World Solve

Astronomical observations demand extra unseen mass, but candidate particles from extensions of the Standard Model remain undetected. New detector designs, astrophysical surveys, and theoretical models are needed to pin down its nature.

Mechanisms behind superconductivity in cuprates and iron-based materials remain contested. Combined experimental and theoretical work is needed to unlock room-temperature materials.

Engineering constraints and ethical questions hinder development. Research into autonomous systems and governance frameworks could move concepts forward.

General relativity governs massive scale gravity while quantum mechanics governs atomic scales, but they break down together at black hole singularities. Developing a unified Theory of Quantum Gravity is the holy grail of theoretical physics.

Cosmic strings are theoretical linear defects in space-time that could explain early cosmic structure formation. Advanced gravitational lensing networks are required to detect their unique space-bending signatures.

Sphere-packing problems are solved for a few specific dimensions, but the general pattern across all possible dimensions remains unknown. This affects fields ranging from error-correcting codes to theoretical physics.

While the standard cube's maximum was determined through massive computation, generalized versions with more dimensions or larger sizes remain computationally and theoretically unresolved. This connects group theory with combinatorial optimization.

Sorting algorithms have been optimized extensively, but proving a true absolute lower bound across all possible sorting methods remains an unresolved question in computational theory. This affects the fundamental efficiency limits of computing.

Physical laws impose some theoretical limits on computation speed and energy use, but the exact universal boundary, if one truly exists, remains unresolved. This connects computer science directly to fundamental physics.

This is the famous Halting Problem, proven impossible to solve in full generality, yet many partial and practical questions around predicting program behavior remain actively studied. This shapes the theoretical limits of what computers can ever determine about themselves.

Even our best physical models rely on approximations or idealized assumptions, and whether a truly complete and exact mathematical simulation is even theoretically possible remains unresolved. This touches on the deep relationship between mathematics and the physical world.

Some lower bounds on computational efficiency are proven for specific tasks, but a fully unified theory covering every possible algorithmic problem remains unresolved. This unresolved question shapes the outer limits of computer science.

Modern cryptography largely depends on problems assumed, but not proven, to be computationally hard, leaving a theoretical gap in fully guaranteed security. This unresolved foundation underlies much of digital security today.

Probability theory offers strong predictive tools for many games, but a fully complete and general model covering every conceivable game of chance remains theoretically unresolved. This touches both pure mathematics and the philosophy of randomness.

Scheduling problems appear throughout logistics and computing, and while efficient solutions exist for many specific cases, a fully general efficient method remains unresolved for the broader problem family. This unresolved question connects theoretical computer science with real-world efficiency.

Information theory provides strong bounds on efficiency for many specific cases, but proving whether truly optimal encoding always exists for every possible scenario remains an unresolved theoretical question. This connects mathematics directly to modern data compression and communication.

Statistical and mathematical tools can detect many kinds of patterns efficiently, but a fully general and guaranteed method covering every possible hidden pattern type remains an unresolved theoretical question. This connects pure mathematics with the practical challenges of modern data analysis.

Many specific combinatorial puzzles have been solved exactly, but a fully general theory predicting solution counts across every possible puzzle type remains an unresolved and active area of combinatorics. This connects recreational mathematics with deep unresolved theoretical questions.

If moral status depends on capacities like reasoning or suffering rather than being human specifically, then sufficiently advanced machines or aliens could theoretically deserve equal consideration. This unresolved question has growing relevance as artificial intelligence advances.

Crop residue and animal waste could theoretically be converted into biogas or other clean energy sources, but the infrastructure needed remains too costly for many farms to adopt. Scaling this technology affordably remains an unresolved opportunity.