Marian Slingeneyer directly taught Kihara Kagun very little.

Just by having the existence of magic proven to him, Kihara Kagun then put together spells and the means of refining magic power almost entirely on his own.

[...]

“He’s not worth teaching. There are tons of things I could teach him, but when I teach him even one thing according to the textbook, it becomes something else within him. In the end, having him learn things on his own is the only way. All I can do is correct things. I guess you could say I can’t give him the power to fire a missile, but I can correct the trajectory of a falling bomb with its tail. …Ha ha. I think he infected me with those science analogies.”

When they joined Gremlin, Kihara Kagun’s contributions were primarily as a heretical researcher of the science side rather than as a magician. Whenever Gremlin magicians used scientific technology, Kihara Kagun’s knowledge was at the base of it. Most likely, his knowledge would remain after his death and function as a major power within Gremlin.

Toaru Majutsu no Index New Testament vol.4 sub.33