World Solve

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.

Partition numbers grow in a complex, only partially understood way, and while excellent approximations exist, a complete exact predictive formula for all cases remains elusive. This continues to be an active area within combinatorics and number theory.

Certain classes of expressions can be checked for equivalence efficiently, but a fully general and guaranteed method covering every possible mathematical expression remains unresolved. This unresolved question has real consequences for automated theorem proving and symbolic computation.

The Prime Number Theorem offers an excellent approximation, but the finer details of exactly how actual prime counts deviate from this smooth prediction remain tied to the still-unproven Riemann Hypothesis. Fully resolving this would refine one of number theory's most central results.

Dissection problems, which ask how shapes can be cut and rearranged, often lack complete general solutions beyond specific well-studied cases. This remains an open and often surprisingly difficult area of combinatorial geometry.

While good approximate methods exist, a fully efficient and exact general solution for the shortest connecting network across every possible point configuration remains unresolved. This connects computational geometry with practical network design.

Specific techniques exist for counting solutions in many cases, but a complete and general method covering every possible polynomial system remains an unresolved goal in algebraic geometry. This continues to be an active area of mathematical research.

Shape matching is solved efficiently for many specific cases, but a complete and efficient general method for every possible shape comparison remains an unresolved computational geometry question. This has real applications in computer vision and pattern recognition.

Some believe unresolved anger should eventually give way to forgiveness for the sake of personal peace, while others argue there's no moral deadline for healing from serious harm. This unresolved tension shapes both personal relationships and broader restorative justice practices.

Some argue refusing to forgive certain wrongs preserves a person's dignity and sense of justice, while others see prolonged resentment as ultimately corrosive rather than protective. This unresolved tension shapes how we understand forgiveness and self-respect.

Unsolicited help is often given with good intentions, but it's unclear whether the recipient owes any gratitude if the assistance wasn't specifically requested or wanted. This unresolved tension complicates everyday interactions around generosity and obligation.

Various criteria like intelligence, capacity to suffer, or self-awareness have been proposed to justify different treatment, but none commands universal agreement. This unresolved question shapes debates over animal rights and factory farming.

Some ethical theories suggest we're obligated to give up significant comfort to help distant strangers, while common intuition treats this as admirable but optional. Reconciling these views remains an unresolved challenge in ethics.

Some philosophers argue that creating new life is never straightforwardly good given the guaranteed hardships of existence, while most people reject this conclusion intuitively. This unresolved tension underlies debates in population ethics.

If someone truly couldn't have chosen differently given the exact circumstances, some argue they can't be fairly held responsible, while others maintain responsibility doesn't require this kind of freedom. This unresolved debate remains central to philosophy of action.

Wild animals experience enormous suffering from disease, starvation, and predation, and it's unclear whether humans have any duty to intervene, given the massive scale and complexity involved. This unresolved question is a growing but underexplored area of ethics.

Surveillance can prevent crime and terrorism, but it also erodes personal freedom, and there's no consensus on where the right balance lies. Different societies draw this line in very different places.

More people are weighing whether having children is fair to those children, given the environmental future they may inherit. This is a deeply personal question without any broadly agreed answer.

Most democratic input happens only at the ballot box, leaving years between elections where citizens have little formal say in major decisions. Better tools for ongoing public input could make governance more responsive.

Some volcanoes give warning signs, but many erupt with little notice, putting nearby populations at serious risk. Better prediction could prevent mass casualties near active volcanoes worldwide.