![]() To the early Greeks, they started to get even Us to feel really good that that is definitely true? And then once you got ![]() The distance across it? And is that the same Themselves, what is the ratio? Or what is the relationship There's something similar about this opening hereĪnd this opening here. What is the relationship here? Or they might have Two twigs on the ground that looked somethingĪnother pair of twigs that looked like that and You could imagine the veryįirst humans might have studied geometry. And Euclid is considered toīe the father of geometry not because he was the first Used to something like the metric system. It says something very fundamental about nature. God, whether or not God exists or the nature of God, I include this quote is because Euclid is considered Mathematical thoughts of God." And this is a quote byĮuclid of Alexandria, who was a Greek mathematician Math seems to me to be the antithesis of that process. I have a background in biology and I enjoy the cautiousness with which biologists and biochemists approach the process of proving or testing a hypothesis. For example, why should 2 x 2 = 4? Why not 5, or 0 or 100? It is similar to a language, the inventors of which came up with grammatical rules according to their whims and fancies, and which new learners are expected to accept as gospel truth. It seems to me that math is filled with assumptions with no rhyme or reason whatsoever. This is part of my fundamental gripe with math and why I never understood anything beyond how to count my change. But how does one come up with a postulate? Are we free to assume whatever we want? What is to prevent me from assuming any kind of nonsense I want and then building a system of proofs from it - something like building lego buildings? Of course the lego structures will be 'internally consistent' in that it forms a complete world by itself, but for practical purposes, it would be totally useless. Not a great proof and written after it was proven that this could not be proved.Īs I understand it, the postulates/axioms are assumptions and they are used to construct theorems. On a side note, in 1890, Charles Dodgson (aka Lewis Carroll author of Alice in Wonderland) published a book with a "proof" of the parallel postulate using the first 4 postulates. We can see different versions of systems where the parallel postulate is false by assuming that either there are no parallel lines, or that for any line and point not on a line there are an infinite number of parallel lines. Later (1868) it was proved that the two systems were equally consistent and as consistent as the real number system. In the late 19th century (approximately 1823), three different mathematicians (Bolyai, Lobachevsky and Gauss) proved independently that there was a different system that could be used that assumed the 5th postulate was incorrect. Some really great proofs were created by mathematicians trying to prove the parallel postulate. Mathematicians kept trying to prove that the 5th postulate (commonly known as the parallel postulate) could be proved from the first four postulates and thus was unnecessary. There was a big debate for hundreds of years about whether you really needed all 5 of Euclid's basic postulates.
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