Yes (edit: accidentally said the opposite of what I meant!). What you need to be able to do is pass the exams. BUT -- plenty of people with math degrees fail these exams. It's a hell of a lot harder than learning how to hack together a RoR site.
See e.g., various discussions on http://www.actuarialoutpost.com
You can also e.g., fill a number of supporting roles around actuaries without a college degree and then demonstrate competence by taking exams.
> I wonder if maybe software developers are a little more inclined, as a "profession", toward paths that are less formalized.
I think the fact that everyone in software has the same job title makes a huge difference wrt medicine and engineering.
The guy hacking together cookie-cutter single server websites calls himself a software developer/engineer just the same as the Ph.D. hacking on compilers or ML algorithms. Everyone inside the field knows there's a huge difference between these two jobs, and that becoming the latter is basically requires a degree (perhaps even an advanced one) or really extraordinary dedication while the former probably doesn't even need a degree at all.
So when someone says "do I need a degree to become a software developer? / Is a degree the fastest path to becoming a software developer?", it's an ill-defined question. What do you mean by software developer? Do you want a good salary doing whatever in boom times or do you want to do really technically interesting work with job security even in bust times?
Conversely, most other fields tend to differentiate between job titles that require lots of skill and jobs that don't.
For example, the difference between various levels of non-doctor healthcare workers (the whole range of nurses, and then everything up/down from there) is very institutionalized. Something similar happens in engineering -- plenty of non-engineers do engineer-y things in engineering firms, but some things you'd be insane to delegate to someone who doesn't have formal engineering education.