Unsolved Problems

TOPICS Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld Foundations of MathematicsMathematical ProblemsUnsolved ProblemsThere are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The Goldbach conjecture. 2. The Riemann hypothesis. 3. The conjecture that there exists a Hadamard matrixfor every positive multiple of 4. 4. The twin prime conjecture (i.e., the conjecture that there are an infinite number of twin primes). 5. Determination of whether NP-problems are actuallyP-problems. 6. The Collatz problem. 7. Proof that the 196-algorithm does not terminatewhen applied to the number 196. 8. Proof that 10 is a solitary number. 9. Finding a formula for the probability that two elements chosen at rando...