Why is intuition important in mathematics?

[Mathguy15]

A funny thing happened to me recently...

I solved a complicated math problem (for me anyway), and it was almost as if I had no idea of what I was doing. I just started writing... and it kind of came out, unconsciously...
I think I know why Poincare said that intuition creates while logic verifies...

Can anyone elaborate on intuition in mathematics?

 

[lavinia]

A funny thing happened to me recently...

I solved a complicated math problem (for me anyway), and it was almost as if I had no idea of what I was doing. I just started writing... and it kind of came out, unconsciously...
I think I know why Poincare said that intuition creates while logic verifies...

Can anyone elaborate on intuition in mathematics?

my experience is that mathematical truths appear in the mind suddenly rather than coming from algorithms. Often insight even happens when you are not consciously thinking about math, I do not know why this is true,

 

[Mathguy15]

my experience is that mathematical truths appear in the mind suddenly rather than coming from algorithms. Often insight even happens when you are not consciously thinking about math, I do not know why this is true,

Hm... I think that is broadly true. I think that the mind produces such occurrences after plugging away at the problem while you aren't. However, it is important to note that the breakthroughs often come as a result of much conscious work.

 

[johnqwertyful]

I think it's important to HAVE intuition, and to keep developing it. But at a certain point, intuition can be more of a burden than anything else. Intuition lies. Especially when dealing with things that don't behave nicely (infinity, for example).

 

[lisab]

my experience is that mathematical truths appear in the mind suddenly rather than coming from algorithms. Often insight even happens when you are not consciously thinking about math, I do not know why this is true,

That's how it is for me, too - not with just math but with physical problems, too. But wrt math, I always thought that I get insight-all-at-once because I never took very advanced math (just up to advanced calculus).

I've also found that getting solutions suddenly makes it very difficult to explain my problem-solving process to someone who's struggling. I mean, "Read the problem, think a bit, and then the answer just comes into your head!" is not very helpful .