World Solve

Simple geometric fairness questions like this remain surprisingly open for many classes of shapes, especially in three or more dimensions. Solving them has practical relevance to resource division and computational geometry.

Primes appear scattered with no obvious repeating pattern, and finding a true predictive formula, rather than just an approximation, remains unsolved. This is closely tied to the deeper mysteries of the Riemann Hypothesis.

Classifying all finite simple groups was a monumental achievement, but fully understanding how all groups relate to and build from these simple pieces remains an ongoing task. This shapes our foundational understanding of symmetry itself.

Quantum computers show promise for specific problems like factoring, but whether they offer a genuine speedup across all hard computational problems remains unproven. This question sits at the intersection of mathematics, physics, and computer science.

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.

Certain constructions, like doubling a cube's volume using classical tools, were proven impossible, but a full classification of every possible constructible versus non-constructible case remains an evolving area. This connects ancient geometry with modern algebra.

Some games are proven to always end in a draw or a specific winner under perfect play, but for many complex games, this remains unresolved due to sheer computational scale. This unsolved area touches game theory, logic, and computer science.

While specific solutions exist for certain rectangles, a full general theory predicting exactly which rectangles allow this kind of tiling remains incomplete. This puzzle blends recreational mathematics with serious combinatorics.

Gödel's incompleteness theorem confirms this for many systems, but fully mapping which systems are exempt, if any, from this limitation remains an open and active question. This continues to shape foundational debates in mathematical logic.

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.

Arrow's Impossibility Theorem proved certain fairness conditions can't all hold at once for common voting systems, but the full landscape of tradeoffs across all possible systems remains an active research area. This has real implications for the design of democratic institutions.

The Continuum Hypothesis asks whether there's a size of infinity strictly between the countable and uncountable, and it has been shown to be independent of standard mathematical axioms. This unresolved question touches the very foundation of set theory.

Fair division problems become extremely complex once individual preferences differ, and general efficient solutions for many people remain incompletely understood. This connects mathematics to real-world negotiation and resource allocation.

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.

Knot theory offers tools for identifying and classifying tangles, but calculating a guaranteed minimal ontangling path for every possible knot remains computationally unresolved. This connects abstract mathematics to physical intuition about rope and cords.

Some modern proofs rely heavily on computer verification because they're too long or complex for any person to check by hand, raising open questions about whether shorter, purely human-verifiable proofs must always exist. This unresolved tension touches both mathematics and epistemology.

Palindromic and reversible primes show interesting patterns, but whether infinitely many exist across all number bases remains unconfirmed. This is one of many number-theoretic curiosities still lacking rigorous proof.