Goldbach conjecture

But humans are the only animals with the sort of general braininess needed to build aeroplanes, write poetry or contemplate the Goldbach conjecture.

For all practical purposes, we’re 0% of the way to checking that the Goldbach conjecture is true for numbers up to Graham’s number.

Terence Tao, who proved last year that every odd number can be written as the sum of at most five primes, wrote on Google Plus that “the circle method is very unlikely to be able to settle the even Goldbach conjecture by itself.” Helfgott wrote that the problem is essentially that the strong Goldbach conjecture would require asymptotic estimates—more refined information about the values of certain quantities—at key points, rather than the coarse upper bounds available through current methods.

I can only hope that Vi Hart or another talented person is writing a song about the Goldbach conjecture to the tune of the theme from the Goldberg Variations.

The strong Goldbach conjecture states that every even number greater than 2 can be written as the sum of two primes.