[Sniffnoy]

> As Gauss famously said, there is "no royal road" to mathematical mastery.

This is not the point, but the saying "there is no royal road to geometry" is far older than Gauss! It goes back at least to Proclus, who attributes it to Euclid.

[troymc]

I never understood that quote until recently.

The story goes that the (royal) pharaoh of Egypt wanted to learn geometry, but didn't want to have to read Euclid. He wanted a faster route. But, "there is no royal road to geometry."

[FilosofumRex]

The last Egyptian pharaoh was Nectanebo II, who ruled from 358 to approximately 340 BC. Alexander founded Alexandria in 331 BC as the crown jewel of his empire where Euclid wrote his magnum opus, The Elements in 300 BC!

Unless the royal pharaoh of Egypt, refers to Ptolemy I Soter, Macedonian general who was the first Ptolemaic Kingdom ruler of Egypt after Alexander's death.

[troymc]

Yep, exactly. Here's a translation of Proclus:

"He [Euclid] lived in the time of Ptolemy the First, for Archimedes, who lived after the time of the first Ptolemy, mentions Euclid. It is also reported that Ptolemy once asked Euclid if there was not a shorter road to geometry that through the Elements, and Euclid replied that there was no royal road to geometry."

Source: http://aleph0.clarku.edu/~djoyce/java/elements/Euclid.html