Without knowing the right theorems to use in the proof you are trying to compose ... all your efforts might be futile despite having excellent problem solving skills.
Math uses mountains of knowledge derived over many years by hundreds of the smartest people in history.
You just can't physically repeat their work for the purpose of making your proof. You just have to know what is known so far.
For me one of the most fun parts of educations was non-organic chemistry in primary school. So little to learn and you could attempt to solve problems that twisted your brain like a pretzel (and succeed). I could solve problems my teacher couldn't because I was probably smarter then him and we both knew the same about the problem domain because it was all that was to know.
Research math is more open-ended but the idea is the same. The quantity of genius mathematicians who sit down, a la Newton or Gauss, and invent their own mathematics out of thin air is exceedingly small. Most research in math today, even among the "big" papers, is pretty incremental.
There are a lot of facts to be learned in mathematics; it is more like a language, with a huge vocabulary. And, like language, very little of mathematics is actively justified as to whether it is or is not the best way to go about solving problems. People just build on the existing mathematics as a basis... in a similar way to how people write novels in a language.
The attitude of mathematicians is as an imperial, aristocratic attitude to courtly protocol. The true problem-solving mathematician is more like the wild barbarians, who break all the protocols to achieve actual outcomes. One might say: empirical not imperial.
But the aristicratic attitude makes a lot of sense, because facts and protocols are things that one can learn and advance with, whereas a problem solver is only as good as their last solution. It's a bit magical. While one can practice problem solving, the return on that investment is no where near as reliable as the return on investing in learning established, conventional, standard facts. It's a good investment; it gives you a sustainable competitive advantage.
However, there is something massively cool about being one of the people on the frontier, who germinate and disseminate facts, rather than passively receive them.