I'm not sure if I can ask this question clearly, but anyway... We have this collection of 17 or so particles. Some of them have been known to exist for a very long time and were found when physics was still in its relative infancy, because they were trivial to detect and distinguish. I'm talking abundant, everyday particles like protons, electrons. Then we have the more 'fancy' particles like top quarks and tau neutrinos whose discovery came later. We also have this labrynthine body of mathematics that gets called the Standard Model, which I believe falls under the wider umbrella of being a collection of 'quantum field theories'. Every now and then when I get a chance, I sit down and chip away at some introductory QFT and QED material. However, I have not gotten deep into it enough yet to answer a question that I've wondered about it: Do you start off by guessing at the nature of your particle before fiddling around with a bit of mathematics & some physical laws, and seeing if some testable equation crops up? Or do you start off with the mathematics & the physics and find that lo and behold, some particle pops out that should have certain properties? The real reason I'm asking this is that I want to understand why each standard model particle (I'll worry about any extras later) should exist based on theoretical understanding rather than, for example, just postulating that something neutrino-ish must exist based on observing the energy spectrum of electrons in beta decays or whatever and determining its properties experimentally. Should I be able to look up derivations of every standard model particle? Or am I misunderstanding something?