We still haven't proven whether almost all mathematical truths require infinitely long proofs to establish with full rigor.
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
know
possible
resolved
philosophy-ethics
every
Citation ID: WS01243
Title: We still haven't proven whether almost all mathematical truths require infinitely long proofs to establish with full rigor.
URL: https://www.worldsolve.org/index.php?api=problem&id=1243
We haven't determined the exact minimum number of colors needed to color any map so that no two touching regions share a color, in dimensions beyond a flat plane.
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
possible
every
know
mathematical
resolved
Citation ID: WS01244
Title: We haven't determined the exact minimum number of colors needed to color any map so that no two touching regions share a color, in dimensions beyond a flat plane.
URL: https://www.worldsolve.org/index.php?api=problem&id=1244
We don't know whether every sufficiently well-behaved mathematical pattern must eventually repeat itself in a predictable way.
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
haven
resolved
possible
Citation ID: WS01245
Title: We don't know whether every sufficiently well-behaved mathematical pattern must eventually repeat itself in a predictable way.
URL: https://www.worldsolve.org/index.php?api=problem&id=1245
We still haven't proven whether it's possible to always divide any shape into equal-area pieces using only straight cuts through a single point.
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
every
mathematical
resolved
philosophy-ethics
Citation ID: WS01246
Title: We still haven't proven whether it's possible to always divide any shape into equal-area pieces using only straight cuts through a single point.
URL: https://www.worldsolve.org/index.php?api=problem&id=1246
We haven't proven whether there's a formula that always predicts the next prime number without simply checking numbers one by one.
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
every
possible
know
mathematical
Citation ID: WS01247
Title: We haven't proven whether there's a formula that always predicts the next prime number without simply checking numbers one by one.
URL: https://www.worldsolve.org/index.php?api=problem&id=1247
We don't know whether every finite group can be understood as a piece of some larger, simpler family of groups in every possible case.
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
possible
haven
philosophy-ethics
resolved
mathematical
Citation ID: WS01248
Title: We don't know whether every finite group can be understood as a piece of some larger, simpler family of groups in every possible case.
URL: https://www.worldsolve.org/index.php?api=problem&id=1248
We still haven't resolved whether quantum computers can efficiently solve every problem that's currently considered intractable for classical computers.
open
Global / Unspecified, Global
Quantum computers show promise for specific problems like factoring, but whether they offer a genuine speedup across all hard computational problems remains unproven. This question sits at the intersection of mathematics, physics, and computer science.
mathematics-logic
global-unspecified
computers
whether
quantum
haven
resolved
efficiently
solve
every
currently
considered
know
possible
philosophy-ethics
mathematical
Citation ID: WS01249
Title: We still haven't resolved whether quantum computers can efficiently solve every problem that's currently considered intractable for classical computers.
URL: https://www.worldsolve.org/index.php?api=problem&id=1249
We haven't determined whether it's possible to construct a truly random sequence of numbers using only a deterministic mathematical process.
open
Global / Unspecified, Global
True randomness is difficult to define and even harder to prove, since any formula-based sequence is, by definition, predictable if you know the formula. This unresolved tension underlies debates in both mathematics and philosophy of probability.
mathematics-logic
global-unspecified
sequence
haven
determined
whether
possible
construct
truly
random
numbers
only
know
resolved
philosophy-ethics
every
mathematical
Citation ID: WS01250
Title: We haven't determined whether it's possible to construct a truly random sequence of numbers using only a deterministic mathematical process.
URL: https://www.worldsolve.org/index.php?api=problem&id=1250
We don't know the exact largest number of moves required to solve any solvable configuration of a Rubik's Cube-like puzzle in higher dimensions.
open
Global / Unspecified, Global
While the standard cube's maximum was determined through massive computation, generalized versions with more dimensions or larger sizes remain computationally and theoretically unresolved. This connects group theory with combinatorial optimization.
mathematics-logic
global-unspecified
dimensions
don
know
exact
largest
number
moves
required
solve
any
whether
haven
possible
every
resolved
philosophy-ethics
Citation ID: WS01251
Title: We don't know the exact largest number of moves required to solve any solvable configuration of a Rubik's Cube-like puzzle in higher dimensions.
URL: https://www.worldsolve.org/index.php?api=problem&id=1251
We haven't resolved how to efficiently determine, for any given set of logical statements, whether they can all be true at the same time.
open
Global / Unspecified, Global
This boolean satisfiability problem is central to computer science, and no efficient general method is known for solving every possible case quickly. It remains a benchmark problem for understanding computational complexity.
mathematics-logic
global-unspecified
haven
resolved
efficiently
determine
any
given
set
logical
statements
whether
possible
know
every
philosophy-ethics
mathematical
Citation ID: WS01252
Title: We haven't resolved how to efficiently determine, for any given set of logical statements, whether they can all be true at the same time.
URL: https://www.worldsolve.org/index.php?api=problem&id=1252
We don't know whether the set of numbers that can never be precisely constructed using only a compass and straightedge follows any simple, complete pattern.
open
Global / Unspecified, Global
Certain constructions, like doubling a cube's volume using classical tools, were proven impossible, but a full classification of every possible constructible versus non-constructible case remains an evolving area. This connects ancient geometry with modern algebra.
mathematics-logic
global-unspecified
don
know
whether
set
numbers
never
precisely
constructed
only
compass
haven
possible
every
resolved
philosophy-ethics
mathematical
Citation ID: WS01253
Title: We don't know whether the set of numbers that can never be precisely constructed using only a compass and straightedge follows any simple, complete pattern.
URL: https://www.worldsolve.org/index.php?api=problem&id=1253
We still haven't proven whether every possible strategy game with complete information and no chance has a way to force a win or draw for one player.
open
Global / Unspecified, Global
Some games are proven to always end in a draw or a specific winner under perfect play, but for many complex games, this remains unresolved due to sheer computational scale. This unsolved area touches game theory, logic, and computer science.
mathematics-logic
global-unspecified
proven
game
draw
haven
whether
every
possible
strategy
complete
information
know
resolved
philosophy-ethics
mathematical
Citation ID: WS01254
Title: We still haven't proven whether every possible strategy game with complete information and no chance has a way to force a win or draw for one player.
URL: https://www.worldsolve.org/index.php?api=problem&id=1254
We haven't determined whether there exists a general, efficient algorithm for solving all types of polynomial equations exactly, regardless of their degree.
open
Global / Unspecified, Global
Formulas exist for degrees up to four, but general algebraic solutions for higher degrees don't exist in the same closed form, leaving open questions about alternative methods. This shapes ongoing research in both pure and computational algebra.
technology-computing
global-unspecified
general
haven
determined
whether
there
exists
efficient
algorithm
solving
all
mathematics-logic
possible
know
every
resolved
philosophy-ethics
Citation ID: WS01255
Title: We haven't determined whether there exists a general, efficient algorithm for solving all types of polynomial equations exactly, regardless of their degree.
URL: https://www.worldsolve.org/index.php?api=problem&id=1255
We don't know whether every true statement about whole numbers can eventually be verified by a computer given unlimited time.
open
Global / Unspecified, Global
Some mathematical truths may be true but fundamentally unprovable within any given formal system, a possibility raised by Gödel's work but not fully mapped out for all classes of statements. This unresolved boundary shapes the philosophy of computation.
technology-computing
global-unspecified
true
given
don
know
whether
every
statement
whole
numbers
eventually
haven
mathematics-logic
philosophy-ethics
resolved
possible
Citation ID: WS01256
Title: We don't know whether every true statement about whole numbers can eventually be verified by a computer given unlimited time.
URL: https://www.worldsolve.org/index.php?api=problem&id=1256
We still haven't proven whether it's possible to always tile a rectangle perfectly using only squares of different, non-repeating sizes.
open
Global / Unspecified, Global
While specific solutions exist for certain rectangles, a full general theory predicting exactly which rectangles allow this kind of tiling remains incomplete. This puzzle blends recreational mathematics with serious combinatorics.
mathematics-logic
global-unspecified
haven
proven
whether
possible
always
tile
rectangle
perfectly
only
squares
every
know
resolved
mathematical
philosophy-ethics
Citation ID: WS01257
Title: We still haven't proven whether it's possible to always tile a rectangle perfectly using only squares of different, non-repeating sizes.
URL: https://www.worldsolve.org/index.php?api=problem&id=1257
We haven't resolved whether the number of steps needed to sort any list of items can always be reduced below current theoretical best-known limits.
open
Global / Unspecified, Global
Sorting algorithms have been optimized extensively, but proving a true absolute lower bound across all possible sorting methods remains an unresolved question in computational theory. This affects the fundamental efficiency limits of computing.
technology-computing
global-unspecified
limits
haven
resolved
whether
number
steps
needed
sort
any
list
mathematics-logic
know
possible
philosophy-ethics
every
mathematical
Citation ID: WS01258
Title: We haven't resolved whether the number of steps needed to sort any list of items can always be reduced below current theoretical best-known limits.
URL: https://www.worldsolve.org/index.php?api=problem&id=1258
We don't know whether every sufficiently complex logical system must eventually produce a statement that cannot be proven true or false within it.
open
Global / Unspecified, Global
Gödel's incompleteness theorem confirms this for many systems, but fully mapping which systems are exempt, if any, from this limitation remains an open and active question. This continues to shape foundational debates in mathematical logic.
mathematics-logic
global-unspecified
don
know
whether
every
sufficiently
complex
logical
system
must
eventually
possible
haven
philosophy-ethics
resolved
mathematical
Citation ID: WS01259
Title: We don't know whether every sufficiently complex logical system must eventually produce a statement that cannot be proven true or false within it.
URL: https://www.worldsolve.org/index.php?api=problem&id=1259
We still haven't proven whether there's a maximum limit to how efficiently any physical computer, regardless of technology, can perform calculations.
open
Global / Unspecified, Global
Physical laws impose some theoretical limits on computation speed and energy use, but the exact universal boundary, if one truly exists, remains unresolved. This connects computer science directly to fundamental physics.
technology-computing
global-unspecified
physical
computer
haven
proven
whether
there
maximum
limit
efficiently
any
mathematics-logic
possible
know
philosophy-ethics
resolved
every
Citation ID: WS01260
Title: We still haven't proven whether there's a maximum limit to how efficiently any physical computer, regardless of technology, can perform calculations.
URL: https://www.worldsolve.org/index.php?api=problem&id=1260
We haven't determined whether it's possible to find a pattern predicting all the digits of irrational numbers like the square root of two without direct calculation.
open
Global / Unspecified, Global
Irrational numbers have infinite, non-repeating digits, and while we can calculate them to enormous precision, no simple predictive pattern for their exact sequence has been found. This touches on deep unresolved questions in number theory.
mathematics-logic
global-unspecified
pattern
digits
irrational
numbers
haven
determined
whether
possible
find
predicting
know
every
resolved
philosophy-ethics
mathematical
Citation ID: WS01261
Title: We haven't determined whether it's possible to find a pattern predicting all the digits of irrational numbers like the square root of two without direct calculation.
URL: https://www.worldsolve.org/index.php?api=problem&id=1261
We don't know whether it's mathematically possible to create a completely fair voting system that satisfies every reasonable fairness criterion simultaneously.
open
Global / Unspecified, Global
Arrow's Impossibility Theorem proved certain fairness conditions can't all hold at once for common voting systems, but the full landscape of tradeoffs across all possible systems remains an active research area. This has real implications for the design of democratic institutions.
mathematics-logic
global-unspecified
possible
voting
fairness
don
know
whether
mathematically
create
completely
fair
haven
philosophy-ethics
resolved
every
mathematical
Citation ID: WS01262
Title: We don't know whether it's mathematically possible to create a completely fair voting system that satisfies every reasonable fairness criterion simultaneously.
URL: https://www.worldsolve.org/index.php?api=problem&id=1262
