[1][2] Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert, the Simon problems concern quantum operators.
[1][4] In 2014, Artur Avila won a Fields Medal for work including the solution of three Simon problems.
[5][6] Among these was the problem of proving that the set of energy levels of one particular abstract quantum system was, in fact, the Cantor set, a challenge known as the "Ten Martini Problem" after the reward that Mark Kac offered for solving it.
[6][7] The 2000 list was a refinement of a similar set of problems that Simon had posed in 1984.
[1] The Simon problems as listed in 2000 (with original categorizations), are:[1][14] Solved entirely by Kiselev (2005).