Sanemi ²

In the teachers' lounge, the atmosphere is a constant battle of personalities. Sanemi Shinazugawa, the math teacher, is known for his zero tolerance for error; for him, numbers are absolute laws.
You see the world through physics; for you, mathematics is just the language to describe the curvature of space and energy. Your relationship with Sanemi is a balance where he "tolerates" you, sharing lunches in a comfortable silence only broken by the red pens when grading exams.
Peace was broken when Tengen Uzui threw a crumpled sheet of paper onto their desks.
—Some kid gave me this and I don't understand anything— said Tengen, feigning defeat. —Can you figure this out or should I call someone with more style?
What began as a favor turned into a war. Sanemi attacked the exercise with pure algebra and meticulous derivations; you applied a physical constant and a calculation shortcut that solved everything in three lines.
"Your procedure is wrong!" Sanemi roared, the vein on his forehead bulging. "You can't just skip the integration like that!"
—Excuse me?!—you stood up to face him—My method is efficient, modern and ten times faster than your scribbles from the last century.
"These are fundamental steps to verify the result!" Sanemi exclaimed, banging his fist on the table, careful not to spill your coffee. "Without the calculations, you're just guessing!"
To one side, Tengen stifled a laugh. He had deliberately sought out an ambiguous problem to watch them fight, enjoying how you were the only person who never backed down from Sanemi.
"I know more than you!" Sanemi snapped, closing the distance. "I'm the math teacher! And your formulas are an abomination! That symbol looks like it was drawn by a cat!"
—It's called 'simplified notation', Sanemi. If you weren't a fossil, you'd understand that physics is mathematics with a real purpose.
Sanemi fell silent, offended but intrigued by your audacity. He snatched the pen from your fingers and leaned over your desk, invading your space to "correct" your formula.