[sova]

Splendid, I really appreciate your taking the time to formulate a response -- it's very interesting to consider a metaphysical or Platonic realm where maths, although it may not exist in isolation, ends up arriving at the same points and valleys and landscapes and landforms time and time again. That is actually quite peculiar, the regularity with which mathematics works. I spent some time at the end of my university studies [the first go-round] trying to understand how we as humans came to discover multiplication and division. There are many possible operations we can do on numbers but only some yield a useful symmetry whereas others result in a jumbled chaos.

A close friend of mine refers to humans as "symbol makers" and I hold firmly that everything in the flow of life is meaningful, but it's really astounding that we can filter out useful patterns from our surroundings. Your point alludes to me in a similar way the beauty of a leaf or a tree: it's been speculated and suggested that over many millennia our sensory systems (namely sight) have tuned in and honed in on being able to find tasty ripe fruits and berries (why they may appear red and bright or purple and bright when in full ripeness and before ruin .. to pilfer an Alt-J lyric).

In that way, perhaps maths is some sort of tree or leaf or forest that is naturally existent, not actually separate from the earth or the forest or the consciousness of man, but still somehow a useful set of patterns our [mind] intellect-sense has been able to pick out and find the tasty and juicy bits of.

One very fascinating part of the whole narrative of mathematics is Progress. For example, Kepler and his assistant's calculated observations of the planets, mathematicians dedicating their lives to figuring out n-many decimal places of logarithms and creating reference books, and also equations and derivations. Although maths may somehow "exist" naturally because a set of equations or a set of inferences or physical phenomena may have a mathematical representation, they still need to be discovered (and often re-discovered) to stick around and be of any use to us. To me it still echoes of the personal mission of understanding and critical thinking -- one must come to the solution on their own and verify it in their personal experience to truly feel it and know it to be truthful.

Would you categorize maths as more of an invention or as a discovery? Pure discovery would imply that maths exists on its own like a tree does (or "might" if we consider that a perceiving consciousness must also be part of the 'tree'). Whereas, an invention is something deliberately put together to solve a functional need in the life of man.