World Solve

As climate disasters become more frequent, insurance premiums in high-risk areas are rising sharply or disappearing altogether, leaving residents financially exposed. A sustainable model for insuring these regions remains unresolved.

Sudden spikes in the price of staple commodities like wheat or rice can trigger food crises in import-dependent countries almost overnight. A more resilient global system to buffer these shocks remains unbuilt.

Some island nations face the real possibility of becoming uninhabitable within decades due to sea level rise. Cheap, effective coastal protection or relocation planning remains urgently unsolved for these communities.

These particles carry more energy than anything we can produce on Earth, and we still don't know exactly what cosmic event launches them our way. Identifying the source could reveal entirely new astrophysical processes.

Detecting gravitational waves was a breakthrough, but modeling exactly what happens during these violent mergers pushes our computing power and physics equations to their limits.

Certain simple-sounding tiling and packing puzzles remain surprisingly resistant to a complete general solution. These problems test the limits of combinatorics and geometric reasoning.

This question, closely related to the once-open Poincaré Conjecture, has been resolved in three dimensions but opens further mysteries in higher-dimensional analogues. Exploring these generalizations remains an active area of topology.

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.

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.

Various conjectures link the number of prime factors a number has to specific patterns of behavior, but many of these connections remain only partially proven. This continues to be explored within analytic number theory.

Additive combinatorics explores these kinds of guaranteed substructure questions extensively, but many specific cases remain without a fully general proof. This continues to be an active and evolving research area.

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.

Many ethical frameworks tie moral status to rationality or self-awareness, which complicates how we justify the strong obligations most people feel toward those without these capacities. This unresolved gap remains ethically significant.

Some frameworks argue we should maximize felt happiness, while others argue people should get what they actually want, even if it doesn't make them happier. These can produce very different, sometimes conflicting, ethical conclusions.

Common intuition strongly favors family and community, while some ethical theories argue all suffering deserves equal moral weight regardless of relationship. Reconciling these competing pulls remains a central unresolved tension in ethics.

Kelp forests support diverse marine ecosystems but are increasingly vulnerable to warming waters and invasive species that outcompete them once they weaken. Restoring and protecting these ecosystems at scale remains an unresolved conservation challenge.

Some of the world's largest aquifers are being pumped for irrigation and drinking water far faster than natural processes can refill them. Once fully depleted, these ancient water reserves may take centuries to recover, if they recover at all.

Algal blooms can produce toxins that harm both wildlife and humans, and they're becoming more frequent as waters warm and nutrient pollution continues from agricultural runoff. Preventing these blooms before they form remains an unresolved challenge.

Many major rivers depend on glacial melt for a steady water supply, and as these glaciers shrink, the long-term water security of downstream populations becomes increasingly uncertain. Protecting or planning around this shrinking resource remains unresolved.

A fungal disease combined with habitat destruction has driven sharp declines in amphibian populations across many regions, and effective large-scale intervention remains limited. Protecting these ecologically important species remains an unresolved conservation priority.