Q:

Learning to Patch Synthesizers - "Synth Theory"

I'm currently in the process of learning to produce music, and one thing I'm finding absent in any of the resources I come across is what I guess I'd call "synth theory".
For someone who's very experienced with synths, they can pick up a subtractive synthesizer they've never seen, let alone used, and after a short time, come up with a rough approximation of their intent (i.e. "asian-ish plucked string instrument") - this being because they understand how the different waveforms interact in subtractive synthesis, as well as how the ADSR envelope can change that, and thus the best route to their intended sound (short some tweaking and fine tuning).
I want to learn how to work with synths at that very root level. So far, the best and only resource I can find on how to do so is to look at presets/patches for my various synths, and try to dissect why and how they work. Eventually, after enough of that, I'd begin developing a more broad understanding.
I do this, but I feel like I'm missing something. There's got to be a name to the discipline, some kind of resource, some formalized, real thing around that particular science of music... right? Maybe additive is a bit of unexplored territory, but subtractive and FM are older than I am.
Where should I be looking, to learn this kind of thing? (Aside from experimentation / dissecting patches)

A:

There's got to be a name to the discipline, some kind of resource, some formalized, real thing around that particular science of music... right? 

You are looking for sound synthesis and sound design. I'll present you some popular resources.
Synth Secrets
One of the most popular resources (if not the most popular) is Gordon Reid's Synth Secrets series. It is robust, easy to follow (if you do it incrementally), and free. Math and physics are presented as a side note, you don't need to dive into them to follow the articles (although it would be very helpful, not everyone has the background needed).
The whole course was presented as a series of articles in the SOS magazine. Studying part 1 to 10 should be enough for you to comfortably patch a subtractive synth, which is the most common type.
Once you have the basics and subtractive synthesis down, you can move to other types of synthesis. Synths Secrets does this very well, parts 11 to 13 see modulation synthesis (AM and FM), and part 14 introduces you to additive synthesis.
That would be the end of the introductory part of that series. It's not officially labeled as such, but the subjects after part 14 are more mid-level focused (vocoders, physical modeling, etc).
Andy Farnell's Designing Sound
If you are into physics and math, Designing Sound might be a better starting point. The first part of the book is a crash introductory course into sound physics, acoustics, waves, etc. The exercises are presented in Pure Data.
It's a great book, but definitely not for everyone, and it's focused on synthesis environments and acoustics, not the typical subtractive synthesizer.
Brian Shepard's Refining Sound
Introduction to synthesis and synthesizers. It's somewhat similar to Synth Secrets, but both have stuff the other does not. It's great by itself, but it's also great as complement/companion for any other introductory synthesis course you might find.
Other resources (all free)

Wikibooks entry on sound synthesis.
MOOCs like Berklee-Coursera's Introduction to Music Production or Emory-Coursera's Introduction to Digital Sound Design.
Youtube has some great resources for all levels. Search for sound synthesis and sound design and see what you can find out. I found stuff like this, and this.

Some observations
A great way to understand synthesis is to learn a synthesis environment, like Pure Data, Max, or Reaktor. Through them you can learn how to build synthesizers (digitally), you'll put your hands in the very guts of the synths. Nothing can build a better understanding of synthesis than learning a synthesis environment (from a practical context). They are patch-based (you connect modules), so you get an actual, literal, visual representation of what's going on.
If you rather be coding than patching, you can try stuff like SuperCollider (C-like syntax), CSound (has its own syntax), or Tonic (audio synthesis in C++).
In general, if you want a soft ride through synthesis, you want to do it in this order:

Basics of sound. Waves, frequency, phase, amplitude, overtones, timbre, etc. This part scares a lot of people, but in reality they all are very simple and easy to understand concepts. You can view them in one sit.
Basics of synthesis. Envelopes, oscillators, modulators, filters, etc. Again, these are very simple and easy to understand concepts (assuming you already absorbed the basics of sound in step 1).
Some type of synthesis. There are countless types of sound synthesis, and you need a starting point and path. A common order is: subtractive, FM, AM, additive. Some teach additive first, as it goes very well with a lesson on overtones.

Once you have the theory down, it's all about practice, experience, and imagination. 

