two or similar numbers are irrational. That was the Greeks. The fact that much of this happened in Alexandria -- a Greek colony in Egypt -- is beside the point.
Of course all that was before the Egyptians, or anyone else, became Muslim.
Those "Arabic" numerals and the base 10 system, introduced to Europe by the Muslims , especially in Spain, were actually stolen from the Indians, as you point out.
All the assertions in this article need to be taken with a few hekats of salt.
The Egyptian calendar was 365 days long. The peoples living in Mesopotamia mastered positional astronomy to a far greater degree than anything ever acheived in Egypt. And yes, Egyptian mathematics was inductive and proscriptive, meaning it was strictly limited as to what it could achieve.
There was an article in Nature a few years ago showing that the alignment of the Pryamids of different eras drifted with the precessions of the poles, meaning that even if they "found" the celestial pole once, their alignments drifted with their guide stars.
See http://www.grahamhancock.com/forum/BauvalR1-p1.htm for a lively discussion.
Cherrypicking one good alignment in a population of 90 is not convincing evidence that they understood positional astronomy or geodesy.
The Hindus, not the Arabs created the positional number system, which was adopted by the Arabs and from them, by Europeans.