World Solve

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.

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.

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.

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.

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.

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.

This long-standing conjecture claims there's always at least one prime number between any two consecutive perfect squares, and while verified extensively by computer, no general proof exists. Solving it would sharpen our understanding of prime distribution.

Various conjectures link the number of prime factors a number has to specific patterns of behavior, but many of these connections remain only partially proven. This continues to be explored within analytic number theory.

History has shown some conjectures hold for enormous ranges before finally failing, raising the unresolved question of how confidently mathematicians can ever trust patterns observed only in finite testing. This shapes ongoing debates about the reliability of computational evidence in mathematics.

Some conjectures hold true for infinitely many tested cases without yet having a general proof, raising open questions about whether extensive verification alone can ever substitute for full mathematical certainty. This unresolved tension shapes ongoing debates about the nature of mathematical proof.

Known as Goldbach's Conjecture, this simple-sounding statement has been checked for enormous numbers without exception, but never formally proven true for all numbers. It remains one of the oldest unsolved problems in mathematics.

This century-old conjecture predicts a hidden pattern in how prime numbers are distributed, but nobody has ever proven it true. A proof would deepen our understanding of numbers in ways that ripple into cryptography and physics.