World Solve

Most food waste in large cities still ends up in landfills producing methane, despite composting being a relatively simple, well-understood solution. Scaling this to city-wide adoption remains logistically unresolved in most places.

Chronic fatigue syndrome leaves patients severely limited in daily function, yet its underlying biological cause remains poorly understood and often dismissed. Without a clear cause, effective treatment remains extremely difficult to develop.

Food allergy rates have been rising for decades, and the exact reasons behind this trend remain only partially understood. Understanding the cause could help prevent, not just manage, this growing health issue.

A small number of people show natural resistance to certain infections or conditions, and understanding why could reveal entirely new treatment approaches. This resistance remains only partially understood at a genetic level.

Earth's magnetic field protects us from solar radiation, but the dynamo process that generates it deep underground is still only partly understood. This matters for predicting how long that protection will last.

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.

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.

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.

Game theory has solved many two-player scenarios completely, but multiplayer games with shifting alliances and incomplete information remain far less understood in full generality. This unresolved question has real implications for economics and political strategy.

Reconstruction problems in geometry ask how much partial information is truly enough to rebuild a full shape with certainty, and general limits for all shape classes remain incompletely understood. This connects pure mathematics to practical fields like imaging and tomography.

While average behavior is well understood statistically, predicting the exact factor count for any specific number without direct calculation remains fundamentally elusive. This unresolved question touches the probabilistic side of number theory.

The three-body problem famously resists the same clean, closed-form solutions available for two-body systems, and general long-term predictability for all such systems remains incompletely understood. This unresolved question connects pure mathematics directly to astrophysics.

Certain forms of deception are broadly accepted as part of specific social contexts, but this creates unresolved tension with the general principle that honesty is a core moral virtue. Where exactly context excuses deception remains unclear.

As demand grows for minerals used in batteries and electronics, deep-sea mining is expanding into ecosystems that remain poorly understood and could take centuries to recover from disruption. Regulating this before major damage occurs remains an unresolved governance and environmental challenge.

Diet and exercise advice hasn't solved the obesity epidemic, and the biological reasons weight loss is so hard to sustain remain only partly understood. A deeper understanding could lead to treatments that actually last.

Low-income households in Kenya have almost no financial protection against climate-driven income shocks, and existing microinsurance products remain too costly or poorly understood to achieve meaningful uptake.