> Tests and deadlines provide motivation to do the actual work.

This is so true in my experience. As a young man I could listen to the lecture and say "Yeah, yeah, I got this." and then try to work the homework problems and realize that no, I didn't really understand it. It is hard to force yourself to do the work if you don't have a negative externality for not doing it.

> Having a curriculum means that the content is laid out in a logical order that the professor believes should be achievable.

> There is a stupid amount of information out there. Breaking it down into a progression that students can follow in order to learn and understand it is incredibly important.

You can get all this from a textbook. The curricula of most undergraduate math classes are based textbooks anyway. Many math textbooks even have a roadmap in the preface that tells you which chapters can be skipped for shorter versions of a course, which ones discuss advanced topics, etc.

> Tests and deadlines provide motivation to do the actual work.

The person who asked the original question already seems to have the motivation to learn math for a specific purpose. They're not a random undergrad who has to complete a math course just because it's a requirement for graduation and never expects to use the knowledge.

Also, the downside of studying based on arbitrary deadlines is that if it takes you even slightly longer than average to understand the material, you fall progressively further behind the class. If you learn at your own pace, you can study a topic until you really understand it.

I'm from Germany and so the cost of being enrolled amounts to ~600 euros a year (and I get free public transport), so in cases like mine you'd be absolutely right - I'm mostly working freelance jobs and doing the odd course here when I feel like it, and it's pretty great. I get access to the curriculum, social contacts, a motivation kick and a general sense of immersion.

Though I don't think I'd be still doing that if I have to pay a substantial amount of money, so maybe other people just aren't as lucky? I don't know the exact situation in the US, apart from the ridiculous twenty-grand-a-semester colleges I know of, are there cheaper options?

What you're saying is agreeable: taking a class provides a certain level of motivation that self-study doesn't provide, for most people. That doesn't conflict with the idea that typical college courses have little tangible value added. If you're ok paying a couple of grand for extra motivation, then I hope you truly have a good reason to be doing so, and that it pays off. This type of system doesn't really support people who just want to learn for the sake of it though.