In truth every time an issue fit for 3D printing has come up in my life, I solved it easily with wood and cardboard. I'm starting to recognize I might be a craftsman at heart.
My also out of date but slightly less so page: https://victorliu.neocities.org
Maybe now I will be inspired to actually update these.
As an immediate example, my wife's business needs p-channel small signal JFETs. These apparently are no longer fabricated, and with the way the semiconductor industry moves, they are likely never coming back in any appreciable quantity. So once the world's supply of obsoleted semiconductors dries up, the technology will basically be lost.
So yes, generally not starting with ZFC.
I can't speak to "truth" in that sense. The skepticism here is skepticism of the utility of the ideas stemming from Cantor's Paradise. It ends up in a very naval-gazing place where you prove obviously false things (like Banach-Tarski) from the axioms but have no way to map these wildly non-constructive ideas back into the real world. Or where you construct a version of the reals where the reals that we can produce via any computation is a set of measure 0 in the reals.
My Raise3D printer is high quality and reliable. It's a nice piece of hardware. The PCBs I order from JLC are high-quality, built-to-specs, and whenever there's an error, it's a design fault. They are cheap, and arrive in 10 days.
I don't like the idea of being this dependent on China, but it's where we are. Weaponizing patents a risk? Problem. Placing the knowledge of how to build civilization in a single country? Problem. At least someone is carrying the torch forward, so it could be worse.
To me this is the fundamental problem with the notion of intellectual property and its protection: so much of it is trade secret and undocumented (let's be real, we disclose as little in patents as we can get away with). Companies come and go, and in the process, institutional knowledge of how to do things is lost because there is no incentive to make it public for others to replicate. This also means that once lost, it must be rediscovered later.
For general polynomials, it matters a great deal in what basis it is represented. The typical monomial basis is usually not the best from a numerical standpoint. I am aware of some modern methods such as this: https://arxiv.org/pdf/1611.02435
For polynomials expressed in e.g. a Bernstein basis, there are often much faster and stable tailored methods working solving for the eigenvalues of a companion matrix of a different form.