"The great mathematician Euclid is said to have told his students 'There is no royal road to geometry." Thus begins an otherwise nice article in the Canadian Globe and Mail newspaper on line by Anna Stokke. The article describes her concern with what she sees as a failure of the "hands-on, manipulative approach" to math education in Alberta, and across Canada. After thirty years of teaching, I share many of her concerns. Read the article for yourself here.
If Ms Stokke was just any journalist, I might commend her for her (somewhat sketchy) math history connection. But she is NOT just any journalist. She is an assistant professor at the University of Winnipeg, and a co-founder of the non-profit organization Archimedes Math School. (I know absolutely nothing about the Archimedes Math School except that it is named for an ancient Greek Mathematician and therefore suggests a connection to math-historical knowledge.)
Perhaps the requirements of producing text for print required editing the first quote down to a triviality, and so I can not be too critical of a bit of historical vagueness without knowing the nature of her task better than I do. For most of her readers, I am sure the omission went without note and provided a little verbal quip to support the idea of greater analytic rigor in their children's education.
I, on the other hand, am retired, write mostly for teachers and students, and fully believe that one of the things that build the interest in mathematical studies for students are stories that make the math, and the mathematicians come alive. Just as a million kids grew to learn and love baseball sitting on the couch with dad or mom watching the home team, hearing their stories of the heroes of their youth, and maybe even memories of their own exploits. They lean the history, and the culture of the practice, and so are more willing to spend time learning to do it well. Few kids complain about Dad helping them learn to hit better. To me, math teachers have a mini-opportunity to do the same thing by mixing stories of the history and development of mathematics, the false starts, and the great insights, and the mysterious connections that intertwine mathematical (and scientific and social) topics.
So if you are a student learning the culture, or a teacher who wants to share it, here is a little bit more that might be told about the cast off "quip" at the start of Ms Stokke's column:
So, in the manor of Ms. Stokke, I will begin with a well known quote, ""Neither snow nor rain nor heat nor gloom of night stays these couriers from the swift completion of their appointed rounds." Yeah you know that one; the U. S. Postal Service motto that is inscribed on the James Farley Post Office in New York City. You can see part of it above the beautiful Corinthian Columns in this photo from Wikipedia.
The quote itself was from a history written by Herodotus, a 5th century BC Greek. The couriers he was speaking of were not the US Postal Service, but the riders on Persian King Darius I road throughout his empire. Herodotus added, " "There is nothing in the world that travels faster than these Persian couriers." This "Royal Road" throughout the Persian Empire was over 1600 miles long, and the riders could cover it in 7 days; a very early Pony Express.
Let one hundred plus years pass and Alexander the Great has a general named Ptolemy who decides when Alexander dies to make himself the ruler of Egypt, Ptolemy I. Also in Alexandria about this time was a mathematician who was putting together all the mathematical knowledge of the Greeks into a set of "Elements" which could be used to derive other mathematical knowledge. Ptolemy was a big fan, but a busy man, and he found the Elements difficult to digest.
AND..... It was this student, Ptolemy I, whose continued requests for an "easier" way to learn the Elements" that supposedly moved Euclid to remind him that there was no "Royal Road", such as the one still stretching across Persia at that time, to speed the learning of mathematics.
Did it ever really happen? Maybe not. The first known record of the event comes over five centuries later at the pen of Proclus, around 450 AD. Even if he never said it, we imagine he would have.
I usually closed this story by reminding my students of the lost guy driving in New York City looking for Carnegie Hall as the hour of his concert approached. The seemingly empty streets held little hope when he saw a vagrant looking fellow leaning against the wall of a building, eyes closed. He tapped his horn and when the guy opened his eyes, asked, " Can you tell me how to get to Carnegie Hall?"
The vagrant shook his head a moment, eyes closed, then opened them again to declare , "You gotta' practice man, you gotta' really practice."