Definition
Conjecture
A conjecture is a mathematical claim suggested by evidence but not yet proved.
What it means
A pattern can give you a strong idea about what always happens. Write that idea as a clear claim, then try hard to break it. If no example breaks it, the claim is still a conjecture until a proof explains why it must work every time.
Remember it
Examples suggest; a counterexample breaks; proof settles.
Example
After testing n = 1, 2, 3, 4, and 5, you conjecture that n(n + 1) is always even for whole numbers n. The tests support the claim, but a proof is still needed.
Watch for
A conjecture is not a random guess: it should be precise and supported by mathematical evidence.
Common mix-up
Checking many cases can strengthen a conjecture, but it cannot replace a proof for all cases.
Exact meaning
A conjecture is a mathematical statement proposed as true because of patterns, examples, or reasoning, but for which a proof has not yet been established. One counterexample disproves a universal conjecture; many supporting examples do not prove it.