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We still haven't resolved whether every infinite set of numbers must have a size that matches one of the specific mathematical infinities we've already identified.

open Global / Unspecified, Global

The Continuum Hypothesis asks whether there's a size of infinity strictly between the countable and uncountable, and it has been shown to be independent of standard mathematical axioms. This unresolved question touches the very foundation of set theory.

mathematics-logic global-unspecified whether set size mathematical haven resolved every infinite numbers must know possible philosophy-ethics

WS01263 · Logged by The Internet (seaglass) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01263 Title: We still haven't resolved whether every infinite set of numbers must have a size that matches one of the specific mathematical infinities we've already identified. URL: https://www.worldsolve.org/index.php?api=problem&id=1263

We haven't proven whether it's always possible to divide a cake fairly among any number of people, each with completely different preferences, using a finite number of straight cuts.

open Global / Unspecified, Global

Fair division problems become extremely complex once individual preferences differ, and general efficient solutions for many people remain incompletely understood. This connects mathematics to real-world negotiation and resource allocation.

mathematics-logic global-unspecified number people preferences haven proven whether always possible divide cake know philosophy-ethics resolved every mathematical

WS01264 · Logged by The Internet (open_thinker) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01264 Title: We haven't proven whether it's always possible to divide a cake fairly among any number of people, each with completely different preferences, using a finite number of straight cuts. URL: https://www.worldsolve.org/index.php?api=problem&id=1264

We don't know whether the digits of most well-known mathematical constants, like Euler's number, ever settle into any predictable long-term statistical pattern.

open Global / Unspecified, Global

Despite extensive computation, no proof confirms whether these digits behave truly randomly forever or eventually reveal some hidden structure. This remains an open question bridging number theory and statistics.

mathematics-logic global-unspecified whether digits number don know well-known mathematical constants like euler haven possible philosophy-ethics resolved every

WS01265 · Logged by The Internet (curious_mind93) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01265 Title: We don't know whether the digits of most well-known mathematical constants, like Euler's number, ever settle into any predictable long-term statistical pattern. URL: https://www.worldsolve.org/index.php?api=problem&id=1265

We still haven't determined the exact smallest number of unit distances that must repeat among any large set of points drawn on a plane.

open Global / Unspecified, Global

This problem, part of a broader family of questions in combinatorial geometry, has known bounds but no exact general formula for every configuration. Solving it would refine our understanding of how simple geometric constraints shape complex arrangements.

mathematics-logic global-unspecified exact haven determined smallest number unit distances must repeat among whether possible every know mathematical resolved

WS01266 · Logged by The Internet (curious_mind93) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01266 Title: We still haven't determined the exact smallest number of unit distances that must repeat among any large set of points drawn on a plane. URL: https://www.worldsolve.org/index.php?api=problem&id=1266

We haven't resolved whether every possible tangle of a rope, when idealized mathematically, can be untangled using a provably minimal number of moves.

open Global / Unspecified, Global

Knot theory offers tools for identifying and classifying tangles, but calculating a guaranteed minimal ontangling path for every possible knot remains computationally unresolved. This connects abstract mathematics to physical intuition about rope and cords.

mathematics-logic global-unspecified every possible rope minimal haven resolved whether tangle idealized mathematically know philosophy-ethics mathematical

WS01267 · Logged by The Internet (late_night_reader) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01267 Title: We haven't resolved whether every possible tangle of a rope, when idealized mathematically, can be untangled using a provably minimal number of moves. URL: https://www.worldsolve.org/index.php?api=problem&id=1267

We don't know whether every mathematical proof can, in principle, be shortened to a version that a human could fully verify without computer assistance.

open Global / Unspecified, Global

Some modern proofs rely heavily on computer verification because they're too long or complex for any person to check by hand, raising open questions about whether shorter, purely human-verifiable proofs must always exist. This unresolved tension touches both mathematics and epistemology.

mathematics-logic global-unspecified whether computer don know every mathematical proof principle shortened version haven philosophy-ethics resolved possible

WS01268 · Logged by The Internet (the_lurker) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01268 Title: We don't know whether every mathematical proof can, in principle, be shortened to a version that a human could fully verify without computer assistance. URL: https://www.worldsolve.org/index.php?api=problem&id=1268

We still haven't proven whether there are infinitely many prime numbers that remain prime when you reverse the order of their digits.

open Global / Unspecified, Global

Palindromic and reversible primes show interesting patterns, but whether infinitely many exist across all number bases remains unconfirmed. This is one of many number-theoretic curiosities still lacking rigorous proof.

mathematics-logic global-unspecified prime whether infinitely haven proven there numbers remain you reverse know possible every resolved philosophy-ethics mathematical

WS01269 · Logged by The Internet (wiki_reader) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01269 Title: We still haven't proven whether there are infinitely many prime numbers that remain prime when you reverse the order of their digits. URL: https://www.worldsolve.org/index.php?api=problem&id=1269

We haven't resolved the exact minimum number of moves required to solve the hardest possible configuration of many classic sliding puzzles.

open Global / Unspecified, Global

While specific puzzle sizes have been fully solved computationally, generalizing the worst-case difficulty formula across all puzzle sizes remains an open combinatorial question. This links recreational mathematics with formal complexity theory.

mathematics-logic global-unspecified haven resolved exact minimum number moves required solve hardest possible whether know every philosophy-ethics mathematical

WS01270 · Logged by The Internet (echo_chamber_no) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01270 Title: We haven't resolved the exact minimum number of moves required to solve the hardest possible configuration of many classic sliding puzzles. URL: https://www.worldsolve.org/index.php?api=problem&id=1270

We don't know whether it's possible to build a computer program that can always determine, for any given program, whether it will eventually stop running.

open Global / Unspecified, Global

This is the famous Halting Problem, proven impossible to solve in full generality, yet many partial and practical questions around predicting program behavior remain actively studied. This shapes the theoretical limits of what computers can ever determine about themselves.

technology-computing global-unspecified program whether determine don know possible build computer always any haven philosophy-ethics mathematics-logic resolved every

WS01271 · Logged by The Internet (field_notes) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01271 Title: We don't know whether it's possible to build a computer program that can always determine, for any given program, whether it will eventually stop running. URL: https://www.worldsolve.org/index.php?api=problem&id=1271

We still haven't proven whether every sufficiently large prime number can be written as the sum of three smaller prime numbers in a predictable, structured way.

open Global / Unspecified, Global

Related conjectures about how primes combine remain only partially proven for specific ranges, without a fully general confirmed pattern. This connects to broader unresolved questions about the additive structure of prime numbers.

mathematics-logic global-unspecified prime proven numbers haven whether every sufficiently large number written know possible mathematical resolved

WS01272 · Logged by The Internet (open_thinker) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01272 Title: We still haven't proven whether every sufficiently large prime number can be written as the sum of three smaller prime numbers in a predictable, structured way. URL: https://www.worldsolve.org/index.php?api=problem&id=1272

We haven't determined whether there's an efficient way to solve every instance of the traveling salesman problem exactly, rather than through approximation.

open Global / Unspecified, Global

Finding the shortest possible route through many locations becomes exponentially harder as the number of locations grows, and no efficient exact solution is known for all cases. This unresolved question sits at the heart of computational optimization theory.

mathematics-logic global-unspecified efficient haven determined whether there way solve every instance traveling possible know resolved philosophy-ethics mathematical

WS01273 · Logged by The Internet (seaglass) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01273 Title: We haven't determined whether there's an efficient way to solve every instance of the traveling salesman problem exactly, rather than through approximation. URL: https://www.worldsolve.org/index.php?api=problem&id=1273

We don't know whether every regular geometric tiling pattern that appears possible in theory can actually be physically realized without gaps or overlaps.

open Global / Unspecified, Global

Some tiling patterns work perfectly in abstract mathematical space but haven't been proven physically constructible under all real-world constraints. This connects pure geometry with material and structural engineering.

mathematics-logic global-unspecified tiling physically don know whether every regular geometric pattern appears haven possible resolved mathematical philosophy-ethics

WS01274 · Logged by The Internet (citizen_of_earth) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01274 Title: We don't know whether every regular geometric tiling pattern that appears possible in theory can actually be physically realized without gaps or overlaps. URL: https://www.worldsolve.org/index.php?api=problem&id=1274

We still haven't resolved whether it's possible to always predict the long-term behavior of any chaotic mathematical system using a finite set of rules.

open Global / Unspecified, Global

Chaotic systems are famously sensitive to initial conditions, and whether their long-term patterns can ever be fully captured by simpler predictive rules remains an unresolved question in dynamical systems theory. This has real implications for weather prediction and other complex natural systems.

mathematics-logic global-unspecified whether long-term chaotic rules systems haven resolved possible always predict philosophy-ethics know every mathematical

WS01275 · Logged by The Internet (field_notes) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01275 Title: We still haven't resolved whether it's possible to always predict the long-term behavior of any chaotic mathematical system using a finite set of rules. URL: https://www.worldsolve.org/index.php?api=problem&id=1275

We haven't proven whether the number of distinct ways to partition any given number into smaller whole numbers follows a fully understood, predictable growth pattern.

open Global / Unspecified, Global

Partition numbers grow in a complex, only partially understood way, and while excellent approximations exist, a complete exact predictive formula for all cases remains elusive. This continues to be an active area within combinatorics and number theory.

mathematics-logic global-unspecified number partition numbers understood haven proven whether distinct ways any possible every know mathematical philosophy-ethics resolved

WS01276 · Logged by The Internet (longform_fan) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01276 Title: We haven't proven whether the number of distinct ways to partition any given number into smaller whole numbers follows a fully understood, predictable growth pattern. URL: https://www.worldsolve.org/index.php?api=problem&id=1276

We don't know whether every finite mathematical structure with a certain kind of internal symmetry must always contain a smaller, simpler symmetric structure within it.

open Global / Unspecified, Global

Ramsey-type problems ask whether order must always emerge within sufficiently large or complex systems, and while some cases are proven, the general boundaries remain incompletely mapped. This connects deeply to combinatorics and the philosophy of mathematical order.

mathematics-logic global-unspecified structure whether mathematical must always don know every finite certain haven possible resolved philosophy-ethics

WS01277 · Logged by The Internet (late_night_reader) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01277 Title: We don't know whether every finite mathematical structure with a certain kind of internal symmetry must always contain a smaller, simpler symmetric structure within it. URL: https://www.worldsolve.org/index.php?api=problem&id=1277

We still haven't resolved whether it's possible to fully simulate any physical system using a finite, exact mathematical model without any approximation.

open Global / Unspecified, Global

Even our best physical models rely on approximations or idealized assumptions, and whether a truly complete and exact mathematical simulation is even theoretically possible remains unresolved. This touches on the deep relationship between mathematics and the physical world.

mathematics-logic global-unspecified any physical whether possible exact mathematical haven resolved fully simulate know philosophy-ethics every

WS01278 · Logged by The Internet (curious_mind93) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01278 Title: We still haven't resolved whether it's possible to fully simulate any physical system using a finite, exact mathematical model without any approximation. URL: https://www.worldsolve.org/index.php?api=problem&id=1278

We haven't determined whether every sufficiently complex network of connections must always contain a smaller, predictable pattern regardless of how it's built.

open Global / Unspecified, Global

Graph theory offers many partial answers about guaranteed patterns within large networks, but a fully general and complete theory covering every possible network structure remains incomplete. This affects our understanding of everything from social networks to biological systems.

mathematics-logic global-unspecified every network haven determined whether sufficiently complex connections must always possible know mathematical resolved philosophy-ethics

WS01279 · Logged by The Internet (offline_mode) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01279 Title: We haven't determined whether every sufficiently complex network of connections must always contain a smaller, predictable pattern regardless of how it's built. URL: https://www.worldsolve.org/index.php?api=problem&id=1279

We don't know whether there's a maximum theoretical limit to how efficiently any sorting or searching algorithm can ever perform, regardless of future computing advances.

open Global / Unspecified, Global

Some lower bounds on computational efficiency are proven for specific tasks, but a fully unified theory covering every possible algorithmic problem remains unresolved. This unresolved question shapes the outer limits of computer science.

technology-computing global-unspecified don know whether there maximum theoretical limit efficiently any sorting haven philosophy-ethics mathematics-logic resolved possible every

WS01280 · Logged by The Internet (future_watch) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01280 Title: We don't know whether there's a maximum theoretical limit to how efficiently any sorting or searching algorithm can ever perform, regardless of future computing advances. URL: https://www.worldsolve.org/index.php?api=problem&id=1280

We still haven't proven whether every possible three-dimensional knot can be distinguished from every other knot using only a finite, computable set of properties.

open Global / Unspecified, Global

While many invariants help distinguish specific knots, no single finite and fully general method has been proven to work for absolutely every possible pair of knots. This remains a central unresolved question in the mathematical study of knots.

mathematics-logic global-unspecified every knot proven possible finite knots haven whether three-dimensional distinguished know resolved mathematical philosophy-ethics

WS01281 · Logged by The Internet (citizen_of_earth) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01281 Title: We still haven't proven whether every possible three-dimensional knot can be distinguished from every other knot using only a finite, computable set of properties. URL: https://www.worldsolve.org/index.php?api=problem&id=1281

We haven't resolved whether it's possible to always find a shorter, simpler mathematical proof for any theorem that currently requires an extremely long one.

open Global / Unspecified, Global

Some proofs are famously long and complex, and it remains unknown whether shorter, more elegant proofs must always exist in principle, even if we haven't yet found them. This unresolved question touches on both mathematics and the philosophy of mathematical elegance.

mathematics-logic global-unspecified haven whether always shorter mathematical long resolved possible find simpler know philosophy-ethics every

WS01282 · Logged by The Internet (wiki_reader) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01282 Title: We haven't resolved whether it's possible to always find a shorter, simpler mathematical proof for any theorem that currently requires an extremely long one. URL: https://www.worldsolve.org/index.php?api=problem&id=1282

What World Solve is

We still haven't resolved whether every infinite set of numbers must have a size that matches one of the specific mathematical infinities we've already identified.

We haven't proven whether it's always possible to divide a cake fairly among any number of people, each with completely different preferences, using a finite number of straight cuts.

We don't know whether the digits of most well-known mathematical constants, like Euler's number, ever settle into any predictable long-term statistical pattern.

We still haven't determined the exact smallest number of unit distances that must repeat among any large set of points drawn on a plane.

We haven't resolved whether every possible tangle of a rope, when idealized mathematically, can be untangled using a provably minimal number of moves.

We don't know whether every mathematical proof can, in principle, be shortened to a version that a human could fully verify without computer assistance.

We still haven't proven whether there are infinitely many prime numbers that remain prime when you reverse the order of their digits.

We haven't resolved the exact minimum number of moves required to solve the hardest possible configuration of many classic sliding puzzles.

We don't know whether it's possible to build a computer program that can always determine, for any given program, whether it will eventually stop running.

We still haven't proven whether every sufficiently large prime number can be written as the sum of three smaller prime numbers in a predictable, structured way.

We haven't determined whether there's an efficient way to solve every instance of the traveling salesman problem exactly, rather than through approximation.

We don't know whether every regular geometric tiling pattern that appears possible in theory can actually be physically realized without gaps or overlaps.

We still haven't resolved whether it's possible to always predict the long-term behavior of any chaotic mathematical system using a finite set of rules.

We haven't proven whether the number of distinct ways to partition any given number into smaller whole numbers follows a fully understood, predictable growth pattern.

We don't know whether every finite mathematical structure with a certain kind of internal symmetry must always contain a smaller, simpler symmetric structure within it.

We still haven't resolved whether it's possible to fully simulate any physical system using a finite, exact mathematical model without any approximation.

We haven't determined whether every sufficiently complex network of connections must always contain a smaller, predictable pattern regardless of how it's built.

We don't know whether there's a maximum theoretical limit to how efficiently any sorting or searching algorithm can ever perform, regardless of future computing advances.

We still haven't proven whether every possible three-dimensional knot can be distinguished from every other knot using only a finite, computable set of properties.

We haven't resolved whether it's possible to always find a shorter, simpler mathematical proof for any theorem that currently requires an extremely long one.