Science would be ruined if (like sports) it were to put competition above everything else, and if it were to clarify the rules of competition by withdrawing entirely into narrowly defined specialities. The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
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.