Virtually nothing is known about the personal life of Euclid. Where he was born is a mystery. Some stories describe Euclid as having attended Plato's Academy in Athens, Greece. If that is true, he probably attended during the generation after Plato's death, which occurred around 340 b.c. This circumstance, and the record that Euclid set up a school of mathematics in Alexandria around 300 B.C., places a probable date for the birth of Euclid at around 325 b.c. Euclid's disciple, Apollonius of Perga, is reported to have been the director of Euclid's Alexandrian school around 250 b.c., so a probable date for Euclid's death lies somewhere between 300 and 250 b.c.
Euclid studied and analyzed the entire body of mathematical knowledge that had accumulated in the ancient world up to his time and compiled a book called The Elements. The work is divided into 13 smaller books on the subject of plane geometry, number theory, irrational numbers, and solid geometry. Most of the treatise is not original research, but a brilliant synthesis of the results of centuries of mathematical work. The theorems and axioms of The Elements are clearly stated and arrived at through rigorous logic devoid of any superfluous reasoning. The concise style of The Elements became the world standard for scientific discourse over the next 2,000 years.
Perhaps best known is Euclid's reputation as the principal codifier of plane, or flat, geometry. Indeed, this branch of mathematics is known as Euclidean geometry. The principles of Euclidean geometry were so powerful in their presentation that for thousands of years people assumed that the workings of the entire universe could be described according to them. It was not until the nineteenth century, when the work of Nikolai Lobachevski, János Bolyai, and Georg Riemann demonstrated the usefulness of non-Euclidean geometry, that mathematicians began to seriously consider examining the foundations of Euclid's thought in a critical manner. Albert Einstein's revelation of the non-Euclidean nature of real space finally awakened scientists to the limitations of Euclidean geometry. This discovery did not diminish Euclid's work, but showed it to be only one expression of the many subtle ways in which the universe demonstrates relationships between objects in space and events in time.
From the modern point of view, Euclid's work has certain flaws. Improvements were made on Euclid's postulates in 1899 by David Hilbert and others with the intention of making Euclidean principles the basis from which the entire structure and language of mathematics could be derived using logic alone. The revolutionary discovery by Kurt Gödel in the 1930s that no self-consistent mathematical system could be derived in this way put an end to attempts to extend Euclid's work.
This is the complete article, containing 442 words
(approx. 1 page at 300 words per page).
