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Originally Posted by Qfwfq
Peano's axioms are the standard way of defining the natural numbers, that isn't a "discovery" it's an invention!
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"invent" = "to design and/or create something which has never been made before" (from Cambridge Advanced Learner's Dictionary )
We can't say that
Peano's axioms is an invention simply because it was in nature before Pean's born...Peano did just discovered them like any of us, between all seen and sensed nature's laws but took only those who are the most relevant (because of his mathematical great thinking), then put them down on a paper by using mathematical words (created by other mathematiciens). I think that mathematics is the most useless science for creating or inventing new things..Why? becasue if it did then we can be sure we have made a mistake somewhere in our reasoning.
All created things in mathematics are just "a new view" of it's basics laws...for example :
1+1 = 2 but we can also say that : 3*2 -6 +(9-7) =2. Suppose that human's QI was less than 1...if the first operation took hours to be solved...then the second can be called "Theory of 2" . I'm pretty sure that our most advanced mathematical theorys reflects only our limitations. We are using mathematics to only understand what we already have discovered in nature's laws. Perhaps we already have keys of all the understanding but we can't go much more than we are made for...
