Hi, guys.  @Hmorton:  The mathematical surfaces offered in the Math Function addon are certainly possible to create with standard polygonal subdivision modeling techniques.  In particular, the use of Catmull-Clark Subdivision makes most of the shapes attainable from the most basic surface modeling procedures.  However, they can be complex to achieve, and  in most cases, it's best to simply use the math function addon, since the output is of orthodox quad surface variety anyway.   For example, the first of the several mesh options; the Z Math Surface, can be done simply by modeling a basic planar surface, and then using Catmull Clark subdivision to smooth.  You'd need to mean crease certain edges in order to get the sharply pointed ends.  An umbrella is a good example of a model which can be done in a very similar way.  The other mesh options in the Math Function addon, however, would not be quite as simple.  For example, the snail shell.  The downfall of doing it manually, obviously, is that you lose out on the parametric features of the Math Function primitives, and the ability to quickly change types with simple mouse clicks.  I personally would not see any advantage to being able to reproduce most of these surfaces by hand, other than the personal challenge of being able to do so.

Some mathematical surfaces, on the other hand, can be very beneficial to know how to model by hand, because there aren't any addons which can reproduce them, and the basic objects can help improve your knowledge of the software, and be used as a basis for much larger, more complex objects later on.  I've spent the first several years of my modeling career learning about mathematical surfaces and objects.  In the end, everything we do in 3d, be it hard surface or organic, is based in trigonometric or algebraic equations one way or another, and of course math plays a role front and center in every geometric function.  I have some "math" modeling tutorials on my Youtube channel, and several renders in my gallery of some well known algebraic surfaces.  I just find them so beautiful in every way, and it fascinates me endlessly how nature itself uses math in it's own evolutionary "artistic" endeavor.

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