Euclid (c. 333 - c. 285 BCE) was an ancient Greek mathematician, often called the founder of geometry, who was active in Alexandria during the reign of Ptolemy I. [1] His treatise the Elements became one of the most influential works in the history of mathematics, serving as the principal textbook for teaching geometry from antiquity until the early twentieth century. [2]
Life and historical context
Little is known with certainty about Euclid's life, and few reliable biographical details survive. Ancient sources place his activity in Alexandria, the Hellenistic centre of learning in Egypt, around 300 BCE, during the reign of Ptolemy I. [1] He is traditionally held to have been trained in the mathematical tradition of Plato's Academy in Athens before establishing a school of mathematics in Alexandria. [2] Because so little is documented, some scholars have questioned whether the works bearing his name were the product of a single author or of a group of mathematicians writing collectively. [3]
The Elements
Euclid's best-known work is the Elements, a treatise in thirteen books that gathered and organized the mathematical knowledge of his era into a single logical system. [1] Beginning from a small set of definitions, postulates, and common notions, it derives a large body of results in plane and solid geometry, proportion, and number theory through step-by-step deductive proof. [2] Among its contents are the earliest surviving proof that there are infinitely many prime numbers and a systematic treatment of the five regular polyhedra. The work's insistence on demonstrating each proposition from previously established truths set a lasting standard of rigour known as the axiomatic method.
Other works
Beyond the Elements, several other treatises are ascribed to Euclid, including the Data, on the properties of given geometric figures; the Optics, an early study of perspective and vision; and works touching on astronomy and the mathematics of music. [3] Some texts attributed to him survive only in fragments or through later Arabic and Latin translations, and a number are of uncertain authorship. Together these writings indicate a broad engagement with the mathematical sciences of the Hellenistic world.
Legacy
The Elements remained a standard textbook for well over two thousand years, copied by hand through antiquity and the Middle Ages, translated into Arabic and later Latin, and among the first mathematical works printed after the invention of the printing press. [2] Its geometry, now called Euclidean geometry, dominated the subject until the nineteenth century, when mathematicians developed consistent non-Euclidean geometries by rejecting its parallel postulate. [1] Euclid's method of building knowledge from explicit axioms continues to shape the way mathematics is presented and taught. [3]
