Math: Invented or Discovered?

[camilo]

Im sorry, but this is one of my favorite questions in the world..
Is mathematics invented or discovered.

And just to clarify, I'm not talking about methods or tools we invent to study mathematical ideas. I'm talking about the ideas themselves. Example, congruences or Gauss's "clock calculator" is a tool invented for the investigation of certain divisibility problems, the fact that there exists infinitely many primes 1mod4 is the actual truth discovered by mathematics.

Or another one, topology seems like a bunch of abstract b.s. used to study even more abstract b.s., and at first sight it may seem that topology is a purely invented toolbox (which it is). But certain theorems in topology, such as the Poincare conjecture, that every closed simply connected 3-manifold is homeomorphic to a 3-sphere, is an absolute truth in mathematics so powerful that it even has implications on the shape of our very own universe (if it is simply connected, because Im pretty sure it is closed and unbounded. This is a topic worthy of its own thread, maybe i'll start one in the physics forum.)

So one thing is to argue that our tools or methods are invented, another is to say the ideas we are investigating are inventions.

So where do you stand on this?

[rsoto008]

Camilo where I stand is that I believe that we discovered it and we are still making even more new discoveries as we go deeper. Because look in the past that archaelogist found the work of the famous Archimedes that was written over by some religious people that did not know what they were doing. So that is why I believe that we are discovering it and we have only begun our journey. I believe there are still more questions that we have to make in order to find other answers to many unsolvable questions.

[Eric Wawerczyk]

Mathematics can be thought of as two different aspects: The eternal truth and the human-made language.

When a mathematician chooses to study an object, there are inherent truths present in the nature of the object. In order to obtain verification of the truth we must be able to communicate about the object and it's respective phenomena. Mathematics is both the truth described by the pythagoran theorem and the language we have developed (numbers, line, triangle) to express the statement of the truth.