My also out of date but slightly less so page: https://victorliu.neocities.org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.

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.

For people who have never lived in an area that is both rural and wildfire prone, pile burning to eliminate yard waste is an activity that is entirely foreign. You see, out here, most people believe that the primary method of eliminating yard waste is by burning it in a pile. I happen to live in town where there is trash pickup service available, but I opt to simply take stuff to the dump myself. Most people don't want to pay or don't have such service available. Burning yard waste is almost always extremely polluting. One burn pile full of leaves and pine needles can often smoke out my entire town. Fortunately, pile burning is only allowed on certain days (when the weather is such that wildfire risk is reduced). That is not to say that pile burning is always so bad; it has to be done properly. If the pile is hot enough, there is little smoke. But most people do not burn them hot enough with enough long-burning materials (i.e. wood).

So why did I bring this up, since a wildfire is just this on a massive scale? Well, I do not personally believe that properly managed fuel management would result in as much smoke and particulate pollution, for two reasons. One, indigenous peoples here used to regularly set fire to the forest to manage the fuel load. This was done regularly enough that there simply wasn't as much material to burn, and done when weather was cooperative (e.g. before rains). A modern wildfire can burn with such ferocity that most trees end up burning, instead of just the undergrowth. This represents a much greater release of long-captured CO2. And second, there is now a culture of placing responsibility on individual residents to maintain "defensible space", asking them to perform pile burning regularly. As I mentioned above, this results in what feels like disproportionately dense particulate pollution, with annoying regularity throughout the cooler times of year.