You can take it from one of the most productive living mathematicians:

https://terrytao.wordpress.com/career-advice/theres-more-to-...

I recommend reading the entire post - it's not too long, and links to other great materials - but this is a good relevant quote:

> The point of rigour is not to destroy all intuition; instead, it should be used to destroy bad intuition while clarifying and elevating good intuition.