Researchers prove the k-server conjecture, demonstrating that a deterministic online algorithm can achieve competitive ratio k on any metric space using the work function algorithm. The proof employs an algebraic matrix representation where work function values correspond to matrix determinants, with updates via basis changes and amortized analysis using potential functions.
A Lean 4 formalization project invites collaborative proof attempts for the Berge–Fulkerson conjecture, an outstanding open problem asserting that every bridgeless cubic graph admits six perfect matchings covering each edge exactly twice. The conjecture, attributed to Berge and Fulkerson (1971), is known to hold for 3-edge-colorable graphs and relates to broader questions about edge coloring in cubic graphs.
The Andrews–Curtis Conjecture Challenge is a competition organized by the SAIR Foundation to find short trivializations of group presentations and to prove or disprove the Andrews–Curtis conjecture and its stable version.