Euclid of Alexandria, commonly known as the “father of geometry” collected, organized, and categorized the Greek geometry of his time into a collection of volumes called The Elements. The Elements is the most widely used mathematics textbook in all of history and has formed the basis of what is now called Euclidean Geometry. As a result of the masterpiece that is The Elements, Euclid of Alexandra has been referenced as one of if not the most influential men in mathematics history. Despite his monuments impact on the field of mathematics little to nothing is known about his life; while his life might have been written about in his day nothing has been discovered documenting his life or describing his physical appearance as a result all depictions of him are products of imagination (van der Waerden and Taisbak, 2018). Euclid is often referred to as the author of the elements rather than by name. Lack of information on Euclid can be best attributed to the fact that most books and literature from the 3rd Century BC have not survived the test of time. Regardless of the absence of information pertaining to Euclid’s life, his impact on the field of mathematics continues in classes all around the world.
One of Euclid’s contemporaries, Proclus, mentions Euclid of Alexandria briefly in his Commentary on the Elements. According to Proclus, Euclid belonged to Plato's "persuasion" and brought together the Elements, drawing on prior work by several pupils of Plato (particularly Eudoxus of Cnidus, Theaetetus and Philip of Opus) and that he must have lived during the time of Ptolemy (287–212 BC) possibly teaching him in Alexandria. Proclus later retells a story that, when Ptolemy I asked if there was a shorter path to learning geometry than Euclid's Elements, "Euclid replied there is no royal road to geometry (Morrow, 1970).” This is not the only surviving quote by Euclid as he had also been known to say “the laws of nature are but the mathematical thoughts of god.”
Since there is little written about Euclid’s life this has caused many scholars to speculate such as a group of Arabian authors who wrote a biography of Euclid in which they state that he was the son of Naucrates and that he was born in Tyre. However, it is believed by historians of mathematics that this is entirely fictitious and was merely invented by the authors. Because the lack of biographical information is unusual for the period, some researchers have proposed that Euclid of Alexandria was not, in fact, a historical character and that his works were written by a team of mathematicians who took the name Euclid of Alexandriafrom the historical character Euclid of Megara. However, this hypothesis is not well accepted by scholars and there is little evidence in its favor.
Euclid’s main contribution to the world of mathematics came from his work The Elements, which was mostly a collection of previous postulates from other mathematicians but he also gave some of his own original discoveries, such as the first known proof that there are infinitely many prime numbers. In The Elements he collected important mathematical and geometric knowledge in one book. The Elements are broken up into 13 volumes: books one to six deal with plane geometry, books seven to nine deal with number theory, book eight is on geometrical progression, book ten deals with irrational numbers and books eleven to thirteen deal with three-dimensional geometry. In The Elements Euclid gave definitions, postulates, and axioms. He called axioms "common notions." He presented geometry as a system of axioms; as such each mathematical concept written about in The Elements has a following proof to prove the legitimacy of each postulate.
Euclid of Alexandria is also know for his other works: Data which assesses the properties of figures; Optics which is the first Greek work on perspective; On Divisions which looks at ways to divide a figure into two parts of a ratio; and Phaenomena which is an introduction to mathematical astronomy and gives results on the times stars in certain positions will rise and set.
Euclidean geometry is what is commonly taught in high school and undergraduate levels and describes the normal space we see around us. Modern 'non-Euclidean' geometries describe space over astronomical distances, at near-light speeds, or warped by gravity.
Unfortunately, About half of Euclid's works are lost. We only know about them because other ancient writers refer to them. The lost works of Euclid include Surface Loci, Conics, Porisms, Book of Fallacies and Elements of Music (Lancon 1991).
Euclid of Alexandria left his mark on the field of mathematics most notably with The Elements garnering him a spot among the most influential mathematicians of all time. The writings in The Elements serve as the basis for geometry as we know it. Much of what was written in The Elements is taught in high school geometry classes around the world. Euclid in The Elements gave us context in which to observe the world through, he allowed us to understand and appreciate the shapes, positions, and sizes of the objects around us everyday. Without Euclidean geometry we would not have modern day art and architecture, medicine, or engineering. While much may not be known about the life Euclid of Alexandria led, Euclid’s memory stays alive in his teachings even thousands of years later, still relevant in the modern era.