How to create a mathemaical model

One day I was speaking to a friend of mine we were telling stories about some of the previous jobs we had held. He had been a teller at a bank. He asked me how they train tellers to recognize counterfeit money. It's really easy, he said, they never give them counterfeit money to work with. They always work with real bills when they practice counting and such. Then when you get a counterfeit it feels funny.

I recently recalled this conversation when I was looking for a pattern in some numbers.
As I copied the numbers into excel, I realized the progression kinda looked like a logistic progression with a base of 20. This tiny insight allowed me to do some further searches and find that there is a mathematical model that already represents the data I was looking at: Watts & Strogatz_model

By no means does this make me an expert in this area, but it did drive home for me the value of studying formal mathematical models.

I think the more that one studies formal models, whether they are in your current domain or not,  the more familiar you become with various types of models the better you will be at creating models yourself.

After all, a mathematical model is a set of rules that describe the behavior of data. Understanding how data behaves in various scenarios will improve your ability to recognize a pattern.