Repository of problems worth solving
World Solve is a public institutional repository for identifying real unresolved problems across science, society, health, governance, economics, and local systems. Each entry is intended to be citable, inspectable, and actionable.
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4194Total
4194Open
0Solved
9Humans
open
Global / Unspecified, Global
Graph theory offers many partial answers about guaranteed patterns within large networks, but a fully general and complete theory covering every possible network structure remains incomplete. This affects our understanding of everything from social networks to biological systems.
mathematics-logic
global-unspecified
every
network
haven
determined
whether
sufficiently
complex
connections
must
always
possible
philosophy-ethics
resolved
know
mathematical
open
Global / Unspecified, Global
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.
technology-computing
global-unspecified
don
know
whether
there
maximum
theoretical
limit
efficiently
any
sorting
philosophy-ethics
resolved
haven
mathematics-logic
possible
every
open
Global / Unspecified, Global
While many invariants help distinguish specific knots, no single finite and fully general method has been proven to work for absolutely every possible pair of knots. This remains a central unresolved question in the mathematical study of knots.
mathematics-logic
global-unspecified
every
knot
proven
possible
finite
knots
haven
whether
three-dimensional
distinguished
know
resolved
philosophy-ethics
mathematical
open
Global / Unspecified, Global
Some proofs are famously long and complex, and it remains unknown whether shorter, more elegant proofs must always exist in principle, even if we haven't yet found them. This unresolved question touches on both mathematics and the philosophy of mathematical elegance.
mathematics-logic
global-unspecified
haven
whether
always
shorter
mathematical
long
resolved
possible
find
simpler
philosophy-ethics
know
every
open
Global / Unspecified, Global
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.
economics-resources
global-unspecified
strategy
multiplayer
games
don
know
whether
every
possible
complex
reduced
philosophy-ethics
resolved
haven
mathematics-logic
mathematical
open
Global / Unspecified, Global
Some infinite series have been solved exactly, revealing elegant connections to constants like pi, while many similar-looking series remain stubbornly unresolved. This ongoing challenge continues to drive research in mathematical analysis.
mathematics-logic
global-unspecified
series
infinite
mathematical
constants
haven
proven
whether
exact
value
certain
know
philosophy-ethics
resolved
possible
every
open
Global / Unspecified, Global
Gödel's theorems already limit what's possible here for sufficiently powerful systems, but the full landscape of alternative systems and their limitations remains an active and unresolved area of mathematical logic. This continues to shape our understanding of the foundations of mathematics itself.
mathematics-logic
global-unspecified
possible
mathematical
haven
determined
whether
build
truly
complete
consistent
system
philosophy-ethics
resolved
know
every
open
Global / Unspecified, Global
This long-standing conjecture claims there's always at least one prime number between any two consecutive perfect squares, and while verified extensively by computer, no general proof exists. Solving it would sharpen our understanding of prime distribution.
mathematics-logic
global-unspecified
there
conjecture
always
between
consecutive
perfect
squares
don
know
whether
haven
possible
every
philosophy-ethics
resolved
mathematical
open
Global / Unspecified, Global
Combinatorial geometry problems like this remain partially solved for specific shapes and configurations, but a fully general guarantee across all possible line arrangements is still unproven. This connects visual intuition with rigorous mathematical guarantees.
mathematics-logic
global-unspecified
like
specific
haven
resolved
whether
every
finite
set
straight
lines
know
possible
philosophy-ethics
mathematical
open
Global / Unspecified, Global
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.
mathematics-logic
global-unspecified
whether
possible
mathematical
expressions
haven
proven
always
determine
only
finite
philosophy-ethics
resolved
know
every
open
Global / Unspecified, Global
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.
mathematics-logic
global-unspecified
number
prime
factors
has
don
know
whether
exact
minimum
distinct
haven
possible
every
resolved
philosophy-ethics
mathematical
open
Global / Unspecified, Global
Some cellular automata, like simple grid-based rule systems, produce behavior so complex that no shortcut prediction method has been proven to exist beyond simply running the simulation. This unresolved question touches on computational irreducibility and the philosophy of prediction.
philosophy-ethics
global-unspecified
complex
cellular
shortcut
haven
determined
whether
possible
perfectly
predict
outcome
know
mathematics-logic
resolved
every
mathematical
open
Global / Unspecified, Global
Economic models often assume equilibrium is reachable under certain conditions, but proving this holds true across every possible complex real-world scenario remains mathematically incomplete. This connects pure mathematics directly to economic theory.
economics-resources
global-unspecified
every
possible
mathematically
equilibrium
haven
resolved
whether
strategy
resource-limited
economy
mathematics-logic
know
philosophy-ethics
mathematical
open
Global / Unspecified, Global
Modern cryptography largely depends on problems assumed, but not proven, to be computationally hard, leaving a theoretical gap in fully guaranteed security. This unresolved foundation underlies much of digital security today.
mathematics-logic
global-unspecified
don
know
whether
possible
construct
truly
unbreakable
code
only
mathematical
philosophy-ethics
resolved
haven
every
open
Global / Unspecified, Global
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.
mathematics-logic
global-unspecified
number
smooth
approximation
haven
proven
whether
primes
below
any
given
know
possible
every
philosophy-ethics
resolved
mathematical
open
Global / Unspecified, Global
Fair division theory has strong results for two-party negotiations, but multi-party fairness guarantees become significantly harder to prove in full generality. This unresolved area connects mathematics with real-world conflict resolution.
mathematics-logic
global-unspecified
fair
don
know
whether
mathematically
possible
guarantee
perfectly
outcome
any
philosophy-ethics
haven
resolved
every
open
Global / Unspecified, Global
Random graph theory offers probabilistic guarantees for many structures, but proving certainty, rather than high likelihood, for every possible case remains an unresolved and active research area. This affects our understanding of networks in biology, technology, and social systems.
mathematics-logic
global-unspecified
every
haven
resolved
whether
sufficiently
large
randomly
generated
network
must
philosophy-ethics
know
possible
mathematical
open
Global / Unspecified, Global
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.
mathematics-logic
global-unspecified
general
haven
proven
whether
there
method
determining
exact
number
ways
philosophy-ethics
know
possible
resolved
every
mathematical
open
Global / Unspecified, Global
Some deterministic functions produce output so irregular it resembles randomness, and a complete classification of exactly which rules produce this behavior remains incomplete. This unresolved boundary connects number theory, chaos theory, and computer science.
mathematics-logic
global-unspecified
deterministic
don
know
whether
possible
fully
characterize
every
mathematical
function
haven
philosophy-ethics
resolved
open
Global / Unspecified, Global
Games involving bluffing or incomplete knowledge, like certain card games, resist the same clean mathematical solutions available for games of complete information. This unresolved question remains central to advanced game theory research.
mathematics-logic
global-unspecified
game
information
hidden
games
haven
determined
whether
every
possible
strategy
philosophy-ethics
resolved
know
mathematical
