Home›Open QuestionsCategoryOpen Questions16 entries. Click any to see everything it connects to.BrowseCompareCompare At A Past YearEnter a year to compare these entries as the atlas records them at that moment. Leave it empty for the present. A year before the common era is entered with a minus sign, so 44 BCE is minus 44.Show This YearSelect all 16Can every even integer greater than two really always be written as the sum of two primes?Open Questions2 linksDo all nontrivial zeros of the Riemann zeta function really lie on the critical line?Open Questions2 linksDo infinitely many twin prime pairs really exist, or does the last one eventually appear?Open Questions2 linksDo smooth, globally defined solutions to the three dimensional Navier-Stokes equations always exist, or can a solution break down in finite time?Open Questions2 linksDoes a nontrivial quantum Yang-Mills theory really exist for every compact simple gauge group in four dimensions, with a strictly positive mass gap?Open Questions2 linksDoes every finite union-closed family of sets, other than the family holding only the empty set, really contain an element belonging to at least half of the sets in the family?Open Questions2 linksDoes every runner on a circular track, moving at its own constant and distinct speed, really become lonely at some moment, for every number of runners n?Open Questions2 linksDoes the Collatz process really always reach one, from every possible starting number?Open Questions2 linksDoes the Erdos-Straus equation 4/n = 1/x + 1/y + 1/z really have a positive-integer solution for every integer n of 2 or more?Open Questions2 linksDoes the rank of an elliptic curve's group of rational points really equal the order of vanishing of its L-function at s equals one, for every elliptic curve?Open Questions2 linksIs every efficiently checkable problem also efficiently solvable, or is checking genuinely easier than solving?Open Questions2 linksIs every Hodge class on a smooth complex projective algebraic variety really a rational combination of the cohomology classes of actual algebraic subvarieties?Open Questions2 linksIs the abc conjecture actually true, and does Shinichi Mochizuki's inter-universal Teichmuller theory really prove it?Open Questions2 linksIs there really a size of infinity strictly between the integers and the real numbers, and if not, does that fact hold absolutely or only relative to which further axioms mathematicians choose to accept?Open Questions2 linksIs there really always at least one prime number between n squared and (n plus one) squared, for every positive integer n?Open Questions2 linksWhenever A to the x plus B to the y equals C to the z, with x, y and z all greater than two, do A, B and C really always share a common prime factor?Open Questions2 links