- P versus NP
- Hodge conjecture
- Riemann hypothesis
- Yang–Mills existence and mass gap
- Navier–Stokes existence and smoothness
- Birch and Swinnerton-Dyer conjecture
- Poincare conjecture
- Smooth four-dimensional Poincare conjecture

2.1 Algebra

2.2 Algebraic geometry

2.3 Analysis

2.4 Combinatorics

2.5 Differential geometry

2.6 Discrete geometry

2.7 Euclidean geometry

2.8 Dynamical systems

2.9 Games and puzzles

2.10 Graph theory

2.10.1 Paths and cycles in graphs

2.10.2 Graph coloring and labeling

2.10.3 Graph drawing

2.10.4 Miscellaneous graph theory

2.11 Group theory

2.12 Model theory

2.13 Number theory

2.13.1 General

2.13.2 Additive number theory

2.13.3 Algebraic number theory

2.13.4 Combinatorial number theory

2.13.5 Prime numbers

2.14 Partial differential equations

2.15 Ramsey theory

2.16 Set theory

2.17 Topology

2.18 Other

5.1 Books discussing recently solved problems[needs update]

5.2 Books discussing unsolved problems