If your design work is not based upon science and mathematics, it is not engineering.

Not saying engineering is required to build or improve a product; it is not.

"try this" is not engineering.

I disagree. For example, the Wright brothers did air foil engineering empirically without full knowledge of the underlying fluid mechanics. Early and innovative engineering will often be less based on existing scientific or mathematical knowledge, while still using some of the methods. It's still absolutely defined as engineering.

Of course it is. The science comes from reproducing what you tried and getting the same results.

You may not have a good enough model for this observation to allow you to predict the results of other starting conditions, but it’s a model nonetheless, one that narrowly applies to the conditions you tried.