THE CLASSICAL LIBERAL ARTS included logic, grammar, rhetoric, and geometry. Just as today's liberal arts, they were not for the purpose of learning a trade. They served the purpose of education, which, as Albert Einstein once observed, "is not the learning of many facts but the training of the mind to think."
Geometry, moreover, embraced logic, grammar and rhetoric, because it was approached purely verbally. There was no algebra, no symbols for "angle" or "equals." What the student saw, he explained. For geometry is based on looking, and the sensitivity it develops is the essence of science.
In the 4th century B.C., Alexandria in Egypt was the center of culture and learning, and it was there that the Greek mathematician Euclid assembled the most remarkable textbook the world has ever seen: the Elements of geometry and arithmetic. Written in simple, straightforward language, the Elements has been translated the world over, and through the centuries it has been the model for clear and eloquent reasoning. It was the first written work to introduce what is called rigor into mathematics. That same rigor -- What gives us the right to say that we really know? -- is part of the culture of mathematics today, and it is the model followed in theoretical physics. Anyone truly interested in what mathematics is, can have no firmer foundation than Euclid.
Efforts have always been made to express the Elements in the language of each time and place. The pages that follow are adapted from the translation by Sir Thomas Heath (Dover) as well as the edition of Isaac Todhunter (Elibron Classics)...
Friday, July 23, 2010
a liberal art
from The Math Page: