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There exists a place that we access through our minds, which some call our spirit, higher self, enlightened self, etc ... and through it comes this thing, something that Socrates and Theaetetus called being "with the muses" Those who we deem to be great minds are often adept at accessing this place. I am a believer in the allegory of the cave. The great things that we hold to be the greatest and most fundamentally true things in this world do not, in fact exist in this world. Three of these are Math, Logic, and Music.It has been said that the numbers belong to god, and as such with set theory and other forms of fundamental and abstract mathematics. The proof that numbers are otherworldly is very simple: Show me a number. That is, show me something that is purely an number, and not a representation of an idea of what that number is. "1" is a character that we have given the idea of "oneness" to. Likewise with "2" and so on. In fact, depending on the use of the representations, we can completely substitute these things and come up with a system of things that we will conclude to be "numbers." All we know is that they come with the structure of something which has a fundamental representation in our brains which we seems to just ... some up with out of necessity of thinking and in seeing the systems of the natural world.
The same argument can be made for logic. It is a structure of thought which we seem to have gotten from somewhere out of the necessity of thinking and interacting with systems in the real world. The structures already exist in that divine place and we discover them through thought.
Most mathematicians and philosophers agree with the above conclusions. But then, where do the solutions, which we have proved could not have been the product of pure systematic reasoning, come from? Some of us are so bold to say that the greatest of solutions have come with this "closeness with the muses" that Socrates had talked about.
Some people have come to me after recitals and, after hearing about my being a math major, comment on the connection between music and math. It saddens me, though, that they are referring to the physical connotations of the harmonic series and modal symmetries. If only they realised that both math and music exist in a realm which only gods can occupy. That is the connection, and the mystery.
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Apparently it wasn't too cliche' of an execution, considering how many people were stupid enough to fall for it.