true or false...

Would you say this is true or false:  one of the essentials to being a "good" programmer is being able to implement mathematical concepts even if you don't immediately fully understand the theory behind them.  Like implementing what you see verbatim from a math book into your program, even if you still have no idea most of what the math reference is saying, you still get it to work properly in your program.

like quaternions... I got tired of trying to figure out *why* they work, and *why* imaginary numbers would have anything to do with geometry with very little success in figuring it out... so I ignore that part and just **trust** that my math references are correct, and go straight to the implementation.

I sometimes feel like a "bad programmer" when i do this, but... maybe I'm just a bad mathematician (calculus certainly held me back a couple of college semesters) and maybe actually a better programmer than i give myself credit for, if I'm able to implement concepts working that I don't fully understand in my own mind in my software, perhaps?

Imagine that the square root symbol is like a little prison for numbers.  Positive numbers can escape by sacrificing a part of themselves, like 25 must give up 20 to escape.  Negative numbers on the other hand are sentenced to live in the jail until they die.  That is until they meet another prisoner like themself, and they can conspire together to escape.  In the process one of them dies, so you are only left with one of the negative numbers.