Home›Categories›Open QuestionsCategoriesOpen QuestionsCitation FormatsGeneral ReferenceGeneral Reference Citation TextMathematics Atlas. "Open Questions." Accessed August 30, 2026. https://mathematics.interactiveatlas.org/categories/open-questions-index.Copy General ReferenceAPA StyleAPA Style Citation TextMathematics Atlas. (n.d.). Open Questions. Retrieved August 30, 2026, from https://mathematics.interactiveatlas.org/categories/open-questions-indexCopy APA StyleBibTeXBibTeX Citation Text@misc{mathematicsatlas-open-questions, author = {Mathematics Atlas}, title = {Open Questions}, year = {2026}, url = {https://mathematics.interactiveatlas.org/categories/open-questions-index}, note = {Accessed August 30, 2026} }Copy BibTeXReference and ClassificationDevelopingCross-Tradition ConnectionsComments (0)Reader Challenges (0 open reader challenges)Cross-Tradition ConnectionsContainsCan every even integer greater than two really always be written as the sum of two primes?, Open Questions Well-attested Do all nontrivial zeros of the Riemann zeta function really lie on the critical line?, Open Questions Well-attested Do infinitely many twin prime pairs really exist, or does the last one eventually appear?, Open Questions Well-attested Do smooth, globally defined solutions to the three dimensional Navier-Stokes equations always exist, or can a solution break down in finite time?, Open Questions Well-attested Does a nontrivial quantum Yang-Mills theory really exist for every compact simple gauge group in four dimensions, with a strictly positive mass gap?, Open Questions Well-attested Does 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 Questions Well-attested Does 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 Questions Well-attested Does the Collatz process really always reach one, from every possible starting number?, Open Questions Well-attested Does 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 Questions Well-attested Does 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 Questions Well-attested Is every efficiently checkable problem also efficiently solvable, or is checking genuinely easier than solving?, Open Questions Well-attested Is every Hodge class on a smooth complex projective algebraic variety really a rational combination of the cohomology classes of actual algebraic subvarieties?, Open Questions Well-attested Is the abc conjecture actually true, and does Shinichi Mochizuki's inter-universal Teichmuller theory really prove it?, Open Questions Well-attested Is 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 Questions Well-attested Is there really always at least one prime number between n squared and (n plus one) squared, for every positive integer n?, Open Questions Well-attested Whenever 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 Questions Well-attested Comments (0)No comments yet. Be the first to share a thought.Sign in to join the discussion.Reader Challenges (0 open reader challenges)No disputes yet. Spotted an error or a better source? Open the first one.Sign in to dispute this or suggest a correction.View At A Past YearThe atlas records no dated fact of its own for this entry, so there is no other year to choose.Show This Year