Conjectures must be proved for the mathematical observation to be fully accepted. When a conjecture is rigorously proved, it becomes a theorem. A conjecture is an important step in problem solving; it is not just a tool for professional mathematicians.

Why can conjectures be considered theorems?

A conjecture is considered proven only when it has been shown that it is logically impossible for it to be false. There are various methods of doing so; see methods of mathematical proof for more details. ... When a conjecture has been proven, it is no longer a conjecture but a theorem.

Is conjecture the same as theorem?

Theorem — a mathematical statement that is proved using rigorous mathematical reasoning. In a mathematical paper, the term theorem is often reserved for the most important results. ... Conjecture — a statement that is unproved, but is believed to be true (Collatz conjecture, Goldbach conjecture, twin prime conjecture).