Say you drop a stitch. Not only will your knitting unravel, but subsequent rows will have the incorrect number of stitches. That's a very simple example. Something like turning the heel on a sock requires greater mathematical precision, and miscounting the number of stitches at any point in the pattern will lead to a very distorted sock.
Say you're finding the differential of a function of two or more variables, like pressure of a gas as a function of temperature and volume: P = 8.31T/V. First you have to take the derivative of P with respect to T. Then you take the derivative of P with respect to V. Then you find dV (the change in V) and dT (change in T) based on the values you're given. Plug all those values into the formula for the differential. Mess up at any point (or omit a negative sign, like I did), and your answer will be wrong.
Educational application: does knitting create mathematical minds?
