A conjecture is an educated guess based on incomplete information. When you make a conjecture, you're proposing what you think might be true without having all the facts yet. A detective studying clues might conjecture about who committed a crime. A scientist observing patterns might conjecture about why something happens before running experiments to test the idea.

The word comes from putting together pieces of evidence you do have to form an opinion about what you don't know for certain. If three friends are absent from school on the same day, you might conjecture they're all sick with the flu, but you won't know until you check. A conjecture is smarter than a wild guess because it's based on real observations and logical thinking, but it's not yet proven true.

In mathematics, a conjecture has a special meaning: it's a statement that seems true based on examples but hasn't been formally proven. Some famous mathematical conjectures have taken centuries to prove or disprove. The Goldbach Conjecture, which proposes that every even number greater than two can be written as the sum of two prime numbers, has remained unproven since 1742.

When something is conjectural, it's based on conjecture rather than solid proof. The difference between conjecture and knowledge is evidence: conjecture is your best thinking with the information you have, while knowledge comes from testing and confirmation.