Euclid was one of the great mathematicians of Greece. He lived circa 300 B.C. His chief work, the Elements, a comprehensive treatise on mathematics, in 13 volumes, on such subjects as plane geometry, proportion in general, the properties of numbers, incommensurable magnitudes, and solid geometry. He probably was educated at Athens by pupils of Plato. He taught geometry in Alexandria and there founded a school of mathematics. The Data, a collection of geometrical theorems; the Phenomena, a description of the heavens; the Optics; the Division of the Scale, a mathematical discussion of music; and several other books have long been attributed to Euclid; most historians believe, however, that some or all of these works (other than the Elements) have been spuriously credited to him. Historians disagree as to the originality of some of his other contributions. Probably the geometrical sections of the Elements were primarily a rearrangement of the works of previous mathematicians such as those of Eudoxus, but Euclid himself is thought to have made several original discoveries in the theory of numbers.
The great English mathematician G.H. Hardy, in his book A Mathematician’s Apology invokes Euclid and Pythagoras to illustrate what he means by serious mathematics in the following paragraph:
I can hardly do better than go back to the Greeks. I will state and prove two of the famous theorems of Greek mathematics. They are ‘simple’ theorems, both in idea and in execution, but there is no doubt at all about their being theorems of the highest class. Each is as fresh and significant as when it was discovered – two thousand years have not written a wrinkle on either of them … The first is Euclid’s proof of the existence of an infinity of prime numbers. … My second example is Pythagoras’s proof of the ‘irrationality’ of √2 …
Euclid’s Elements was used as a text for 2,000 years, and even today a modified version of its first few books form the basis of high school instruction in plane geometry. The first printed edition of Euclid’s works was a translation from Arabic to Latin, which appeared at Venice in 1482. The lasting influence of Euclid’s work, was captured in the following beautiful paragraph by the mathematician De Morgan in 1848:
There never has been, and till we see it we never shall believe that there can be, a system of geometry worthy of the name, which has any material departures (we do not speak of corrections or extensions or developments) from the plain laid down by Euclid.
