Sorry, the question in title sounds naive. I have no doubt that math is essential in programming, but I am thinking about philosophy of programming and want to summarize when they're needed in programming. My attempt is below:

Most applications of programming are making electronics do things through their interfaces. Whether that's telling a screen to display something, a network wire to transport data, a hard disk to persist data.

But we often need math because we often transform data, or we might make said electronics do things based on user input, or an event. Transforming an event to data is a mathematical construction.

Some applications are almost purely mathematical, like banking, crypto currency, or encryption.

In your opinion, does this fully explain why we need math in programming? Is there a better way to sum it up?