To be fair, the Greeks stole all their eurekas from Babylon and the Egyptians anyway.
Not all. In fact, it would be more accurate to say that the Greeks built on any Eurekas they got from Babylon and the Egyptians. Cases in Point:
The Greeks built large stone temples and monumental buildings like the two earlier Civs, but the Greeks were the first ones to reinforce stone structures with metal (in the
Propylaea on the Acropolis in Athens, 440 - 430 BCE)
In those same monumental stone structures, the Greeks were the first to use cranes with mechanical advantage pulleys to lift and move stones (515 BCE, Corinth) - probably because the Greek city states didn't have access to the massive amounts of manpower available to the Egyptian and Babylonian builders.
And there was nothing anywhere else in the world like the Greek Hoplon shield, built of a combination of steamed formed wood, bronze/brass and leather, that defined the Hoplite from 600 BCE on.
And when the Greek and Mesopotamian/Egyptian science really got fused - in Hellenistic Alexandria around the
Mouseion or Library there - it produced an explosion of scientific advances in numerous fields, like:
Euclid's
Elements was published under Ptolemy I in Egypt around 300 BCE - probably the single most influential book on mathematics ever written.
The horizontal-axis waterwheel was invented in Alexandria around 240 BCE
Hipparchus discovered and described a Supernova and created the first star catalogue calculating positions of the stars by Precession, in 135 BCE - essentially the start of modern astronomy, building on both Greek and Middle Eastern predecessors.
In the first century CE Democritus wrote the first known 'textbook' on Alchemy, the
Four Books, basing his study on a combination of Egyptian metallurgical knowledge and Greek natural philosophy
In that same century, by 70 CE Dioscorides wrote
Peri hules latrikes (better known by its Latin title:
De Materia Medica), a 5 volume compendium of herbal and medicinal plants, the basis for virtually all natural pharmacopeas written since.
About 100 years later Klaudios Ptolemaios wrote the treatise on astronomy later known as the
Almagest, the standard work on the subject for the next 1500 or so years, and a Geography of the classical world in which he accurately measured the circumference of the earth.
And finally, at the beginning of the 2nd century CE Claudius Galenus (Galen) wrote up his new research on anatomy, pharmacology, medical diagnosis - even covering mental illness: another set of works that influenced the field of medicine for the next 1000 years.
No question that the Greeks owed a lot to the earlier work done in Egypt, Babylon, Assyria - but they added to it a distinctly Non Religious outlook they called Natural Philosophy which, especially when turned lose in the concentration of knowledge and information represented by Alexandria's Museum/Library, took the original work far beyond anything that the Egyptians or Babylonians ever achieved. All Science, in the memorable phrase, "stands on the shoulders of Giants" - but Greek science produced some Giants of its own.
On that note, Akkad and Assyria are Civilizations that I'd love to see. 
