> 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.
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.
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."
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.
"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