Are mathmatics invented or discovered?

August 22, 2011

The first thing that comes to mind is that Sir Isaac Newton and Gottfried Leibniz both invented/discovered calculus by themselves in at the same time without knowledge of the others work. This leads one to believe it must be a discovery and not invention. Another argument I would make for this is if the light bulb was invented by two people separately, the light bulb could have been created in two different ways, different filaments, gases, LEDs, or a method we have not yet discovered. The value of pi on the other hand would be exactly the same no matter how many people discover it. The ratio of a circle's circumference to it's diameter is always 3.141592653589793238462643383...

To call this a discovery it is necessary to determine what exactly is being discovered. We may call it a formula or law, but what it is fundamentally is information. Our everyday experience tells us information must be stored in some way, either symbols on paper (letters) or sequences of 0s and 1s on a hard drive. If the equation is discovered, where was that information being stored?

There are two possibilities I can figure. Either there is some other plane of reality with the information of every mathematical question that has ever been asked or will ever be asked and somehow humans are able to tap into it, or the information is somehow an innate part of our universe.

Would another universe with different laws of physics have a different value of pi? Perhaps the idea of pi wouldn't apply in another universe, or perhaps pi is a truth that would span every possible incarnation of a universe. Even in a 1 dimensional universe, assuming such a place could support intelligent life, they would still be able to calculate above their dimension as we can calculate above ours and determine the value of pi.

I feel like I could write a book about this one question but I will end it here for now.

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