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A mathematical statement that has been put forward as a true statement, but that no one has been able yet to prove or disprove; in mathematics, a conjecture and a hypothesis are essentially the same thing. When a conjecture has been proven to be true, it becomes known as a theorem.

Famous conjectures include the Riemann hypothesis, the Poincaré conjecture, the Goldbach conjecture, and the twin primes conjecture. Just to show how terminology can be used inconsistently, however, the most famous of all conjectures, for centuries before its proof in 1995, was always known as Fermat's last theorem!

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