Euclid's proof process

Out of all of the many different disciplines of the sciences, mathematics is the only science that uses the rigorous proof concept. Steven G, Krantz, author of "The History and Concept of Mathematical Proof", said that "There is no other scientific or analytical discipline that uses proof as readily and routinely as does mathematics." Even though there were several well known mathematicians that used some sort of proof concept in their work and findings, for his time, no one quite solidified the bluepring of mathematical proof as fluently as "the Father of Geometry",  Euclid.

It was Euclid of Alexandria (325 BC - 265 BC) who first truly formalized the way that we now think about mathematics. Unlike his predecessors like  Thales (640 B.C.E - 546 B.C.E) who did actually prove some of his theorems in geometry, Euclid was the first person to have definitions, axioms and then theorems, in that particular order. This proving schematic that Euclid followed is mathematics done right. Euclid's process was so powerful that 2300 years later, it is still the way in which many practice mathematics, today.

Euclid's first task was to create definitions that could be used in the proof process. Euclid would use words outside of mathematics to explain particular mathematical "things" that could later on be used in other definitions. For example, Euclid defined a "point" to be "that which has no part"(Dunham, "Journey through Genius"). Since "point" has no been defined, Euclid could now use the term "point" in the process of defining other mathematical "things".

The next step for Euclid was axioms. An axiom is a proposition regarded as self-evident true without proof. "axiom" is a slightly archaic synonym for postulate (mathworld.wolfram.com/Axiom.html). Euclid would formulate axioms using previously created definitions. Once Euclid had a solid foundation of axioms and definitions, he then would start constructing proofs for his theorems.

Euclid's method of proving theorems was always approached from a geometrical perspective, which is only one of many tools used today would working towards proving theorems. Even though the modern day mathematical proof still tends to the traditional form of Euclid that goes back 2300 years, technology and science has advanced so much that there are many, many different methods that can be used today in order to proof a mathematical theorem. For example, while Euclid only used a compass and straightedge as his tools for proving theorems (Dunham, "Journey through Genius"), today, someone might prove a theorem that would consist of a computer calculation, or it could even consist of the construction of a physical model. Furthermore, one's modern day proof method might consist of using a computer simulation or model, or a computer algebra computation using software like Mathematica, Maple, or MatLab. 

Even with all of our technological advances that did not exist during the time of Euclid, no writings or books have had an impact on mathematical thought and exact sciences as has Euclid's Elements. the only other book that has been revered more so then the elements is The Bible, which to me, is astonishing, considering it was written so long ago. Indeed, I would agree, that Euclid is in fact the "Father of Geometry."