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
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.
mathematics-logic
global-unspecified
property
specific
don
know
whether
every
finite
set
numbers
must
haven
philosophy-ethics
resolved
possible
mathematical
open
Global / Unspecified, Global
Probability theory offers strong predictive tools for many games, but a fully complete and general model covering every conceivable game of chance remains theoretically unresolved. This touches both pure mathematics and the philosophy of randomness.
mathematics-logic
global-unspecified
possible
complete
model
every
game
chance
haven
proven
whether
construct
know
resolved
philosophy-ethics
mathematical
open
Global / Unspecified, Global
Many famous fractals are built from simple recursive rules, but whether every possible fractal pattern can always be reduced to such a finite description remains an open mathematical question. This connects geometry, computer science, and the study of natural patterns.
mathematics-logic
global-unspecified
whether
every
possible
fractal
pattern
finite
simple
rules
haven
determined
know
resolved
philosophy-ethics
mathematical
open
Global / Unspecified, Global
Proof by contradiction is a powerful and common technique, but whether every such proof has an equivalent direct version remains an open question in mathematical logic. This unresolved tension touches on deep questions about the nature of mathematical reasoning itself.
mathematics-logic
global-unspecified
proof
mathematical
whether
every
contradiction
direct
haven
resolved
relies
assuming
know
philosophy-ethics
possible
open
Global / Unspecified, Global
Discrete mathematics, dealing with countable structures, and continuous mathematics, dealing with smooth changes, sometimes resist clean translation between one another, and a fully unifying framework remains an unresolved and ambitious mathematical goal. This touches the deepest foundations of how mathematics is structured.
mathematics-logic
global-unspecified
mathematics
mathematical
framework
fully
discrete
continuous
haven
determined
whether
possible
philosophy-ethics
resolved
know
every
open
Global / Unspecified, Global
Some constraint puzzles, like certain scheduling or coloring problems, can be solved efficiently under specific conditions, but a fully general and efficient method covering every possible case remains unresolved. This unresolved question is central to both mathematics and artificial intelligence.
mathematics-logic
global-unspecified
artificial-intelligence
possible
efficient
method
every
constraint
don
know
whether
guarantee
solving
philosophy-ethics
resolved
haven
mathematical
open
Global / Unspecified, Global
History has shown some conjectures hold for enormous ranges before finally failing, raising the unresolved question of how confidently mathematicians can ever trust patterns observed only in finite testing. This shapes ongoing debates about the reliability of computational evidence in mathematics.
mathematics-logic
global-unspecified
haven
proven
whether
every
mathematical
theorem
holds
true
small
cases
know
resolved
philosophy-ethics
possible
open
Global / Unspecified, Global
Specific techniques exist for counting solutions in many cases, but a complete and general method covering every possible polynomial system remains an unresolved goal in algebraic geometry. This continues to be an active area of mathematical research.
mathematics-logic
global-unspecified
possible
general
method
solutions
system
polynomial
haven
determined
whether
construct
philosophy-ethics
resolved
know
every
mathematical
open
Global / Unspecified, Global
Chaos theory has revealed hidden order within some seemingly random systems, but whether this holds true for every possible chaotic process remains an open and unresolved question. This connects mathematics with physics, biology, and the philosophy of determinism.
mathematics-logic
global-unspecified
whether
every
possible
process
chaotic
some
order
don
know
infinite
philosophy-ethics
resolved
haven
mathematical
open
Global / Unspecified, Global
Symmetry groups have been classified extensively for finite cases, but infinite symmetry structures present ongoing classification challenges that remain incompletely resolved. This shapes foundational research in both algebra and geometry.
mathematics-logic
global-unspecified
resolved
infinite
haven
whether
possible
fully
classify
every
mathematical
structure
philosophy-ethics
know
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
