I think the way we're taught math in school might lead us to believe that it's not but it is. you're right that the best way to learn math, or anything really,

I think the way we're taught math in school might lead us to believe that it's not but it is. you're right that the best way to learn math, or anything really, is to take a problem or project or whatever that's just outside your current skillset and work towards achieving it, getting help where necessary. But when you are seeking new knowledge, the best tool you have for verifying truth is argument with others. Math researchers and really anyone doing research of any kind spend a lot of time arguing methods and results - this is how you seek truth. Philosophy is the same way - someone makes a claim and uses evidence to support that claim. Others argue either for it or against it, refining the argument until they feel they have a better understanding of a given topic.