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
Every lunar mission so far has been short-term, relying entirely on supplies brought from Earth. A base that grows its own food, recycles its own water, and generates its own power would prove long-term space settlement is possible.
science-space
global-unspecified
base
its
own
haven
figured
out
build
permanent
self-sustaining
moon
whether
philosophy-ethics
mathematics-logic
resolved
know
possible
open
Global / Unspecified, Global
If P equaled NP, countless hard problems in logistics, cryptography, and optimization could be solved efficiently, but most computer scientists suspect they can't. This remains the most famous open question in computer science.
technology-computing
global-unspecified
whether
don
know
equals
some
fundamentally
harder
solve
check
computer
philosophy-ethics
resolved
haven
mathematics-logic
possible
determine
open
Global / Unspecified, Global
This conjecture about the zeros of a specific complex function would, if proven, tighten our understanding of how primes are distributed among all integers. It's considered one of the most important unsolved problems in mathematics.
mathematics-logic
global-unspecified
proven
haven
riemann
hypothesis
predicts
exactly
building
blocks
prime
numbers
whether
know
every
possible
mathematical
resolved
open
Global / Unspecified, Global
Gödel's incompleteness theorems already showed some truths escape any fixed formal system, but the full boundary between provable and unprovable truths remains an active area of exploration. This shapes how we understand the limits of formal reasoning itself.
mathematics-logic
global-unspecified
system
don
know
every
mathematical
statement
seems
true
eventually
proven
whether
philosophy-ethics
resolved
haven
possible
open
Global / Unspecified, Global
Many Diophantine equations, which ask for whole-number solutions, resist any general method for predicting how many solutions exist. Solving specific cases has taken decades and earned major mathematical prizes.
mathematics-logic
global-unspecified
solutions
equations
haven
determined
whether
number
certain
simple
whole
numbers
possible
know
every
philosophy-ethics
resolved
open
Global / Unspecified, Global
This weaker cousin of Goldbach's Conjecture illustrates how even modest-sounding claims about primes can remain unproven for centuries. It highlights how little we still understand about the raw arithmetic of prime numbers.
mathematics-logic
global-unspecified
prime
even
numbers
don
know
whether
every
sufficiently
large
number
haven
possible
philosophy-ethics
mathematical
resolved
open
Global / Unspecified, Global
If pi is what mathematicians call 'normal,' every string of digits, including your birthday or an entire book encoded in numbers, would appear infinitely often. No proof exists either way, despite pi's digits being computed to trillions of places.
mathematics-logic
global-unspecified
digits
every
numbers
haven
resolved
whether
contain
possible
finite
sequence
know
philosophy-ethics
mathematical
open
Global / Unspecified, Global
This difficulty is exactly what keeps most modern encryption secure, since multiplying primes together is easy but reversing the process is not. If an efficient method were found, it could upend the security of the internet as we know it.
mathematics-logic
global-unspecified
know
don
efficiently
factor
extremely
large
numbers
prime
components
difficulty
whether
haven
philosophy-ethics
possible
resolved
every
open
Global / Unspecified, Global
Sphere-packing problems are solved for a few specific dimensions, but the general pattern across all possible dimensions remains unknown. This affects fields ranging from error-correcting codes to theoretical physics.
science-space
global-unspecified
haven
determined
exact
boundary
densely
objects
packed
higher-dimensional
spaces
dimensions
whether
mathematics-logic
philosophy-ethics
possible
resolved
every
open
Global / Unspecified, Global
Despite chess being fully deterministic with no hidden information, its complexity is so vast that no one has proven who truly holds the advantage under perfect play. Solving smaller games has offered clues, but full chess remains unresolved.
mathematics-logic
global-unspecified
chess
has
proven
haven
whether
principle
always
guaranteed
winning
drawing
philosophy-ethics
resolved
possible
know
every
mathematical
open
Global / Unspecified, Global
Mathematicians have many tools for distinguishing knots, but no single method works perfectly and efficiently for every possible case. This unsolved problem sits at the heart of the mathematical field of knot theory.
mathematics-logic
global-unspecified
every
knot
don
know
whether
told
apart
simple
efficient
resolved
philosophy-ethics
haven
possible
mathematical
open
Global / Unspecified, Global
Starting from any positive number and repeatedly applying a basic rule always seems to eventually reach the number one, but no proof confirms this holds for every possible starting point. Its simplicity contrasted with its difficulty has made it famous among mathematicians and hobbyists alike.
mathematics-logic
global-unspecified
rule
seems
always
haven
proven
collatz
conjecture
strikingly
simple
lead
whether
know
possible
every
mathematical
resolved
open
Global / Unspecified, Global
Certain simple-sounding tiling and packing puzzles remain surprisingly resistant to a complete general solution. These problems test the limits of combinatorics and geometric reasoning.
mathematics-logic
global-unspecified
haven
resolved
unit
squares
needed
minimum
tile
square
given
odd
whether
possible
know
every
mathematical
philosophy-ethics
open
Global / Unspecified, Global
This question, closely related to the once-open Poincaré Conjecture, has been resolved in three dimensions but opens further mysteries in higher-dimensional analogues. Exploring these generalizations remains an active area of topology.
mathematics-logic
global-unspecified
don
know
whether
every
simply
connected
three-dimensional
shape
holes
always
haven
resolved
philosophy-ethics
possible
open
Global / Unspecified, Global
Some conjectures suggest that most true statements in sufficiently complex systems may have no short proof at all, only extremely long or even infinite ones. This unresolved question challenges our basic assumptions about what makes mathematics knowable.
mathematics-logic
global-unspecified
all
long
haven
proven
whether
almost
mathematical
truths
require
infinitely
philosophy-ethics
resolved
know
possible
every
open
Global / Unspecified, Global
The famous four-color theorem was resolved for flat maps, but generalizing the problem to more complex or higher-dimensional surfaces remains unsettled in several cases. This continues to be explored in graph theory and topology.
mathematics-logic
global-unspecified
color
flat
haven
determined
exact
minimum
number
colors
needed
any
whether
philosophy-ethics
know
resolved
possible
every
open
Global / Unspecified, Global
Some sequences and structures appear chaotic without ever settling into repetition, and proving whether repetition is truly avoidable in specific systems remains unresolved. This connects deeply to dynamical systems and number theory.
mathematics-logic
global-unspecified
whether
don
know
every
sufficiently
well-behaved
mathematical
pattern
must
eventually
philosophy-ethics
resolved
haven
possible
systems
open
Global / Unspecified, Global
Simple geometric fairness questions like this remain surprisingly open for many classes of shapes, especially in three or more dimensions. Solving them has practical relevance to resource division and computational geometry.
mathematics-logic
global-unspecified
haven
proven
whether
possible
always
divide
any
shape
equal-area
pieces
know
resolved
philosophy-ethics
every
mathematical
open
Global / Unspecified, Global
Primes appear scattered with no obvious repeating pattern, and finding a true predictive formula, rather than just an approximation, remains unsolved. This is closely tied to the deeper mysteries of the Riemann Hypothesis.
mathematics-logic
global-unspecified
formula
haven
proven
whether
there
always
predicts
next
prime
number
know
possible
every
philosophy-ethics
mathematical
resolved
open
Global / Unspecified, Global
Classifying all finite simple groups was a monumental achievement, but fully understanding how all groups relate to and build from these simple pieces remains an ongoing task. This shapes our foundational understanding of symmetry itself.
mathematics-logic
global-unspecified
every
groups
finite
don
know
whether
group
understood
piece
some
philosophy-ethics
resolved
haven
possible
mathematical
