Saturday, September 12, 2015

History of Math Proofs

I can remember back to my Sophomore year in high school, when my Geometry teacher said "Today, we are going to be proving some basic trigonometry concepts." I sat there with a blank look on my face and braced myself. This was the first day in my mathematical career where I will actually be proving a math concept is valid. Previously, I had a lot of trust in my teachers, I believed them that 1+1=2, the area of a rectangle is base times height, and a negative times a negative is actually a positive number. 
Although this task of proving a statement seemed to be daunting, I had a sense of pride, joy, and excitement when I got to the end and finally proved the theorem. This is one of the reasons why I enjoy and appreciate mathematics so much. 

This idea of a proof has dated back 2300 years ago with Euclid. He was the first to formalize the process. This process included "definitions and axioms and then theorems—in that order" (Krantz 5). According to Steven  Krantz article The History and Concept of Mathematical Proof, "A proof is a rhetorical device for convincing another mathematician that a given statement (the theorem) is true" (6). Most of the time we use logical statements within a theorem in which we will prove it is true, this is type dates back to Euclid. However, there are different types of proofs, such as calculations and building a model. 

History of Proofs:
  • Babylonians - had diagrams that showed why Pythagoras Theorem was true
  • Pythagoreans  (as a society, 569–500 B.C.E.) - discussed that the geometry statements should be proven for validity purpose 
  • Eudoxus (408–355 B.C.E.) -  first to use the word theorem and made a collection of these theorems
  • Euclid (325–265 B.C.E.) - developed the process of a proof
Euclid, developed this process the correct way. Collect all the definitions and axioms first then come up with a proposition to then prove. Since Euclid, the process that we go about proving a theorem has stayed the same however, we have discovered new definitions and axioms where we can there prove more theorems. The topic of mathematics expands daily. 

Proofs are a beautiful thing. They hold power.  They are a sense of validity in mathematics. They are an intellectual form of communication.  

Although, a proof can be challenging and daunting to take on it has great rewards. From my experience in Geometry in high school to my Senior Math Capstone in college, I appreciate and realize how complex, but yet simple math is. This is all because of proofs. 

Nature of Mathematics Blog 1


  1. I remember feeling the same way in geometry. It took me about a month to fully grasp the concept of a proof. Once I caught on, I loved the fact that I could prove something with 100% certainty. That being said, your statement "[proofs] hold power" is definitely true. More so than the diagrams they first started with. I am assuming that they realized they needed more than a diagram to prove things when they started thinking about abstract concepts such as infinity. I think it is interesting that Euclid noted that proofs are essential to prove a given statement is true to ANOTHER MATHEMATICIAN. I wonder when they realized that proofs can also be applied to non-mathematical concepts...

  2. Love this history. For complete it just needs a little more. Maybe add a bit expanding that last paragraph. "I appreciate and realize how complex, but yet simple math is." is a loaded sentence! Will proof continue to have a role in your life? Is it just a school thing? Should it be a school thing?

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