personal observations: Problem solving is an absolute requirement to be able to do most things in math. Programming can encompass one or more different domain

personal observations: Problem solving is an absolute requirement to be able to do most things in math. Programming can encompass one or more different domains. The domain ranges can vary from "problem & implimenation are turn key solution just customize/use to get 'automated results'" to full blown figure out from scratch what/how things need to be developed and what/how to impliment issue/request/problem. aka difference between biologist using database management system to 'program' needed forms/reports to make use of data vs. software engineer developing/implimenting the requirements/design for a database management system from scratch; for which a biologist will use of to generate forms/reports/store data.