Is mathematics a discovery or an invention?
I believe that the hunger humans naturally have for certainty cannot be overlooked. Did our need for certainty result in the invention of the least ambiguous area of knowledge; mathematics? Or was mathematics discovered when Adam and Eve realised that they each had 5 fingers on each hand, and had even more when they put both their hands together?
Monday, March 23, 2009
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8 comments:
hmensa,
That question has been kicking around for a very long time, but that doesn't make it any less pertinent today. Thanks for raising it.
The idea that mathematical objects actually exist independently of us humans (and are thus discovered) is sometimes known as mathematical platonism, after Plato's claims about the existence of a world of ideas or forms. On the other hand, the notion that mathematical concepts are invented by mathematicians is often called mathematical formalism.
It has been quipped that mathematicians are platonists during the week and formalists at the weekend! What do you think this means? What does your mathematics teacher think?
The answer that we give to this question raises important implications about our relationship with mathematics as a whole.
Here is an article that includes some treatment of the invention/discovery debate and also the idea of communicating with aliens using primes.
http://plus.maths.org/issue30/features/wilson/index.html
Thanks Mr. Kitching. I found the article quite interesting, especially the way Phil Wilson described mathematics with trousers. At this point, I am of the opinion that, Mathematics is a quarter invented, a quarter discovered, and half amazing.
In the first place i do not think mathematics is discovered. I am of the opinion that it is invented to explain some claims we have about the physical world. I believe mathematics is invented over the years when we sort of find out something about ourselves and your example about adam and eve and their fingers supports this. To address your question about about certainty, i agree to some extent that mathematics increses our certainty but then i have some doubts since some ambiguity can be seen in mathematics. Ooops i have forgotten the particular instance of ambiguity in mathematics but i will find it and get back to you.
in my point of view mathematics is discovered.this is because formulas and mathematical equations we are using naturally exist.When we are describing or explaining the discovery people get confused that mathematics is invented.
Given their incontrovertible nature, I think mathematical proofs are discovered. At least, this is what occurs to me instinctively.
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