Mathematics
5 questions
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Are there infinitely many twin primes?
Pairs of primes just two apart, like 11 and 13, keep turning up however far we look. Nobody can prove they never stop.
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Does P equal NP?
If a solution is easy to check, is it also easy to find? The answer decides what computers can ever do.
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Fermat's Last Theorem
A note in a margin claimed a proof that wouldn't fit. Finding one took mathematicians 358 years.
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Is the Collatz conjecture true?
Halve even numbers, triple odd ones and add one. Every number tried falls to 1. Nobody can prove that all of them do.
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Is the Riemann hypothesis true?
A single statement about where a function equals zero would tell us how the prime numbers are scattered.