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The difficulty, Halx, is that you're operating under a false dichotomy. Either math is invented and is not universally valid, or it is discovered and is universally valid. But my point is that it is 'invented', but is universally valid. I would also say time and space are 'invented', but would you say that that means they are universally valid?
I'm putting invented in quotes here, because I don't mean, and I assume you don't mean, that some guy sat down some day and decided that 2+2=4. Sure geometry and calculus were invented in this way, but arithmetic? That's why I used the analogy of language. No one invented language, it simply arose out of changes in the human condition.
Science is, I think, a different sort of thing from mathematics. Math really does describe the way the world is. Science may or may not. There are lots of disputes about this, and I'm no philosopher of science. But the position that science is nothing more than a useful predictive heuristic is a reasonable one to hold; I don't think that, at the end of the day, such a position can be maintained with respect to math.
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"Die Deutschen meinen, daß die Kraft sich in Härte und Grausamkeit offenbaren müsse, sie unterwerfen sich dann gerne und mit Bewunderung:[...]. Daß es Kraft giebt in der Milde und Stille, das glauben sie nicht leicht."
"The Germans believe that power must reveal itself in hardness and cruelty and then submit themselves gladly and with admiration[...]. They do not believe readily that there is power in meekness and calm."
-- Friedrich Nietzsche
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