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
Palindromic and reversible primes show interesting patterns, but whether infinitely many exist across all number bases remains unconfirmed. This is one of many number-theoretic curiosities still lacking rigorous proof.
mathematics-logic
global-unspecified
prime
whether
infinitely
haven
proven
there
numbers
remain
you
reverse
know
possible
philosophy-ethics
resolved
every
mathematical
open
Global / Unspecified, Global
While specific puzzle sizes have been fully solved computationally, generalizing the worst-case difficulty formula across all puzzle sizes remains an open combinatorial question. This links recreational mathematics with formal complexity theory.
mathematics-logic
global-unspecified
haven
resolved
exact
minimum
number
moves
required
solve
hardest
possible
whether
know
philosophy-ethics
every
mathematical
open
Global / Unspecified, Global
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.
technology-computing
global-unspecified
program
whether
determine
don
know
possible
build
computer
always
any
haven
resolved
philosophy-ethics
mathematics-logic
every
open
Global / Unspecified, Global
Related conjectures about how primes combine remain only partially proven for specific ranges, without a fully general confirmed pattern. This connects to broader unresolved questions about the additive structure of prime numbers.
mathematics-logic
global-unspecified
prime
proven
numbers
haven
whether
every
sufficiently
large
number
written
know
possible
philosophy-ethics
resolved
mathematical
open
Global / Unspecified, Global
Finding the shortest possible route through many locations becomes exponentially harder as the number of locations grows, and no efficient exact solution is known for all cases. This unresolved question sits at the heart of computational optimization theory.
mathematics-logic
global-unspecified
efficient
haven
determined
whether
there
way
solve
every
instance
traveling
know
possible
philosophy-ethics
resolved
mathematical
open
Global / Unspecified, Global
Some tiling patterns work perfectly in abstract mathematical space but haven't been proven physically constructible under all real-world constraints. This connects pure geometry with material and structural engineering.
mathematics-logic
global-unspecified
tiling
physically
don
know
whether
every
regular
geometric
pattern
appears
haven
resolved
possible
philosophy-ethics
mathematical
open
Global / Unspecified, Global
Chaotic systems are famously sensitive to initial conditions, and whether their long-term patterns can ever be fully captured by simpler predictive rules remains an unresolved question in dynamical systems theory. This has real implications for weather prediction and other complex natural systems.
mathematics-logic
global-unspecified
whether
long-term
chaotic
rules
systems
haven
resolved
possible
always
predict
philosophy-ethics
know
society-governance
open
Global / Unspecified, Global
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.
mathematics-logic
global-unspecified
number
partition
numbers
understood
haven
proven
whether
distinct
ways
any
know
possible
philosophy-ethics
resolved
every
mathematical
open
Global / Unspecified, Global
Ramsey-type problems ask whether order must always emerge within sufficiently large or complex systems, and while some cases are proven, the general boundaries remain incompletely mapped. This connects deeply to combinatorics and the philosophy of mathematical order.
mathematics-logic
global-unspecified
structure
whether
mathematical
must
always
don
know
every
finite
certain
haven
resolved
philosophy-ethics
possible
open
Global / Unspecified, Global
Even our best physical models rely on approximations or idealized assumptions, and whether a truly complete and exact mathematical simulation is even theoretically possible remains unresolved. This touches on the deep relationship between mathematics and the physical world.
mathematics-logic
global-unspecified
any
physical
whether
possible
exact
mathematical
haven
resolved
fully
simulate
philosophy-ethics
know
every
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
