Math skills (esp proofs) shape the way you approach problems, giving the problem structure and providing you the tools to reduce it into components, relations,

Math skills (esp proofs) shape the way you approach problems, giving the problem structure and providing you the tools to reduce it into components, relations, and dependencies. To make mysteries unmysterious, such tools are indispensable. I'd go so far to disagree with you that people do well without learning math skill (those tools of thinking). If you can deconstruct a problem, then you certainly learned that skill somewhere, just not in a math class. Abstraction and reductionism are unusual capabilities to acquire on your own. As I recall, they're almost nonexistent in pre-linguistic societies like hunter-gatherers. If you have no words for abstract concepts, your thinking will be strictly concrete.