Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
Fractals : Form, chance and dimension (San Francisco, 1977).
Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory.
A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don't get something smooth, but irregularities at a smaller scale.
Natura non facit saltum or, Nature does not make leaps ... If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).
Now that I near 80, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years ahead of my time.
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