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I can't quite wrap my around a few things in math.

Is math true? If it is something that is constantly discovered by intelligent beings around the Universe then why is there no empirical basis for Mathematics. From my perspective, math seems to be based on intuition as it defines itself. An intuitive basis on the validity of a conjecture (I suppose in this case an axiom) is generally poor proof or a poor starting point in the study of the natural/physical sciences.

To give an example, an intuitive statement on a natural phenomenon would be "organisms are <i>designed</i> because of the specificity of their anatomy and behaviour to their lifestyle or environment".

Is math man-made and completely subjective like painting or writing? This would imply that math has no basis in the physical/natural world but (as Wigner would say) "Math is unreasonably effective in the natural sciences." Math can potentially arise in a light of an observation/question (Newton's invention of calculus to determine instantaneous velocities) but there are many cases where math seems to exist on the sole foundation of math itself and has no known application or basis in the physical world. What's more unfathomable is that this math with no known application is suddenly an amazing descriptor of the behaviour of some newly discovered particle or something of that sort.