What is a conjecture in math?

A conjecture in math is a statement that is believed to be true but has not been proven to be true yet. Conjectures are often based on patterns, observations, or results from specific cases, but they have not been rigorously proved using mathematical reasoning.

Conjectures play a crucial role in mathematics as they often serve as the starting point for further exploration and development of mathematical theory. They can inspire new ideas, stimulate research, and lead to the discovery of new results. However, it is important to note that a conjecture is not considered a valid mathematical result until it has been proven to be true.

Some famous examples of conjectures in math include the Collatz Conjecture, the Goldbach Conjecture, and the Twin Prime Conjecture. These conjectures have captured the interest of mathematicians for centuries, and while they have not yet been proven, they continue to be actively studied and researched in the mathematical community.