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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4094Total
4094Open
0Solved
9Humans
open
Global / Unspecified, Global
Some extremal problems in combinatorics have only been resolved through massive computational brute force, without a more elegant general proof explaining why the answer must be exactly what it is. This unresolved gap raises questions about the nature of mathematical understanding itself.
mathematics-logic
global-unspecified
possible
resolved
mathematical
haven
whether
prove
exact
largest
size
certain
know
philosophy-ethics
every
open
Global / Unspecified, Global
Certain recursively defined sequences appear statistically random for enormous stretches, yet whether hidden structure always eventually emerges remains an open and evolving question. This connects deeply to both number theory and the study of pseudorandomness.
mathematics-logic
global-unspecified
whether
always
eventually
don
know
digits
numbers
produced
simple
recursive
haven
philosophy-ethics
resolved
possible
every
mathematical
open
Global / Unspecified, Global
While many specific systems have proven solutions, a complete general guarantee across every well-posed nonlinear system remains one of mathematics' harder open questions. This affects fields ranging from physics to engineering that rely on such systems.
mathematics-logic
global-unspecified
proven
guarantee
every
well-posed
system
nonlinear
haven
whether
possible
solution
philosophy-ethics
resolved
know
mathematical
open
Global / Unspecified, Global
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.
mathematics-logic
global-unspecified
shape
haven
determined
whether
every
finite
geometric
always
perfectly
reconstructed
know
resolved
possible
philosophy-ethics
mathematical
open
Global / Unspecified, Global
Complex systems in nature and mathematics often arise from remarkably simple starting rules, yet no unified theory fully explains or predicts when and how this complexity will emerge. This unresolved question bridges mathematics, physics, and biology.
mathematics-logic
global-unspecified
theory
fully
predicts
complexity
simple
rules
don
know
whether
possible
philosophy-ethics
haven
resolved
every
mathematical
open
Global / Unspecified, Global
Self-referential paradoxes have challenged logicians for over a century, and while specific paradoxes have been addressed with targeted fixes, no single unified framework has resolved every possible version. This unresolved tension remains central to the foundations of mathematical logic.
mathematics-logic
global-unspecified
resolved
every
possible
haven
whether
logical
paradox
fully
neutralized
some
philosophy-ethics
know
determine
open
Global / Unspecified, Global
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.
mathematics-logic
global-unspecified
number
predicting
don
know
whether
possible
find
general
rule
exactly
haven
resolved
philosophy-ethics
every
open
Global / Unspecified, Global
While many algebraic structures have been classified, some corners of abstract algebra still lack a fully confirmed and complete classification of their most basic components. This ongoing effort shapes the foundations of modern algebraic research.
mathematics-logic
global-unspecified
fully
complete
algebra
haven
determined
whether
possible
construct
list
every
philosophy-ethics
resolved
know
mathematical
open
Global / Unspecified, Global
Some optimization problems are proven solvable efficiently, others proven intractable, but a complete boundary map covering every conceivable variation remains incomplete. This unresolved question is central to computational complexity theory.
mathematics-logic
global-unspecified
boundary
solvable
optimization
every
don
know
whether
exact
between
unsolvable
resolved
haven
philosophy-ethics
possible
mathematical
open
Global / Unspecified, Global
Combinatorial arrangement problems like this remain surprisingly resistant to full general solutions despite their simple appearance. This connects recreational mathematics with deeper unresolved questions in combinatorics.
mathematics-logic
global-unspecified
every
haven
proven
whether
finite
list
numbers
always
rearranged
sequence
know
possible
resolved
philosophy-ethics
mathematical
open
Global / Unspecified, Global
Symmetry classification has succeeded for many specific structures, but a fully complete and general classification covering every conceivable symmetric object remains an ongoing and unresolved mathematical project. This shapes foundational research in group theory and geometry.
mathematics-logic
global-unspecified
possible
fully
every
mathematical
object
remains
haven
determined
whether
characterize
philosophy-ethics
resolved
know
open
Global / Unspecified, Global
Formal proof systems capture enormous portions of mathematical reasoning, but whether a truly complete and finite rule set exists for absolutely every valid form of proof remains philosophically and technically unresolved. This touches the very foundations of what mathematics is capable of expressing.
mathematics-logic
global-unspecified
possible
proof
whether
complete
finite
set
every
valid
mathematical
haven
resolved
know
philosophy-ethics
open
Global / Unspecified, Global
Many geometric constants have been linked to constants like pi through elegant proofs, but numerous others remain isolated without any confirmed deeper connection. This unresolved gap continues to intrigue mathematicians working in geometry and analysis.
mathematics-logic
global-unspecified
constants
geometry
have
connection
haven
proven
whether
every
mathematical
constant
resolved
philosophy-ethics
know
possible
open
Global / Unspecified, Global
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.
mathematics-logic
global-unspecified
long-term
don
know
whether
possible
fully
predict
stability
any
mathematical
systems
philosophy-ethics
resolved
haven
society-governance
open
Global / Unspecified, Global
Self-referential systems often run into paradoxes, and while specific fixes exist for particular cases, no fully general and complete solution has been proven for every possible self-describing system. This unresolved tension remains central to mathematical logic and computer science.
mathematics-logic
global-unspecified
every
mathematical
fully
haven
determined
whether
sufficiently
complex
language
unambiguously
philosophy-ethics
resolved
possible
know
open
Global / Unspecified, Global
While good approximate methods exist, a fully efficient and exact general solution for the shortest connecting network across every possible point configuration remains unresolved. This connects computational geometry with practical network design.
mathematics-logic
global-unspecified
possible
network
exact
efficient
shortest
connecting
haven
resolved
whether
guarantee
know
philosophy-ethics
every
mathematical
open
Global / Unspecified, Global
Ramsey-type theorems guarantee certain patterns emerge under specific conditions, but a fully general guarantee covering every conceivable infinite sequence remains an incomplete and active area of study. This connects deeply to combinatorics and the philosophy of mathematical order.
mathematics-logic
global-unspecified
every
infinite
mathematical
sequence
specific
don
know
whether
possible
must
haven
resolved
philosophy-ethics
open
Global / Unspecified, Global
Self-verifying proofs raise deep questions tied to Gödel's incompleteness results, and whether any sufficiently powerful system can ever fully confirm its own consistency remains unresolved. This continues to shape foundational debates in mathematical logic.
mathematics-logic
global-unspecified
whether
mathematical
its
own
any
system
haven
determined
possible
construct
resolved
philosophy-ethics
know
every
open
Global / Unspecified, Global
Some patterns appear irregular indefinitely despite simple underlying construction rules, and whether hidden symmetry always eventually emerges remains an open and unresolved geometric question. This connects to both pure mathematics and the study of natural patterns.
mathematics-logic
global-unspecified
whether
geometric
simple
rules
eventually
hidden
symmetry
don
know
every
haven
resolved
philosophy-ethics
possible
mathematical
open
Global / Unspecified, Global
Some sets in mathematics resist having a consistent notion of size under standard rules, and a complete classification of every such case remains an unresolved and active area of measure theory. This connects to foundational questions about the nature of mathematical infinity.
mathematics-logic
global-unspecified
possible
every
mathematical
size
measure
haven
resolved
whether
fully
classify
philosophy-ethics
know
