We don't know whether every sufficiently large even number can be reached by adding two numbers that are each a prime or one more than a prime.
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.
prime
numbers
know
whether
every
mathematics-logic
Citation ID: WS01233
Title: We don't know whether every sufficiently large even number can be reached by adding two numbers that are each a prime or one more than a prime.
URL: https://worldsolve.org/index.php?api=problem&id=1233
We still haven't proven whether there are infinitely many prime numbers of the form found in Mersenne's sequence.
open
Global / Unspecified, Global
Mersenne primes, of the form two raised to a power minus one, are the largest primes ever discovered, but no one has proven that the list never ends. Finding new ones remains an active computational hunt.
proven
form
mersenne
haven
whether
mathematics-logic
Citation ID: WS01234
Title: We still haven't proven whether there are infinitely many prime numbers of the form found in Mersenne's sequence.
URL: https://worldsolve.org/index.php?api=problem&id=1234
We haven't resolved whether the digits of pi contain every possible finite sequence of numbers somewhere within them.
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.
digits
every
numbers
haven
resolved
mathematics-logic
Citation ID: WS01235
Title: We haven't resolved whether the digits of pi contain every possible finite sequence of numbers somewhere within them.
URL: https://worldsolve.org/index.php?api=problem&id=1235
We don't know how to efficiently factor extremely large numbers into their prime components.
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.
know
efficiently
factor
extremely
large
mathematics-logic
Citation ID: WS01236
Title: We don't know how to efficiently factor extremely large numbers into their prime components.
URL: https://worldsolve.org/index.php?api=problem&id=1236
We still haven't determined the exact boundary of how densely objects can be packed into higher-dimensional spaces.
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.
haven
determined
exact
boundary
densely
mathematics-logic
Citation ID: WS01237
Title: We still haven't determined the exact boundary of how densely objects can be packed into higher-dimensional spaces.
URL: https://worldsolve.org/index.php?api=problem&id=1237
We haven't proven whether chess, in principle, always has a guaranteed winning or drawing strategy for one side from the starting position.
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.
chess
proven
one
haven
whether
mathematics-logic
Citation ID: WS01238
Title: We haven't proven whether chess, in principle, always has a guaranteed winning or drawing strategy for one side from the starting position.
URL: https://worldsolve.org/index.php?api=problem&id=1238
We don't know whether every knot can be told apart from every other knot using a simple, efficient test.
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.
every
knot
know
whether
told
mathematics-logic
Citation ID: WS01239
Title: We don't know whether every knot can be told apart from every other knot using a simple, efficient test.
URL: https://worldsolve.org/index.php?api=problem&id=1239
We still haven't proven the Collatz Conjecture, a strikingly simple rule that seems to always lead back to one.
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.
rule
seems
always
one
haven
mathematics-logic
Citation ID: WS01240
Title: We still haven't proven the Collatz Conjecture, a strikingly simple rule that seems to always lead back to one.
URL: https://worldsolve.org/index.php?api=problem&id=1240
We haven't resolved how many unit squares are needed, at minimum, to tile a square of a given odd size without overlaps or gaps.
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.
haven
resolved
many
unit
squares
mathematics-logic
Citation ID: WS01241
Title: We haven't resolved how many unit squares are needed, at minimum, to tile a square of a given odd size without overlaps or gaps.
URL: https://worldsolve.org/index.php?api=problem&id=1241
We don't know whether every simply connected three-dimensional shape without holes can always be continuously deformed into a sphere.
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.
three
dimensional
know
whether
every
mathematics-logic
Citation ID: WS01242
Title: We don't know whether every simply connected three-dimensional shape without holes can always be continuously deformed into a sphere.
URL: https://worldsolve.org/index.php?api=problem&id=1242
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.
all
long
haven
proven
whether
mathematics-logic
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://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.
color
flat
haven
determined
exact
mathematics-logic
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://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.
whether
know
every
sufficiently
well
mathematics-logic
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://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.
haven
proven
whether
possible
always
mathematics-logic
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://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.
one
formula
haven
proven
whether
mathematics-logic
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://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.
every
groups
finite
know
whether
mathematics-logic
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://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.
computers
whether
quantum
haven
resolved
mathematics-logic
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://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.
sequence
haven
determined
whether
possible
mathematics-logic
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://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.
cube
dimensions
know
exact
largest
mathematics-logic
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://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.
haven
resolved
efficiently
determine
any
mathematics-logic
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://worldsolve.org/index.php?api=problem&id=1252
