Math: A Discovery or an Invention?

Below are some excerpts from various websites/blogs/articles that take part in the long lasting debate of whether mathematics is a discovery or an invention. Please read them and reply. Take a position in this great debate and defend it as best you can. There is no right or wrong answer. (For extra credit, cite a source you have found on your own.)

Discovered

"When Newton saw an apple drop from an apple tree he had an epiphany. That epiphany was the concept of gravity. Even though no one before Newton had ever thought of gravity, it had always existed and had always made apples drop from trees. Newton "discovered" and put a name to the concept of an object being pulled towards the earth; he did not "invent" gravity. Just as gravity wasn't "invented", math wasn't "invented". It was "discovered.""
1/27/10 - http://www.megaessays.com/viewpaper/59728.html

"Although the Neanderthal did not have the knowledge of numbers, he still had a basic understanding of math when he established that more deer would be better than less deer. This sense of math was his ability to distinguish quantities. For example, a Neanderthal knew that the more deer he killed, the better. As long as there is nature and natural events, there is math. Before math was discovered, it existed as relationships in nature. Now that we analyze math and invent symbols and numbers to express it more efficiently, it is still the same math that the Neanderthal experienced, just in a different form."
1/27/10 - http://www.megaessays.com/viewpaper/59728.html

"...how do we know these mathematical truths? Where do we get them from? These mathematical entities, according to the Platonist School of Thought, are “out there” for us to discover, and they exist independently of the human mind. They are abstract and non-spatiotemporal. It parallels Plato’s belief in a “World of Ideas”; that unchanging ultimate reality that the everyday world tries to imitate (but imperfectly). These mathematical entities, such as triangles and fractals, are inherent in nature and cannot be ‘invented’. Our only way of knowing their existence is to try very hard to discover them... ...Pythagoras’s Theorem may be seen as an invention, but even the great Mathematician himself acknowledged that it was a discovery of his."
1/27/10 - http://www.answerbag.com/q_view/420161

Invented

"To some extent this is a matter of definition and semantics. My opinion: Mathematics, as a formal system, is invented in the sense that one starts with a certain set of elements (usually numbers, but not necessarily so) and defines a set of rules regarding various relationships between, and operations of, those elements. And you can invent any rules of the game you desire."

1/27/10 - http://www.newton.dep.anl.gov/askasci/math99/math99117.htm

"Mathematics is an invention according to the Formalists and Intuitionists, who believed that mathematics is an invention of the mind because (1) there is no place in this world for mathematical concepts such as negative and complex numbers, thus they must be a construction of the human mind; and (2) they want to fully explain the absolute certainty of mathematics, and since mathematics is an invention of the human mind, then its certainty is inevitable. Mathematics does not inform us anything about the world that we live it; they were constructed for purely practical purposes."

1/27/10 - http://www.answerbag.com/q_view/420161

"We created math. Math is just something we use to subsitute our world [with] digits or X and Y's. We created math, not discovered it. Discovering something is finding something that already exists, which is not the case [here]. Numbers are inside our minds, we created them."

1/27/10 - http://hypography.com/forums/physics-and-mathematics/4409-math-did-we-discover-or-create-6.html