The most critical thing a programmer needs is a sense of order-of-magnitude, to know when the thing he/she is building or implementing is going to break. And

The most critical thing a programmer needs is a sense of order-of-magnitude, to know when the thing he/she is building or implementing is going to break. And a sense of how likely such a thing is to break, again, within order of magnitude common sense-driven probability. From loops to architecture, this is applicable. Of course, you can apply this deeper, to processing efficiency, fetch times, etc. etc. I think most other fancy equations or theorems can be learned as needed. But sense checking your math with skepticism about your own assumptions, and knowledge of orders of magnitude, is key.