Euclid
Euclid is one of the most influential and best read mathematician of all
time. His prize work, Elements, was the textbook of elementary geometry and
logic up to the early twentieth century. For his work in the field, he is known
as the father of geometry and is considered one of the great Greek
mathematicians. Very little is known about the life of Euclid. Both the dates
and places of his birth and death are unknown. It is believed that he was
educated at Plato's academy in Athens and stayed there until he was invited by
Ptolemy I to teach at his newly founded university in Alexandria. There, Euclid
founded the school of mathematics and remained there for the rest of his life.
As a teacher, he was probably one of the mentors to Archimedes. Personally, all
accounts of Euclid describe him as a kind, fair, patient man who quickly helped
and praised the works of others. However, this did not stop him from engaging in
sarcasm. One story relates that one of his students complained that he had no
use for any of the mathematics he was learning. Euclid quickly called to his
slave to give the boy a coin because he must make gain out of what he learns.
Another story relates that Ptolemy asked the mathematician if there was some
easier way to learn geometry than by learning all the theorems. Euclid replied,
There is no royal road to geometry and sent the king to study. Euclid's fame
comes from his writings, especially his masterpiece Elements. This 13 volume
work is a compilation of Greek mathematics and geometry.
It is unknown how much
if any of the work included in Elements is Euclid's original work; many of the
theorems found can be traced to previous thinkers including Euxodus, Thales,
Hippocrates and Pythagoras. However, the format of Elements belongs to him
alone. Each volume lists a number of definitions and postulates followed by
theorems, which are followed by proofs using those definitions and postulates.
Every statement was proven, no matter how obvious. Euclid chose his postulates
carefully, picking only the most basic and self-evident propositions as the
basis of his work. Before, rival schools each had a different set of postulates,
some of which were very questionable. This format helped standardize Greek
mathematics. As for the subject matter, it ran the gamut of ancient thought. The
subjects include: the transitive property, the Pythagorean theorem, algebraic
identities, circles, tangents, plane geometry, the theory of proportions, prime
numbers, perfect numbers, properties of positive integers, irrational numbers,
3-D figures, inscribed and circumscribed figures, LCD, GCM and the construction
of regular solids. Especially noteworthy subjects include the method of
exhaustion, which would be used by Archimedes in the invention of integral
calculus, and the proof that the set of all prime numbers is infinite. Elements
was translated into both Latin and Arabic and is the earliest similar work to
survive, basically because it is far superior to anything previous. The first
printed copy came out in 1482 and was the geometry textbook and logic primer by
the 1700s. During this period Euclid was highly respected as a mathematician and
Elements was considered one of the greatest mathematical works of all time.
