# Problem Lists

## Lists of Open Problems

### General

- Hilbert's Problems (1900)
- The Scottish Book - problems from the Lwów School of Mathematics (1930's)
- Smale's Problems (1998)
- Clay Institute Millenium Problems (2000)
- Arnold's Problems (2005)
- Tabachnikov - A Baker's Dozen of Problems (2015)
- Nash and Rassias - Open Problems in Mathematics - Springer Book (2016)
- Collection of problem lists from AIM workshops
- Unsolved Problem List from Wolfram Mathworld

### By Field

#### Algebra

- DNIESTER NOTEBOOK: Unsolved Problems in the Theory of Rings and Modules (1993)
- Bestvina - Questions in Geometric Group Theory (pdf) (2004)
- Abert - Some questions (pdf) (2010)
- Mazurov and Khukhro - Unsolved Problems in Group Theory. The Kourovka Notebook. No. 18 (2014)
- Andruskiewitsch, Etingof, Heckenberger, Pevtsova, Witherspoon Zhang - Hopf Algebras (2015)
- Fröberg, Lundqvist, Oneto, Shapiro - Algebraic Stories from One and from the Other Pockets (2018)
- Algebra problems from Wikipedia

#### Algebraic Geometry

#### Analysis

#### Applied Mathematics

#### Combinatorics

#### Complex Analysis

- Barth, Brannan and Hayman - Research Problems in Complex Analysis (1984)
- Eskin and Zorich - Volumes of Strata of Abelian Differentials and Siegel-Veech Constants in Large Genera - (2015)
- Hayman and Lingham - Research Problems in Function Theory (2019)
- Aggarwal, Delecroix, Goujard, Zograf, Zorich - Conjectural Large Genus Asymptotics of Masur–Veech Volumes and of Area Siegel–Veech Constants of Strata of Quadratic Differentials (2020)
- Eremenko - My favorite unsolved problems

#### Discrete and Computational Geometry

#### Dynamical Systems

- Knill - Open problems in Hamiltonian dynamics (2000)
- Ward - Six problems in Algebraic Dynamics (2006)
- Open problems from the 3rd Pingree Workshop on Dynamical Systems. (2010)
- Dragović and Radnović - Periods of Pseudo-Integrable Billiards (2015)
- Boyle - Open Problems in Symbolic Dynamics (2016)
- Gasull - Some open problems in low dimensional dynamical systems (2020)
- Some open problems on multiple ergodic averages (2021)
- Open Problems in Dynamical Systems & Ergodic Theory (2021)
- Fuchs - Billiard Trajectories in Regular Polygons and Geodesics on Regular Polyhedra (2021)
- Reznik, Garcia, Koiller - Fifty New Invariants of N-Periodics in the Elliptic Billiard (2021)
- Bialy, Fierobeov, Tabachnikov - Open problems on billiards and geometric optics (2021)
- Stony Brook Open Problems in Dynamical Systems
- Dynamical Systems problems from Wikipedia

#### Geometry

- Open Problems Project - Computational Geometry
- Chern - Open Problems in Differential Geometry - (1970)
- Croft, Falconer, Guy - Unsolved Problems in Geometry (1991)
- Klee - Old and new unsolved problems in plane geometry and number theory (1991)
- Morgan and Sullivan -Open problems ins soap bubble geometry (1995)
- Furuhata, Matsuzo and Urakawa - Open Problems in Affine Differential Geometry (1998)
- Aubin - Nonlinear Problems in Riemannian Geometry (1998)
- Kapovich - Problems on boundaries of groups and KleinianGroups (2005)
- Brass, Moser, Pach - Research Problems in Discrete Geometry (Springer textbook) (2005)
- Donaldson - Some problems in differential geometry and topology (2008)
- Agrachev - Some open problems in geometric control theory and sub-Riemannian geometry (2013)
- Open Problems and Conjectures Related to the Theory of Mathematical Quasicrystals (2016)
- Gromov - 101 Questions, Problems and Conjectures around Scalar Curvature. (Incomplete and Unedited Version) (2017)
- Morgan and Pansu - A list of open problems in Differential Geometry (2018)
- Karpenkov - Open Problems on Configuration Spaces of Tensegrities (2020)
- Ghomi - Open problems in geometry of curves and surfaces (2019)
- Gromov - Still unsolved problems - video lecture (2021)
- Geometry problems from Wikipedia

#### Graph Theory

#### Logic and Set Theory

#### Mathematical Physics

- Aizenman - Open Problems in Mathematical Physics (1999)
- Simons - Problems (2000)
- Deift - Some Open Problems in Random Matrix Theory and the Theory of Integrable Systems. (2007)
- Deift - Some Open Problems in Random Matrix Theory and the Theory of Integrable Systems. II (2017)
- Five open problems in quantum information (2020))

#### Number Theory

- Landau's Problems (1912)
- Adleman & McCurley - Open Problems in NumberTheory Complexity II (1994)
- Dujella - Diophantine m-tuples (2002)
- Murty and Esmonde - Problems in Algebraic Number Theory - (2004)
- Waldschmidt - Open Diophantine Problems (2004)
- IPAM Workshop on Number Theory and Cryptography – Open Problems (2006)
- Wuthrich - Open problems in Number Theory (2011)
- Kalinin and Shkolnikov - The Number pi and a Summation by SL(2,ℤ) (2018)
- Ramassamy - Modular Periodicity of the Euler Numbers and a Sequence by Arnold (2020)
- Unsolved Problems in Number Theory (Springer Textbook by R. Guy). (1981)
- Unsolved problems in number theory, logic, and cryptography (2021)
- Number Theory problems from Wikipedia

#### Probability

#### Topology

- Kirby - Problems in Low-dimensional topology - (ps format) (1995)
- Calegari - Problems in foliations and laminations of 3–manifolds- pdf (2002)
- Ohtsuki - Problems on invariants of knots and 3-manifolds - pdf (2002)
- Kapovich - Problems on boundaries of groups and Kleinian groups (2005)
- Unsolved Problems in Virtual Knot Theory and Combinatorial Knot Theory (pdf)
- Viro - Space of Smooth 1-Knots in a 4-Manifold: Is Its Algebraic Topology Sensitive to Smooth Structures? (2015)
- Vassiliev - A Few Problems on Monodromy and Discriminants (2015)
- Delp, Hoffoss and Manning - Problems In Groups, Geometry, and Three-Manifolds (2015)
- Farb - Problems on Mapping Class Groups and Related Topics
- Hovey - Algebraic Topology Problem List
- Scott - Problems in Geometric Group Theory
- Topology problems from Wikipedia