I experienced a really good example of why knowledge is an integral part of problem solving this morning. One of my masters students comes to me with what seems to be an intractable programming (coding!) problem. He’s tearing his hair out.
When I check his program, I find that he has defined two separate but closely-related variables, namely x and x’. The result is that he’s getting error notifications and he’s fed up.
Being a chemist and given that it’s a while since he studied maths, he either doesn’t know or hasn’t remembered that x’ is sometimes used as shorthand for dx/dt and that’s what the software ‘thinks’ he’s trying to express. And the result is long, long hours of frustration.