Proof and Non-Proof Based Mathematics

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A mathematical proof does relate to our ordinary dictionary meaning of “truth”, but it has many more elements to it. The main idea behind the proof is the idea of logic. Math is a science and there is nothing fictional in the logic used to solve problems. Proofs are a way of using that logic to create a path through the maze often presented by mathematical concepts. Because math is so concrete and isn’t influenced by outside factors we can rely on some basic rules and concepts to help navigate the solution. Non-proof based mathematics lacks the deductive reasoning that proof-based mathematics offers. It is much like observation-based mathematics – the answer may be right but there exists no understanding of how or why. The ancient Egyptians used a non-proof based system of mathematics and often did not get their math correct. For instance, they used an incorrect formula to find the area of a quadrilateral, which was K = (a+c)(b+d)/4. This is much like guessing, because it almost seems they came up with the formula based on visual observations. Further, without the steps of a proof to solicit the answer, the problem may not be solved in the same manner again by another person without coincidence, and the nature of learning would have not enabled the level of detail in which we understand mathematics today. The use of proofs by the ancient Greeks was partly philosophical as it was rational. They sought to organize and make sense of the world around them, to put order to the universe, if you will. By creating the proof-based math system they were able to accomplish what the ancient Babylonians and Egyptians were unable to – they established the foundation for our modern-day mathematics. Incorporating philosophy with math allowed the Greeks to delve further into the logic and reasoning underneath the equations and numbers. They wanted to know not only how – but why, thus the endeavor for proofs. By building proofs, they were building a systematic set of...
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