Note: Andy, you may want to check out the basic plot of ToV, as its story and yours have quite a lot of overlap.
I really like the concept of Magic being something that's researchable, understandable, quantifiable. A kind of energy, like photons - perhaps even having similar particle/wave properties. Even more fun to think about with this system is how magic manifests itself to the senses. Presumably, it's possible to sense all magic with all five senses. But only some people have really developed the talent to sense it in this manner. To the lay person, magic is just unseen force. A mage casts magic and results start happening. Nothing too flashy unless the mage is going for that. If a person can -sense- magic though, imagine the fireworks and bangs that result from all the heat and light escaping from exciting spells!
ToV did something really neat in that it referred to spells as "Formulas", and that really excited the math-lover in me. I think we could do something similar (many fantasy novels have done it, but I think the idea still has lots of room for exploration).
Basic proposal for division of magic schools based on senses and how they might relate to gameplay.
Sense of Touch: This is probably the most intuitive way to sense magic. You feel it on your skin, in your nerve endings. You don't think about feeling it, it just happens. It's raw, it's alive, and it's easy to shape. I don't think humans would have ever developed anything resembling civilization if a lot of people were able to feel this. They'd be too caught up in the ecstasy or the pain of feeling magic all the time. Alternately, it'd be way too easy for this kind of mage to go crazy with their power.
I imagine a rare few people are born with this ability with any significant level of sensitivity. These people would be very adept at using magic, and require no teaching to use spells. In fact, they would have the opposite problem, they'd be able to learn too much magic... and unable to forget it. With too much sensitivity, they would be unable to -stop- feeling the magic. And I imagine that can be quite painful.
A less sensitive Tactile mage would probably have less trouble with pain, but more trouble in using spells intuitively. They may even require touching their targets to effect them. Or being in contact with magical items to cast proper spells.
Gameplay-wise, Tactile mages intrigue me as an idea. Sensitive ones control magic intuitively, they never have to be taught how. They could essentially be Blue Mages. Once they experience a spell, they will never forget it. They also don't have to think about the magic, much like one doesn't have to think about feeling hot or cold. They would be extremely speedy spellcasters, but would wear out quickly from the backlash of their own spells (HP-reliant spells, or one-use-cooldown spells are some example ideas). Many would be very suited to casting Healing spells as these may counteract the effects of 'old wounds' when used (Healing another person may also cause some 'backlash healing' to the lucky Tactile mage). But also, they sense magic when it touches them, so they have little time to react to it before they are affected by it, so a pure Tactile mage is probably the most magically-frail type. Alternately, they're used to experiencing constant pain, so they might be a bit more physically resistant (or have/need high HP).
A less sensitive Tactile mage is a little luckier in some ways. They wouldn't need to worry about backlash from their own spells, so they can continue to cast more. However, they may require being in contact with the target (melee-range mage!), or consuming magic from a powered-up item to direct long-range spells. These actions are still easily intuitive and would allow the low-sensitivity Tactile mage to cast effects quickly, though the abilities would not be nearly as strong as a high-sensitivity Tactile mage. Also, learning spells just be experiencing them may take more time than simply studying how to cast it. Many low-sensitivity Tactile mages, having a relatively rare sense but not burdened by constant pain, would probably consider becoming Researchers of The Flow as they already have an unteachable talent for understanding it.
Sense of Taste/Smell: Another intuitive method of sensing The Flow. The senses of Smell and Taste are strongly related and separating them seems silly, but perhaps there might be one person who is only skilled at one or the other. Both of these senses are deeply rooted in the primal brain and require little conscious thought. As a result, this kind of mage rarely needs to do much studying or focusing to be talented with their gift. Unlike the other senses, Smell and Taste can only interact with larger substances, long carbon chains and other such molecules, as compared to particles or waves. This generally means that "Flavor mages" perform magic by sensing biological/organic components created in spells, such as some kind of pseudo-proteins created by Healing magic or Transmutation magic.
Flavor mages normally end up specialists in the Healing fields by profession, thanks to their talents. Many supplement their natural affinity for Healing with study on Anatomy and Disease. Though others may take to Animal Husbandry or Botany for similar reasons. This kind of natural affinity for healing would be very beneficial from an evolutionary standpoint, so unless some kind of purging occurred (likely in some cultures, meaning that it may be more prevalent in some civilizations than others), it seems likely that many people have this ability in some capacity, though not all may know how to use it effectively unless they are particularly sensitive to scents/tastes.
Gameplay-wise, Flavor mages are fairly intuitive types, so they would be fairly fast casters, and normally specialize in Healing, though other Biological-based spells would be open to them as well. Since they can sense magic by its scent, they have far better reaction time to offensive magic than Tactile mages. Although Humans tend to have poor senses of smell in general, so it's likely they aren't particular good at reacting to it (average magic defense/evade). Manipulating magic through scent/taste would require tools/ingredients in my mind, so many spells would seem more like witch's concoctions or alchemical potions than the hand-waving Tactile mages. Probably the item-collecting/consuming-type mages in our groups, but some may be capable of using a target's own bodily fluids and humors to cause the magical reactions needed for Healing/Transmutation/Disease-causing spells.
Sense of Hearing: Now we come to the slightly more research-intensive branches of magic. Just like a sense of perfect pitch is an innate talent, sensing magic by sound is something that's primarily innately-known. However, similar to learning music, most people can be taught how to listen for different tones and pitches. Aural mages sense magic as a kind of music, and can control it in the same manner. While most people can be taught to hear the majority of tones accurately, there's a significantly fewer number of people who can manipulate the tones perfectly. The most skilled Aural mages are accomplished musicians in their own right and tend to treat magic as an art, though there are some Aural mages who treat their spells like mathematics formulas as well, especially the ones with less innate talent for hearing tones and singing on-key.
Since Aural magic is based on Sound, it tends to be the hardest to focus type of magic, and most spells are tuned with a general audience in mind. It is relatively easy to remember a spell of this manner once a song is learned and requires few resources from the caster. Some Aural mages may supplement their spellcasting abilities with instruments, lyrics, or dances for added focus. It's notable that vocal-based spells like this are the easiest to accidentally create a mistaken tone and are the most commonly flubbed kind of spell. It's also notable that the strongest spells of Aural magic tend to take a long time to complete the required pattern of tones. The more tone-deaf Aural mages tend to produce some very interesting effects using disjointed tones and pitches instead of more traditional 'songs'. Due to the nature of Dissonance and Resonance in this world, some basic Aural spells are commonly used to demonstrate the effects Dissonant and Resonant spells in even the most rural communities.
Gameplay-wise, Aural mages sense magic by sound and tend to be the most adept of all mages at sensing incoming magic before it strikes (High magic evade). Depending upon the strength of the caster, the effects of Aural magic can range from only during the performance of the chant to more permanent spells like the other schools of magic, though the longer-lasting spells are much harder to learn through this school. Spells for affecting large areas, such as manipulating weather, strengthening a group of people, or clearing a field of trees tend to be common. Casting speed for Aural mages is incredibly variable depending upon the strength of a spell. Weak spells can normally even be powered up by repeating the same chant multiple times in a row. However, mistakes happen frequently, and targeting single areas is difficult, so these spells have a tendency to miss or diffuse their effects, especially the further from the caster they get. Oddly enough, some spells actually grow in strength like a surging wave as they spread out from their caster, especially Dissonant spells.
Sense of Sight: Another research-heavy school of magic. Nearly any mage that takes up a profession in Magic eventually learns to hone their innate ability to see magic, no matter how faint it may be. It is very rare to have no ability at all to see magic, though most people tend to gloss over its subtle colors. Without being able to see it in some form, it becomes very difficult to study indeed. Vision mages are the most common mages around. They perceive magic as a wash of colors and learn to separate, connect, intensify, and erase the various shades of energy to produce physical effects. Vision magic tends to be first thing people think about when someone says the word 'spells' as Vision mages tend to produce a lot of excess energy when casting that escapes as light and heat. Because studying Vision magic is essentially studying energy, Vision mages tend to need a lot of time to study the complicated formulas for manipulating energy and take a relatively long time and a lot of focus to cast their spells, though generally with accurate, spectacular effect. Though more difficult spells may take some time to cast, Vision mages tend to be able to continue to cast simple spells for a long time without growing tired.
Gameplay-wise, I imagine Vision mages play like standard RPG mages. They can see magic long before it reaches them (provided they are paying attention) unlike Tactile and Flavor mages, but they are a bit more limited than Aural mages; giving them good durability to magic (how standard!). They can cast easy spells relatively quickly and frequently, but take more time and energy to cast larger spells (a Suiko-like charge system seems best to me). Manipulating colors means that generally using a single color (and vary shades of it) produces a corresponding elemental effect. Vision spells can be diagrammed on paper, so oftentimes even a lay person can use a simple diagrammed spell as a tool or to power a machine (or to item-cast a spell?). Vision magic has an odd tendency to be seen primarily in the Dissonant form, with very few known Resonant Vision spells in existence.
Sense of Mind/Logic: You didn't think I was going to shortchange you on senses just because I combined Smell/Taste, did you? Our Sixth Sense-type mages are the pure research branch. In no way can you accidentally become a mage like this. These mages devote their life to researching the Flow, to understanding spells, and many of them have some ability at all 4 innate magic senses. They have broken down magic into a set of laws and formulas, mapped its existence as a photon, a particle, a wave, a molecule. They understand -what- Magic is, and this knowledge itself allows them to cast spells unique to this school. They know how expand a singularity, count to infinity, simplify imaginary numbers, and divide by zero. What seems like impossibility to scientists is actually just incomplete data to these Theory mages and they know how to fill in the gaps. Oddly enough, some spiritual and religious leaders have been known to be able to produce magical effects similar to Theory magic through intense meditation and devotion, causing some to wonder about a possible connection, but authorities on both sides claim no relation.
A complex science, Theory magic tends to require complicated diagrams and geometric patterns to generate energy and focus for a spell. Mathematical formulas are commonly necessary to direct and relegate the effects of a spell, which can rapidly go out of control if handled improperly. Theory magic tends to be roughly equal in power and scope to Tactile spells, though takes a significantly longer amount of preparation to cast. As a trade-off, the caster is not directly effected by the spells and they tend to have a longer duration, even if they are not as immediately powerful. Some Theory mages have reported that using these spells is like Sensing the Thoughts of magic itself.
Gameplay-wise, there are probably no pure Theory mages, as it would require having no magical senses and that would make studying it extremely difficult. However, presumably one could exist if they studied hard enough. Being entirely magic-blind means that they have no defenses against magic. However, I suspect that someone completely null of magical senses may be some kind of untouchable blind spot in the Flow itself and might simply immune magic. It would be a rare occurrence, at any rate. Theory mages tend to be capable of some of the most spectacular magical effects, and the learnable nature of the spells makes it the ideal school for having multiple people to aid in the casting of a single spell.
A Theory mage who was quite talented in all the magical senses would be an ideal candidate for delicate tasks such as summoning creatures/deity-like entities or creating homunculi.
Overall, it seems like it wouldn't be uncommon for 'profesional' mages to have more than one magical sense, though most probably have a favored way of relating to magic. People who hold different occupations might have developed one sense in particular without needing the others, though. Gameplay-wise, this means that fighter-type characters might only know a few Taste/Smell-type spells to boost their own strength or something.
So, that's my outline for a magic system. A bit long, but I wanted to tie the gameplay system to world-building as much as possible. Agree, disagree, suggestions for tweaking?