>Science is the business of finding the best explanations that account for all observations.

This is exactly what induction means. Even your wording is almost identical to that of the Wikipedia page on "Inductive reasoning".

> One of the consequences of this methodology is that it turns out that all known observable phenomena can be described by fairly simple mathematical laws. But science does not assume this.

I'm not sure you fully comprehend, it's much simpler. Science does presuppose that observations mean anything related to more general rules, otherwise what would be the point of observations, right? Otherwise all data would be equivalent to TV static and to build a house we would just hope it builds itself. The way you hedge your bets with phrases like "can be described by" and "appear to" makes me think you intuitively understand the limitations of science when it comes to capturing absolute truths, such as analytical a priori truths (e.g. all bachelors are unmarried), which are correct by definition.