[mmarx]

That might suffice for solving real-world problems, but not for doing mathematics itself: Intuition will get you a long way, but for working out some of the finer details, you'll have to resort to rigour. Furthermore, without having gone through the rigorous training, you might not even know when your intuition doesn't reach far enough.

Terence Tao[0] put it this way:

»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. It is only with a combination of both rigorous formalism and good intuition that one can tackle complex mathematical problems; one needs the former to correctly deal with the fine details, and the latter to correctly deal with the big picture.«

[0] https://terrytao.wordpress.com/career-advice/there’s-more-to...

[heimatau]

I think it's pretty clear, in my reply, I'm talking about the masses need for Mathematics. Which is for 'solving real-world problems'.

I agree with Terence Tao's sentiments.

Math, for the masses, is a great way to abstractly teach the masses how to critically think about things. Math, for the masses, shouldn't get bogged down in the rigour. But if one were to go on to Adv Math, then yes, rigour is needed and demanded of the mathematician.