After talking about Euclidean and non-Euclidean geometry in class, I wanted to know more about Euclid and his life. I went to a couple different sources, and found an awesome biography from the MacTutor History of Mathmatics archive that gave me a lot of interesting information.

Euclid of Alexandria was born around 325 BC, but we don’t know exactly *where* he was born. We do know, however, that he died about 265 BC in Alexandria, Egypt. We refer to him as Euclid of Alexandria to avoid confusion with Euclid of Megara, who lived nearly 100 years earlier and was a student of Socrates. (Wikipedia, 2014) We don’t know a whole lot about Euclid’s life. One source of information that exists (although not believed to be very credible) comes from some Arabian authors who claim that Euclid was the son of Naucrates and that he was born in a city called Tyre (present day Lebanon). But, as mentioned, most mathematical historians believe that the claim was invented by the authors. (O’Connor & Robertson, 1999)

Math historians have varying opinions as to the existence of Euclid the mathematician. The most widely held is that Euclid actually was a real person, and that he really did write “The Elements” and the other works published in his name. The second idea is that he was a leader of a team of mathematicians in Alexandria that all contributed in writing the works attributed to Euclid. Some think that this team even continued to publish “The Complete Works of Euclid” in Euclid’s name after his death. The third hypothesis is that Euclid of Alexandria was a creation of this team of mathematicians in Alexandria who used the name Euclid, having derived it from Euclid of Megara. (O’Connor & Robertson, 1999) There exists a great deal of evidence suggesting that Euclid, whether that be an individual person or a team of mathematicians, founded a prestigious mathematics school in Alexandria.

The authors of the article, JJ O’Connor and EF Robertson, point out that while the third hypothesis is unlikely, we see the example of Bourbaki in the 20^{th} century. However, the members were renowned mathematicians in their own right. If “Euclid” was a secret team of competent mathematicians, we don’t know who they were.

I find the argument that Euclid led a team of mathematicians most convincing. I believe Euclid was a person because of the stories and history associated with the man, but I believe that the work he performed was too much for any one man to produce without a team behind him. The Elements became a textbook that was used for centuries after his death, and I just think it’s unlikely that a work that comprehensive is something that came from just one person.

Other pieces of evidence that lead me to believe in the idea that Euclid was an actual person was the different accounts of Euclid’s relationship with others, especially mathematicians. Pappus, known as “the last of the great Greek geometers”, (O’Connor & Roberton, Pappus of Alexandria, 1999) said that Euclid was *“… most fair and well disposed towards all who were able in any measure to advance mathematics, careful in no way to give offence, and although an exact scholar not vaunting himself.*” The fact that Pappus gave such a specific description makes it seem unlikely that Euclid was merely a creation of other mathematicians of that time period. One other story that the authors recounted was originally told by Stobaeus, who was a compiler of works from many ancient Greek authors (Wikipedia, 2014). He said, “…*someone who had begun to learn geometry with Euclid, when he had learnt the first theorem, asked Euclid “What shall I get by learning these things?” Euclid called his slave and said “Give him three pence since he must make gain out of what he learns*.” My favorite story, and one that I had actually heard before in several other circles, is that of the interaction between Euclid and Ptolemy. Proclus says, “*they say that Ptolemy once asked him if there were a shorter way to study geometry than the Elements, to which he replied that there was no royal road to geometry.” *I loved that. I’ve often heard that same phrase applied to other subjects, athletics, and religious pursuits. Indeed, there is no “royal road” to anything that is of worth.

*The Elements, *like we’ve discussed in class, is Euclid’s greatest claim to fame. In the article, Robertson and O’Connor quote Sir Thomas Heath, who was responsible for translating the works of many ancient Greek authors, including Euclid to English. Heath said, “*This wonderful book, with all its imperfections, which are indeed slight enough when account is taken of the date it appeared, is and will doubtless remain the greatest mathematical textbook of all time. … Even in Greek times the most accomplished mathematicians occupied themselves with it: Heron, Pappus, Porphyry, Proclus and Simplicius wrote commentaries; Theon of Alexandria re-edited it, altering the language here and there, mostly with a view to greater clearness and consistency*…” (O’Connor & Robertson, Euclid of Alexandria, 1999) Indeed, Euclid’s name will always be reverenced as one of the formative thinkers in all mathematics for his work on one of the greatest textbooks ever produced by men. However, I maintain my belief that *The Elements* was not the work of one man, but the work of many. I also believe that it should in no way detract from the respect and praise given to Euclid, the individual, as one of the greatest mathematicians of all time.