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Goldbach's Conjecture
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Goldbach's conjecture is one of the oldest open problems in mathematics. The strong version reformulated by Euler states that every even positive integer greater than or equal to 4 can be written as a sum of two primes.
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The Goldbach's Conjecture has been checked by vector computers for all the even integers up to very high values. It is still valid and is still (1998, May) not demonstrated by mathematical means.
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Doug Lenat 's Automated Mathematician rediscovered Goldbach's Conjecture in 1982. This is considered one of the earliest demonstrations that artificial intelligence s are capable of scientific discovery (but see the discussion at Automated Mathematician ).
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Because it is easily understood by laymen, Goldbach's conjecture is a popular target for pseudomathematicians who attempt to prove it, sometimes even disprove it, sometimes using only high-school-level mathematics. It shares this fate with the four-color theorem and Fermat's last theorem, each of which ... has an easily stated problem, but a current proof which is extraordinarily elaborate.
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Goldbach's Conjecture