Yes of course they can be modeled mathematically. Why couldn't they be? The analog circuits I build I simulate ahead of time using LTSpice. You can even output wav files from LTSpice and listen to them. Simulation takes ages since LTSpice isn't all that well optimized for modern Computers, but it works pretty well and matches what I see in analog circuits that I have produced. Sure there are problems where the Spice model for specific parts is too simple, but very often it turns out that these are not important for the characteristic sound of the circuit.

To me a statement as the one you made just showcases how little people know about the matter. Many just repeat talking points they have heard elsewhere.

Don't get me wrong. It is hard to e.g. accurately model a Wasp Voltage Controlled Lowpass Filter so it sounds as good as the real thing. But it is not even remotely impossible. There are much, much harder problems in electrical engineering that have been solved decades ago.