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
While unique prime factorization is proven for standard whole numbers, extending and confirming similar uniqueness properties across various generalized number systems remains an unresolved area. This continues to shape research in algebraic number theory.
mathematics-logic
global-unspecified
number
proven
unique
haven
whether
every
sufficiently
large
has
way
philosophy-ethics
resolved
know
possible
mathematical
open
Global / Unspecified, Global
Some models settle into stability under specific conditions, but a fully general guarantee covering every possible complex real-world system remains an unresolved and actively studied question. This touches applied mathematics, physics, and systems theory broadly.
mathematics-logic
global-unspecified
possible
guarantee
complex
real-world
system
don
know
whether
any
sufficiently
philosophy-ethics
resolved
haven
every
mathematical
open
United States, North America
Some proofs span thousands of pages or rely on massive computer verification, and whether complete, error-free confidence is ever truly achievable for such proofs remains a genuinely unresolved epistemological and mathematical question. This shapes ongoing debates about the future of mathematical certainty.
mathematics-logic
north-america
united-states
mathematical
proofs
whether
haven
resolved
possible
fully
efficiently
verify
correctness
global-unspecified
philosophy-ethics
know
every
open
Global / Unspecified, Global
Logical simplification techniques work well for many cases, but a fully general method guaranteed to simplify every possible logical structure remains unresolved. This connects formal logic with the practical design of computer circuits and databases.
technology-computing
global-unspecified
logical
every
possible
but
structure
don
know
whether
pattern
interconnected
resolved
mathematics-logic
philosophy-ethics
haven
mathematical
open
Global / Unspecified, Global
Gödel's theorems confirm this for many well-known systems, but whether every conceivable finite proof system inevitably faces this limitation remains an unresolved logical question. This continues to shape foundational research into the nature of formal systems.
mathematics-logic
global-unspecified
whether
every
finite
proof
system
haven
determined
mathematical
must
eventually
philosophy-ethics
resolved
know
possible
open
Global / Unspecified, Global
Scheduling problems appear throughout logistics and computing, and while efficient solutions exist for many specific cases, a fully general efficient method remains unresolved for the broader problem family. This unresolved question connects theoretical computer science with real-world efficiency.
technology-computing
global-unspecified
possible
efficient
fully
method
don
know
whether
guarantee
finding
best
philosophy-ethics
resolved
mathematics-logic
haven
every
mathematical
open
Global / Unspecified, Global
Some sequences appear statistically uniform for extraordinarily long stretches before finally revealing subtle bias, and whether this always eventually happens remains an open question in number theory. This connects deeply to the study of pseudorandom number generation.
mathematics-logic
global-unspecified
whether
eventually
bias
haven
proven
every
possible
infinite
sequence
generated
know
resolved
philosophy-ethics
mathematical
open
Global / Unspecified, Global
Shape matching is solved efficiently for many specific cases, but a complete and efficient general method for every possible shape comparison remains an unresolved computational geometry question. This has real applications in computer vision and pattern recognition.
technology-computing
global-unspecified
whether
possible
general
efficient
method
don
know
construct
fully
determining
haven
philosophy-ethics
resolved
mathematics-logic
every
mathematical
open
Global / Unspecified, Global
Stability analysis offers strong tools for many specific systems, but a fully general and precise predictive theory covering every possible system remains incomplete. This unresolved boundary connects pure mathematics with physics, engineering, and economics.
mathematics-logic
global-unspecified
possible
fully
system
haven
resolved
whether
predict
exact
conditions
under
philosophy-ethics
know
every
mathematical
open
Global / Unspecified, Global
Information theory provides strong bounds on efficiency for many specific cases, but proving whether truly optimal encoding always exists for every possible scenario remains an unresolved theoretical question. This connects mathematics directly to modern data compression and communication.
mathematics-logic
global-unspecified
encoding
whether
every
possible
information
always
don
know
way
mathematically
philosophy-ethics
resolved
haven
open
Global / Unspecified, Global
Enclosing shape problems, like finding the smallest circle or polygon containing a set of points, are solved for many specific shape types, but a fully general theory covering every possible enclosing shape remains incomplete. This connects computational geometry with practical applications like facility location.
mathematics-logic
global-unspecified
shape
every
set
points
smallest
possible
specific
haven
determined
whether
resolved
know
philosophy-ethics
mathematical
open
Global / Unspecified, Global
Some equations are proven to have no whole-number solutions through specific clever arguments, but a fully general and unified explanatory framework covering every such case remains an unresolved number-theoretic goal. This continues to drive research into Diophantine equations.
mathematics-logic
global-unspecified
equations
framework
fully
have
solutions
don
know
whether
possible
construct
philosophy-ethics
resolved
haven
every
open
Global / Unspecified, Global
Some conjectures hold true for infinitely many tested cases without yet having a general proof, raising open questions about whether extensive verification alone can ever substitute for full mathematical certainty. This unresolved tension shapes ongoing debates about the nature of mathematical proof.
mathematics-logic
global-unspecified
mathematical
whether
true
infinitely
cases
general
haven
resolved
every
statement
philosophy-ethics
know
possible
open
Global / Unspecified, Global
Statistical and mathematical tools can detect many kinds of patterns efficiently, but a fully general and guaranteed method covering every possible hidden pattern type remains an unresolved theoretical question. This connects pure mathematics with the practical challenges of modern data analysis.
mathematics-logic
global-unspecified
possible
fully
method
hidden
patterns
pure
mathematical
analysis
haven
proven
whether
philosophy-ethics
resolved
know
every
open
Global / Unspecified, Global
Some infinite objects can be perfectly captured by finite descriptions, like certain repeating decimals, but many others resist any such finite representation, and the full boundary between the two remains incompletely mapped. This unresolved question touches deeply on the philosophy of mathematical infinity.
philosophy-ethics
global-unspecified
finite
infinite
mathematical
any
don
know
whether
every
possible
object
resolved
haven
mathematics-logic
open
Global / Unspecified, Global
Mathematicians rely on a diverse toolkit of proof techniques suited to different problems, and whether a single unifying method could ever replace this diversity remains a genuinely open and somewhat philosophical mathematical question. This touches on the deepest structure of how mathematical knowledge is built.
mathematics-logic
global-unspecified
mathematical
whether
proof
single
method
haven
resolved
every
possible
technique
know
philosophy-ethics
open
Global / Unspecified, Global
Many specific combinatorial puzzles have been solved exactly, but a fully general theory predicting solution counts across every possible puzzle type remains an unresolved and active area of combinatorics. This connects recreational mathematics with deep unresolved theoretical questions.
mathematics-logic
global-unspecified
possible
general
theory
predicting
combinatorial
puzzle
haven
proven
whether
construct
philosophy-ethics
resolved
know
every
mathematical
open
Global / Unspecified, Global
Some philosophical traditions argue meaningful experiences hold deeper value than accumulated possessions, while others see this distinction as less clear-cut than it first appears. This unresolved question shapes broader debates about consumerism and what truly constitutes a fulfilling life.
philosophy-ethics
global-unspecified
value
experiences
possessions
life
don
have
resolved
way
determine
whether
know
haven
mathematics-logic
ethical
open
Global / Unspecified, Global
Genuine altruism seems to require giving without expectation, yet human relationships often naturally involve some sense of reciprocal obligation. This unresolved tension complicates our understanding of charity, friendship, and generosity.
philosophy-ethics
global-unspecified
whether
generosity
don
know
fair
expect
gratitude
those
help
true
resolved
haven
determine
mathematics-logic
ethical
open
Global / Unspecified, Global
Many people unknowingly benefit from systems built on past or ongoing injustice, and it remains unclear how much responsibility passive beneficiaries bear for addressing that harm. This unresolved question underlies major debates about privilege and structural inequality.
society-governance
global-unspecified
benefit
haven
resolved
whether
humans
have
obligation
correct
injustices
personally
philosophy-ethics
know
determine
mathematics-logic
don
possible