You discover something that is ALREADY there. You invent something that is totally new or was not there before. Hence, mathematics is an "Invention".

Mathematics has always been here, since the start of the world! The no of stars, solar systems, planets, satellites.. As the world developed people started discovering different aspecs of mathematics. Someone discovered 0, other discovered how to add, substract! But it was always here all the time.

It's a discovery..you can't invent an idea. You discover it. Ü

Mathematics is the system of applying pure logic, usually by means of numbers, to any given problem. Mathematics is studied via understanding the pure logic and all of the systems that are part of it and then finally the applications. Now, true, logic has been around since the dawn of time but not in a useful manner to sentian beings. Thus mathematics was not around before sentian beings. If you choose to believe that God exists then for you mathematics was always around and thus discovered. For those of us that disbelieve in God mathematics was inveted by those that were the first sentain beings.

Knowing mathematical truths require that we be able to prove it in its theory using the set of axioms that determined that theory; the terms by which we used to express this knowledge have their meaning by virtue of or in context of that theory. Yet 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. They are known a priori; we do not need to experience them to know them or for them to exist, and this we know is true in our world, mainly because we do not possess knowledge of everything in this world yet we cannot discount the fact that they are “out there”. Pythagoras’s Theorem may be seen as an invention, but even the great Mathematician himself acknowledged that it was a discovery of his. 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. However it must be noted that the reasons for their stand on mathematics as an invention can be disregarded because an inseparable part of modern science requires the applications of mathematics and if mathematics was purely constructed for practical purposes, why then does science not construct its own rules instead of using mathematics? Also, it is insufficient reason to discount of infinity just because it cannot be experienced empirically (Intuitionists) or have its logical inferences “surveyed” based on objects in its parts (Formalists). If that is the case, then much of modern science will there be left? What we can perhaps consider is that while the mathematical objects in question are perhaps waiting for us to discover, when we do, the construction of the process by which we come to understand these objects is an invention of sorts. Take for example, π. π occurs inherently in nature and is an infinite number, and humans discovered its existence. Yet the explanation and the formula that we used to express and understand it, is an invention of humans. Whether Mathematics is a discovery or an invention is thus dependent on your views on the construction of mathematical knowledge, but I feel that it can be a mix of both.

discovery

Fire was a discovery but using it as a tool was an invention perhaps. My take is that the same applies for mathematics. Was discovery, became invention