This is kind of an interesting question, especially when you think the answer might be "no".
Let me be more specific about the question I am asking since, obviously, a lot of folks fail math and if you can fail at it, it must exist. What I mean is, does mathematics have an existence independent of the existence of humans or is it like the economy and merely a construct of the human mind for dealing with something else we cannot currently comprehend? Or is it like music? Music doesn't exist outside of humans, yet there is a lot of sound in nature.
Another way to think about is, “Is mathematics invented or discovered?”
If cats became sentient, tool using, technology using creatures, would they have the same mathematics as humans, or some completely different metaphor for dealing with that aspect of nature? (likely it would involving burying things).
Mathematics is certainly descriptive of nature, but is it actually part of it?
An interesting view here on the “no” possibility. Also, this is interesting.
"The only mathematics that we know is the mathematics that our brain allows us to know," Dr. Lakoff said in San Francisco last month at a meeting of the American Association for the Advancement of Science. Consequently, he says, any question of math's being inherent in physical reality is moot, since there is no way to know whether or not it is. "Mathematics may or may not be out there in the world, but there's no way that we scientifically could possibly tell," Dr. Lakoff claims. Math succeeds in science, Drs. Lakoff and Nunez argue in their book, only because scientists force it to. "All the 'fitting' between mathematics and the regularities of the physical world is done within the minds of physicists who comprehend both," they write. "The mathematics is in the mind of the mathematically trained observer, not in the regularities of the physical universe."
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This is the philosophical stance that I desperately needed all through school, as I struggled with basic algebra. If math is a constuct of humans, and if math can be considered a way of expressing and interpreting our world, then it seems to me that it is a highly maleable tool for us to read and manipulate our world. I think, though, that it is different than language because language is inherent in our (and other) species.
Even though we came up with names for numbers like one two and three, We did not decide that one and two equals three. They just do. We cannot change that. It's just another way of trying to make man the center of the universe.
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