Continuation of Why would magic and science be split?
So in this world, magic and "science" are split (refer to the above question), and magicians and scientists view each other with absolute skepticism and dismissal because reasons.
Magic is largely based on intuition, and is somewhat personal. Although it takes a lot of learning to become a magician, most of this is learning how one's self interacts with magic, with your magic master being a guide in this learning. They often incorporate their work with arts of various kinds. Magicians study things traditionally associated with fantasy magic.
Scientists (in this setting) on the other hand, use logic and observation. They try to isolate themselves from a system, and try to make it respond in reproducible ways. They often incorporate their work with mathematics of various kinds. Scientists study things reminiscent of 1800s and 1900s science in our world.
So a magician and scientist need to save their town from trolls armed with cannons. They try on there own to stop the trolls but fail. They are desperate, and so come together.
It starts with basically combining their forces, which is initially enough to reply the trolls. They bring reinforcements. This time, the scientist and magician assist each other in their studies. The scientist provides chemicals that help the magician with their alchemical studies, along with a primer on thermodynamics and electricity so that we can use fire and lightning spells more effectively. The magician can manipulate time and conjure up mechanical parts for the scientist, and also teaches him the weaknesses of trolls.
They push back the trolls again. The trolls come back with giant eagle bombers and monkey snipers. Its looking grim for Mr. Magician and Mr. Scientist.
The magician decides he will try to teach the scientist some magic. He starts with basic symbol magic. Although the magician likes the artistic aspects, which are seen as the most powerful, the scientist focuses on the symbols that, although are often included in more complex spells, are seen as boring and unintuitive to the magic community. The magician thinks the scientist is wasting his time for those "filler" symbols, but the scientist persists.
Those symbols in turn focus on the scientist, and his mind starts to be touched by magic. The magician feels something odd happening, a weird mixture of structured thought and intuition that seems paradoxical to him. The scientist begins to create a spell computer. Although he can't really do much else besides that (the scientist lacks the passion to create fireball spells on his own, for example), the magician helps add scrying and attack spells to the scientists algorithmic spells, systematically accomplishing things that have would take magicians years of trial and error (of course, they aren't all powerful or anything, but they have invented a completely unorthodox approach to magic).
Now the scientist wants to teach the magician some science. What science can a magician excel at?
How can a magical perspective enhance science?
Namely, the magical perspective is based on intuition, whereas the science perspective is based on logic.
Note that I'm not saying that he is literally applying magic to science, but just that he uses science in a way that would only be apparent to a magician. Also, the magical perspective by itself, although novel, should require a scientist to make practical use of it. Also, the magician should come to realization about the value of science; the magician simply using magic to replace science doesn't count.
Note that this world's "scientist" does not necessarily need to match our world's scientists. You can introduce blind spots into this world's science perspective that aren't necessarily true of this world's science perspective, as long as it fits with a impersonal and empirical kind of vibe.