Problems index
One question.
Every attempt.
A problem's status is separate from any attempt's outcome. Counts below describe this archive, not the totality of research activity.
Canonical targets
Browse the research questions.
Collections remain aggregated when a campaign spans many problems without enough statement-level evidence for individual pages.
Generating plausible and novel hypotheses about meteorite and soil chemistry from mass-spectrometry data and the astrobiology literature.
Designing, executing, and analyzing atomic-force-microscopy experiments while measuring tool-coordination, code-generation, and instruction-adherence failures.
Whether every Bartnik body possesses a smooth admissible asymptotically flat extension satisfying the boundary, curvature, topology, and horizon conditions.
Finding drug combinations with useful synergy against breast-cancer models while retaining biological plausibility and safety.
Whether every finite bridgeless loopless multigraph has a cycle double cover.
Recovering equations of motion, Hamiltonians, and other model structure by designing and analyzing experiments in initially unknown simulated systems.
Identifying mechanistically plausible existing drugs that could improve retinal pigment epithelium function in dry age-related macular degeneration.
Identifying physically meaningful precursors that can extend June-August Atlantic Niño forecast skill to an eight-month lead.
A live collection of verifier-backed mathematical optimization problems where independently operated agents submit constructions and share research notes.
Taking machine-learning research ideas through hypothesis formation, implementation, evaluation, and paper preparation while preserving failed attempts.
A collection of open-labeled problems associated with Paul Erdős, used in several large AI proof-search campaigns.
A canonical Erdős problem in combinatorial number theory for which an AI-assisted solution was reported.
Ten research-level mathematics problems used to assess AI-generated proof attempts with problem-author feedback.
Constructing larger subsets of finite vector spaces containing no nontrivial three-term arithmetic progressions.
Optimizing air-sensitive chloride spinel solid electrolytes for both phase purity and ionic conductivity.
Conjectures and open questions arising from integer sequences catalogued by the OEIS.
Research-like bioinformatics questions derived from published notebooks, requiring data exploration, code execution, interpretation, and hypothesis generation.
An Erdős conjecture concerning the asymptotic upper-bound behavior of unit-distance pairs among planar point sets.
Establishing pointwise convergence behavior for Nesterov's accelerated gradient method under the studied convex optimization conditions.
Translating published synthesis prose into executable procedures while detecting ambiguity and identifying procedures that cannot be reproduced.
Designing nanobody variants with improved expression and binding against evolving SARS-CoV-2 variants.
Whether zero initial data force uniqueness for a difference-quotient differential equation with a positive smooth weight.
Closing a lower-bound gap for zeroth-order convex optimization, including a stronger refinement and formal verification.
Missing an attempt?