Is mathematics independent of human consciousness?

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I'm strongly inclined to say yes. Here's an argument. If there's even one technological civilization elsewhere in our unimaginably vast universe, then that civilization must have discovered enough math to produce technology. But we have no reason at all to think that it's a human civilization, given the very different conditions in which it evolved: if it exists, it belongs to a different species from ours. So: If math depends on human consciousness, then we're the only technological civilization in the universe, which seems very unlikely to me.

Here's a second argument. Before human beings came on the scene, did the earth orbit the sun in an ellipse, with the sun at one focus? Surely it did. (Indeed, there's every reason to think that the earth traced an elliptical orbit before any life at all emerged on it.) But "orbiting in an ellipse with the sun at one focus" is a precise mathematical description of the earth's behavior, a description that held true long before consciousness emerged here. Kepler may have discovered that description, but the truth of the description predated him and every other human. So at least one true mathematical description is independent of human consciousness.

Here's a third argument. If the answer to your question is no, then there were zero mathematical truths before human beings came along, in which case there weren't more than zero mathematical truths. But the fact that zero isn't more than zero is a mathematical truth. So there couldn't have been zero mathematical truths. So the answer to your question couldn't be no.

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