Euler's Theorem and Natural Rights

My daughter's a college senior majoring in math. She proved Euler's Theorem in her Analysis class last week:

e^i*pi + 1 = 0.

She texted the proof to me. I told her I thought Euler had made his Theorem up.

"It comes from defining e^ix = cos x + i sin x," she said. "When x = pi, it's e^i*pi = -1, so e^i*pi +1 = 0."

"So there's a definition in there? The whole thing's pretty much arbitrary? Like 'natural' rights?"

"Yeah, like natural rights," she conceded. She graduates *summa cum laude* next month.