World Solve

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.

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.

Some mathematical truths may be true but fundamentally unprovable within any given formal system, a possibility raised by Gödel's work but not fully mapped out for all classes of statements. This unresolved boundary shapes the philosophy of computation.

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.

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.

Logical simplification techniques work well for many cases, but a fully general method guaranteed to simplify every possible logical structure remains unresolved. This connects formal logic with the practical design of computer circuits and databases.

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.

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.

As digital platforms increasingly influence what people see, believe, and desire, it's unclear how much this shapes authentic identity versus manufactured preference. This unresolved question grows more urgent as algorithmic influence deepens in everyday life.

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.

Fraudulent warranty claims, sometimes supported by AI-generated fake documentation or images, can cost manufacturers significant money if not caught before payout. Detecting this kind of fraud at scale remains an unresolved operational challenge.

AI-generated voice calls soliciting charitable donations can convincingly target elderly individuals who may be less familiar with distinguishing genuine from fraudulent solicitations. Detection and protective measures for this vulnerable group remain underdeveloped.

Entirely fabricated conference proceedings, complete with fake papers and attendee lists, could potentially be used to pad academic resumes without detection. Verifying the legitimacy of claimed academic activities remains an unresolved challenge.

Fabricated professional licenses generated to appear authentic could potentially deceive employers or clients who don't have direct access to official verification databases. Expanding accessible, reliable verification systems remains an unresolved challenge globally.

Entirely AI-generated academic theses can be difficult for reviewers to distinguish from genuine student work without specialized detection tools, and these tools remain imperfect. Protecting the integrity of academic credentials remains an ongoing unresolved challenge.

Cameras and sensors used in security or autonomous systems still perform noticeably worse in poor visibility conditions than in daylight, creating real safety and reliability gaps. Closing this performance gap affordably remains unresolved.

Developers still occasionally and accidentally commit sensitive credentials directly into shared code repositories, creating avoidable security exposure. More robust default protections against this common mistake remain inconsistently adopted.

GPS doesn't work well inside buildings, and alternative indoor positioning technologies haven't achieved the same reliability and ease of deployment needed for widespread augmented reality navigation use. Solving indoor positioning at scale remains unresolved.