World Solve

This mismatch is part of the evidence for dark matter, but the details of how it shapes galaxy rotation are still not fully worked out. A better model would sharpen our understanding of galaxy formation.

We've confirmed thousands of exoplanets, but identifying which ones could truly support life requires data we mostly don't have yet. A clearer count would refocus the search for life beyond Earth.

Right now we can only detect exoplanets indirectly, through shadows and wobbles in starlight. Direct imaging would let us actually study alien landscapes and atmospheres instead of just inferring their existence.

Every lunar mission so far has been short-term, relying entirely on supplies brought from Earth. A base that grows its own food, recycles its own water, and generates its own power would prove long-term space settlement is possible.

If P equaled NP, countless hard problems in logistics, cryptography, and optimization could be solved efficiently, but most computer scientists suspect they can't. This remains the most famous open question in computer science.

Many Diophantine equations, which ask for whole-number solutions, resist any general method for predicting how many solutions exist. Solving specific cases has taken decades and earned major mathematical prizes.

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.

Despite chess being fully deterministic with no hidden information, its complexity is so vast that no one has proven who truly holds the advantage under perfect play. Solving smaller games has offered clues, but full chess remains unresolved.

The famous four-color theorem was resolved for flat maps, but generalizing the problem to more complex or higher-dimensional surfaces remains unsettled in several cases. This continues to be explored in graph theory and topology.

True randomness is difficult to define and even harder to prove, since any formula-based sequence is, by definition, predictable if you know the formula. This unresolved tension underlies debates in both mathematics and philosophy of probability.

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.

This boolean satisfiability problem is central to computer science, and no efficient general method is known for solving every possible case quickly. It remains a benchmark problem for understanding computational complexity.

Formulas exist for degrees up to four, but general algebraic solutions for higher degrees don't exist in the same closed form, leaving open questions about alternative methods. This shapes ongoing research in both pure and computational algebra.

Irrational numbers have infinite, non-repeating digits, and while we can calculate them to enormous precision, no simple predictive pattern for their exact sequence has been found. This touches on deep unresolved questions in number theory.

Despite extensive computation, no proof confirms whether these digits behave truly randomly forever or eventually reveal some hidden structure. This remains an open question bridging number theory and statistics.

This problem, part of a broader family of questions in combinatorial geometry, has known bounds but no exact general formula for every configuration. Solving it would refine our understanding of how simple geometric constraints shape complex arrangements.

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.

Finding the shortest possible route through many locations becomes exponentially harder as the number of locations grows, and no efficient exact solution is known for all cases. This unresolved question sits at the heart of computational optimization theory.

Chaotic systems are famously sensitive to initial conditions, and whether their long-term patterns can ever be fully captured by simpler predictive rules remains an unresolved question in dynamical systems theory. This has real implications for weather prediction and other complex natural systems.

Graph theory offers many partial answers about guaranteed patterns within large networks, but a fully general and complete theory covering every possible network structure remains incomplete. This affects our understanding of everything from social networks to biological systems.