What is the difference between intuition and conjecture in mathematics?

Question

I don't know any difference between intuition and conjecture.

In my opinion: A conjecture is a mathematical statement that has not yet been rigorously proved. Conjectures arise when one notices a pattern that holds true for many cases. Conjectures must be proved for the mathematical observation to be fully accepted. When a conjecture is rigorously proved, it becomes a theorem, and intuition is prediction of any thing and how it will be in the future.

Question: What is the difference between intuition and conjecture in mathematics ?

Answer 1

Intuition is a quality someone has, a conjecture is a statement someone makes. Intuition leads to conjectures.

For example: Riemann's intuition led him to believe that all the zeros of the zeta function lie on the critical strip. This led him to make a conjecture that all the zeros of the zeta function lie on the critical strip.

Answer 2

In mathematics, when someone says something like

intuitively, this is how it works ...

it's more a way of thinking about something. Usually not something rigorous.

A conjecture is something that is thought to be true (with good reason). Some conjectures can be numerically checked for many many cases and shown to be true but usually "impossible" to check for every possible case (for example if it's a statement about integers, there are infinitely many integers to be checked).