Hi, I'm currently reading a Precalculus textbook, I enjoy quite a lot but something is stressing me out: "I always want to understand everything fully and rigorously", the problem is that most precalculus books aren't rigorous, so when the author makes an assumption, I try to prove it.

You may think that this is a good habit, but I don't think so, it's making me a really slow learner and I sometimes spend hours trying to prove something rigorously.

The problem is that if I'm unable to understand something in depth, I feel like I can't move on to the next thing, even if I'm capable of doing all the problems.

So here's my question: "Can you be successful at mathematics even if you can't be rigorous sometimes?", I like to think that all the blind spots would clear up once I study calculus, analysis and the like, but I don't know if it's the case.