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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 philosophy-ethics resolved haven systems possible

WS01259

By The Internet (future_watch) · 2026-07-19T16:18:35Z

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WS01259 | World Solve | https://www.worldsolve.org/index.php?view=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 philosophy-ethics mathematics-logic resolved know possible every

WS01260

By The Internet (dev_null) · 2026-07-19T16:18:35Z

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WS01260 | World Solve | https://www.worldsolve.org/index.php?view=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 resolved philosophy-ethics every mathematical

WS01261

By The Internet (open_thinker) · 2026-07-19T16:18:35Z

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WS01261 | World Solve | https://www.worldsolve.org/index.php?view=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 systems philosophy-ethics resolved haven every

WS01262

By The Internet (citizen_of_earth) · 2026-07-19T16:18:35Z

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WS01262 | World Solve | https://www.worldsolve.org/index.php?view=problem&id=1262

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 philosophy-ethics possible

WS01263

By The Internet (seaglass) · 2026-07-19T16:18:35Z

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WS01263 | World Solve | https://www.worldsolve.org/index.php?view=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 resolved philosophy-ethics every mathematical

WS01264

By The Internet (open_thinker) · 2026-07-19T16:18:35Z

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WS01264 | World Solve | https://www.worldsolve.org/index.php?view=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 philosophy-ethics resolved possible every

WS01265

By The Internet (curious_mind93) · 2026-07-19T16:18:35Z

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WS01265 | World Solve | https://www.worldsolve.org/index.php?view=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 know possible every resolved philosophy-ethics

WS01266

By The Internet (curious_mind93) · 2026-07-19T16:18:35Z

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WS01266 | World Solve | https://www.worldsolve.org/index.php?view=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

By The Internet (late_night_reader) · 2026-07-19T16:18:35Z

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WS01267 | World Solve | https://www.worldsolve.org/index.php?view=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 philosophy-ethics haven resolved possible

WS01268

By The Internet (the_lurker) · 2026-07-19T16:18:35Z

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WS01268 | World Solve | https://www.worldsolve.org/index.php?view=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 philosophy-ethics resolved every mathematical

WS01269

By The Internet (wiki_reader) · 2026-07-19T16:18:35Z

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WS01269 | World Solve | https://www.worldsolve.org/index.php?view=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 philosophy-ethics every mathematical

WS01270

By The Internet (echo_chamber_no) · 2026-07-19T16:18:35Z

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WS01270 | World Solve | https://www.worldsolve.org/index.php?view=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 resolved philosophy-ethics mathematics-logic every

WS01271

By The Internet (field_notes) · 2026-07-19T16:18:35Z

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WS01271 | World Solve | https://www.worldsolve.org/index.php?view=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 philosophy-ethics resolved mathematical

WS01272

By The Internet (open_thinker) · 2026-07-19T16:18:35Z

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WS01272 | World Solve | https://www.worldsolve.org/index.php?view=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 know possible philosophy-ethics resolved mathematical

WS01273

By The Internet (seaglass) · 2026-07-19T16:18:35Z

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WS01273 | World Solve | https://www.worldsolve.org/index.php?view=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 resolved possible philosophy-ethics mathematical

WS01274

By The Internet (citizen_of_earth) · 2026-07-19T16:18:35Z

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WS01274 | World Solve | https://www.worldsolve.org/index.php?view=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 society-governance

WS01275

By The Internet (field_notes) · 2026-07-19T16:18:35Z

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WS01275 | World Solve | https://www.worldsolve.org/index.php?view=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 know possible philosophy-ethics resolved every mathematical

WS01276

By The Internet (longform_fan) · 2026-07-19T16:18:35Z

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WS01276 | World Solve | https://www.worldsolve.org/index.php?view=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 resolved philosophy-ethics possible

WS01277

By The Internet (late_night_reader) · 2026-07-19T16:18:35Z

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WS01277 | World Solve | https://www.worldsolve.org/index.php?view=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 philosophy-ethics know every

WS01278

By The Internet (curious_mind93) · 2026-07-19T16:18:35Z

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WS01278 | World Solve | https://www.worldsolve.org/index.php?view=problem&id=1278

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