My wife Kathi told me my posts of late have been too serious, so this one has a lighter mood. I am a mathematician by training and this story is to give you insight into how a mathematician thinks.
You come up to a four burner stove and find Jiffy Pop on the front left burner. You turn on the front left burner and the heat does not come on, so no popcorn. So you move the Jiffy Pop to the left rear burner and turn that burner on. Again you find no heat, so no joy and no popcorn. Then you move the Jiffy Pop to the right rear burner, turn on the burner, get heat and have popcorn. It was good popcorn, but needed more butter and salt. I’ll remember that for next time.
A few days later you return to the kitchen and find Jiffy Pop on the front left burner. You turn the burner on and it does not heat, so no popcorn. What do you do next? What would an engineer do? What would a physicist do? What would a mathematician do? Think about it a minute before you read on.
I am not sure what you would do, but my training tells me the engineer will fix the stove, the physicist would move the popcorn to the right rear burner and the mathematician would move the Jiffy Pop to the left rear burner.
You might think the mathematician is dumb, but let me explain how and why I think like a mathematician. Mathematics is a rigorous science. Mathematics has strict rules of operation and everything you prove is true can be used as a starting point for the next step in problem solving.
If I want popcorn, I know how to get it. I have seen this method work. The left front burner does not work, so I go to the left rear burner, try it and it does not work, so I go to the right rear burner, turn it on and have popcorn. I do not have a rule that allows me to skip a step, thus I cannot go directly to the right rear burner.
Someday a brilliant mathematician will come along and develop a better popcorn rule, but until then, I am stuck in the slow method for popcorn.