It's hard to overemphasize the effect WW2 had on science. I'm not just talking about atomic bombs or the ensuing cold war. A huge part of WW2 was shortages of just about everything. Textiles were especially susceptible, because their civilian and military uses are ubiquitous, and, at the time, we pretty much had wool, silk, and cotton (pretty much all you get as far as natural fibers go, save some exotic stuff like processed bamboo and modified celluloses). Obviously, planting things and waiting is kind of hard during the (relatively) short timeline of global war. This shot the young polymer field ahead. Nylon was an early commercially successful polymer.
Nylon is actually a name for a broad class of polyamides - amides are the product you get when an amine adds to a carboxylic acid and water is lost. A common nylon is Nylon 6,6 (six carbons in the carboxylic acid, six in the amine), which is synthesized from adipoic acid (1,6-hexandioic acid) and 1,6-hexanediamine. It can be more easily synthesized from the "pre-activated" adipoyl chloride and 1,6-hexanediamine (see here for a great picture of it in action).
This is kind of neat because it's a polymerization reaction that just requires the removal of water as it goes along. Most require some kind of activator or catalyst.
I salute your salute to the nylons. There is a lot of interesting history that the development of polymer chemistry ties into.
Keep in mind that there is a whole class of polymerization reactions, the products of which, including the nylons and many polyesters, are known as condensation (or step-growth) polymers. They all by-and-large involve individual growth steps that don't have appreciably large equilibrium constants (unlike the addition polymerizations of monomers with double bonds like ethylene or styrene), so they don't necessarily require activator or catalyst for growth to occur as long as water (or hydrogen chloride or alcohol) can be removed from the reaction mixture. For practical purposes, especially with the polyesters, small amounts of catalysts or activators are usually used.
(here's a reasonable intro to the different types of polymer growth processes)