As much as I love math, I’ve realized how little I know about the actual history of it. Completing the square, proving conjectures, and using basic mathematical operations, are concepts that I developed an understanding for. But where did it all come from? Who took the time to figure all this ‘math stuff’ out?
Focusing on Greek mathematics, I began to do some research and was intrigued with my discoveries. (*Note: I will post references at the end of the blog post.)
I found this 2-minute video that gives a nice overview on how Greek mathematics influenced our society today. Watch it here!
Thales, Pythagoras, and Euclid are some of the most well-known mathematicians – not just in ancient Greece, but today too! These three, along with countless others, paved the building blocks for mathematics as we now know it. The Greeks insights/discoveries presided over one of the most dramatic and important revolutions in mathematical thought of all time.
Though they dabbled a bit with number systems and algebra, most of Greek mathematics was based on geometry. Thales, one of the Seven Sages of Ancient Greece, is considered to have been the first to lay down guidelines for the abstract development of geometry – using deductive reasoning first, mind you. He tried to establish axioms, or statements that could be accepted as truths, and thought that all other mathematical laws could be deduced from them.
Thales’ four main mathematical proofs were:
- The diameter of a circle exactly bisects the circle
- The base angles of an isosceles triangle are equal
- The two pairs of angles formed by two intersecting lines are identical
- If one side and the two adjacent angles of a triangle are shared by another triangle, the triangles are identical.
Although they seem extremely easy and obviously correct to us math majors, these first principles fueled an explosion in the study of mathematics, and taught many of the mathematicians that would follow him and build upon his theories (30 years later for Pythagoras and 300 years later was Euclid). Such basic ideas nowadays that came from years of dedication and exploration; it is shocking how long it took these concepts to come about!
Next on our list: Pythagoras.
The Pythagorean Theorem: one of the best known mathematical theorems of all time. I can bet (only hope, really) that a majority of adults can recite this theorem correctly. The theorem has to be the most proven of any mathematical theorem around!
Pythagoras was perhaps the first to realize that a complete system of mathematics could be constructed, where geometric elements corresponded with numbers. Like Thales, he worked upon proving axioms and using these to deduce other mathematical laws, building theorems upon theorems. Pythagoras, along with his Pythagorean friends in a secret society, developed the concept of trigonometry and left us with an understanding of shapes, angles, triangles, polygons and proportions that we continue to use today.
Last the list: Euclid, a very famous name among all mathematicians and is often referred to as the father of geometry. Gathering the work of all of the earlier mathematicians, Euclid created his landmark work, The Elements, which is said to be one of the most influential non-religious books of all time. Here, he established 10 axioms (also referred to as ‘postulates’). Some of these axioms seem self-explanatory, but Euclid operated on the principle that no axiom could be accepted without proof. Euclid’s postulates are shown below:
- Things which are equal to the same thing are also equal to each other.
- If equals are added to equals, the results are equal.
- If equals are subtracted from equals, the remainders are equal.
- Things that coincide with each other are equal to each other.
- The whole is greater than the part.
- A straight line can be drawn between any two points.
- Any finite straight line can be extended indefinitely in a straight line.
- For any line segment, it is possible to draw a circle using the segment as the radius and one end point as the center.
- All right angles are congruent (the same).
- If a straight line falling across two other straight lines results in the sum of the angles on the same side less than two right angles, then the two straight lines, if extended indefinitely, meet on the same side as the side where the angle sums are less than two right angles.
Seems pretty simple, right? Not exactly. Euclid used these 10 postulates to develop 465 propositions, progressing from established principles to the unknown.
The reason that Euclid was so influential is that his work was much more than just an explanation of geometry and math related topics. Euclid provided logical arguments and demanded proof for every theorem that crossed his path. These concepts of proof, mathematical rigor, and deductive reasoning gave mathematics its power and ensures that proven theories are as true today as they were thousands of years ago. Personally, I think this is one of the most important contributions of Greek mathematics.
To be continued another day; thanks for reading! (: