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What was the "state of the art" in engineering, science, and mathematics in Ancient Egypt when the Sphinx and the Giza Pyramids were built during the Third and Fourth Dynasties? How did they accomplish these engineering feats without modern engineering knowledge & tools?

The Great Pyramid of Giza was built to house the remains of the Pharaohs and thus meant to last forever. How did their techniques contribute to the permanency of the Giza structures?

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This question may be off-topic for Historians but I searched through StackExchange but could not find a more suitable engineering site for the question. However, it relates to the great historical monuments built by our amazing ancestors. –  curious Oct 19 '13 at 0:41
Remember: The buildings that lasted a thousand years are well, the ones that lasted. Most ancient buildings and monument did not last. But you don't notice them, because, well, they didn't last. –  Lennart Regebro Oct 19 '13 at 9:28
@LennartRegebro We can build for eternity when we have to. Consider the very interesting topic of nuclear semiotics for 10,000 - 100,000 year fission waste storage. –  LateralFractal Oct 22 '13 at 7:58
Question lacks preliminary research and relies on questionable assumptions. –  Mark C. Wallace Oct 22 '13 at 11:25
@MarkC.Wallace I always thought Teletubbies built the pyramids. Actually no - make that Ancient Aliens in Teletubbie meat-suits. –  LateralFractal Oct 30 '13 at 12:14
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closed as too broad by Razie Mah, Pieter Geerkens, NotVonKaiser, Mark C. Wallace, Kobunite Mar 21 at 9:36

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Modern scientific and mathematical knowledge was not necessary for building structures that would last a long time. For that, empirical knowledge, based on experience, was sufficient.

History of structural engineering:

Pyramids were the most common major structures built by ancient civilizations because the structural form of a pyramid is inherently stable and can be almost infinitely scaled (as opposed to most other structural forms, which cannot be linearly increased in size in proportion to increased loads)

Throughout ancient and medieval history most architectural design and construction was carried out by artisans, such as stone masons and carpenters, rising to the role of master builder. No theory of structures existed and understanding of how structures stood up was extremely limited, and based almost entirely on empirical evidence of 'what had worked before'. Knowledge was retained by guilds and seldom supplanted by advances. Structures were repetitive, and increases in scale were incremental.

It requires no sophisticated math or modern engineering knowledge to build simple structures, even though they are quite large and durable - you simply rely on your experience of what worked before and take it to the next small step.

Modern advances were required only when structures became more complex and sophisticated: Increased ratio of bulk vs usable space - size vs load, for example modern skyscrapers; spanning large expanses of space, for example modern suspension and cantilever bridges; building large, complex forms, for example the Guggenheim Museum; building structures based not on previous experience, but on mathematical predictions, for example the Tacoma-Narrows bridge. (That one didn't work out too well, but it's a well known example...)

Source: Understanding the World's Greatest Structures: Science and Innovation from Antiquity to Modernity - Lectures 1,2 - Professor Stephen Ressler, United States Military Academy at West Point Ph.D., Lehigh University.

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They used lots of very large, very heavy stones.

You will note that these constructions did not have large internal air pockets relative to volume. They qualify as monuments or fortifications more than inhabitable buildings with a decent amount of floorspace.

Having arches or domes or any large enclosed internal space was considered the height of engineering achievement - and most did not survive well. The internal space of an Egyptian pyramid was a fraction (1.3%) of a modern pyramid like the Louvre skylight (probably 99.5%).

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Just as no sophisticated math or engineering is needed by a 4-year old when stacking blocks, none is needed to stack large stones into monumentally sized structures. Of course, there is little room inside such structures for storage or activities. –  Pieter Geerkens Oct 19 '13 at 16:23
Even the Angkor Wat temple in Cambodia is an amazing engineering marvel. –  Pradeep Oct 22 '13 at 6:23
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