I've been thinking about this a lot lately. From an outsider's perspective, programming is all about knowing syntax, function names, eccentricities etc. In reality, it's all about understanding what exactly is the outcome you want, and describing exactly what needs to happen to get there. It's a descriptive science in its entirety, but this isn't how you see most people on social media (read: the Internet) approach the subject.
I think the problem lies in that, from the outsider's perspective, the things you can do with software are a lot more interesting than things you can do with math, so when you see people talking about math, it's because they love and interact with math, however when you see people talking about programming, it's because people love and interact with finished software.
Problem solving is a production topic, but software and programming is more often discussed through the lens of consumption. Software design gets clicks, mathematics less so.
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.