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Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » Subtopicsort iconPosted by
Singmaster's conjectureSingmaster✭✭1Number Theory » Combinatorial N.T.Zach Teitler
A sextic counterexample to Euler's sum of powers conjectureEuler✭✭1Number Theory » Computational N.T.maxal
Counterexamples to the Baillie-PSW primality test✭✭1Number Theory » Computational N.T.maxal
Wall-Sun-Sun primes and Fibonacci divisibility✭✭0Number Theory » Computational N.T.adudzik
Magic square of squaresLaBar✭✭1Number Theory » Computational N.T.maxal
Perfect cuboid✭✭0Number Theory » Computational N.T.tsihonglau
KPZ Universality Conjecture✭✭✭0ProbabilityTomas Kojar
Sums of independent random variables with unbounded varianceFeige✭✭0Theoretical Comp. Sci.cwenner
P vs. NPCook; Levin✭✭✭✭0Theoretical Comp. Sci. » Algorithmszitterbewegung
Exponential Algorithms for KnapsackLipton✭✭1Theoretical Comp. Sci. » Algorithmsdick lipton
The robustness of the tensor productBen-Sasson; Sudan✭✭✭0Theoretical Comp. Sci. » Coding Theoryormeir
Subset-sums equality (pigeonhole version)✭✭✭0Theoretical Comp. Sci. » Complexitymdevos
Complexity of square-root sumGoemans✭✭0Theoretical Comp. Sci. » Complexityabie
Linear-size circuits for stable $0,1 < 2$ sorting?Regan✭✭1Theoretical Comp. Sci. » ComplexityKWRegan
Discrete Logarithm Problem✭✭✭0Theoretical Comp. Sci. » Complexitycplxphil
P vs. PSPACEFolklore✭✭✭0Theoretical Comp. Sci. » Complexitycwenner
One-way functions exist✭✭✭✭0Theoretical Comp. Sci. » Complexityporton
Unconditional derandomization of Arthur-Merlin gamesShaltiel; Umans✭✭✭0Theoretical Comp. Sci. » Complexity » Derandomizationormeir
P vs. BPPFolklore✭✭✭0Theoretical Comp. Sci. » Complexity » DerandomizationCharles R Great...
Refuting random 3SAT-instances on $O(n)$ clauses (weak form)Feige✭✭✭0Theoretical Comp. Sci. » Complexity » Hardness of Approximationcwenner
S(S(f)) = S(f) for reloidsPorton✭✭0Topologyporton
Inscribed Square ProblemToeplitz✭✭0Topologydlh12
Rank vs. GenusJohnson✭✭✭0TopologyJesse Johnson
Smooth 4-dimensional Schoenflies problemAlexander✭✭✭✭0Topologyrybu
Smooth 4-dimensional Poincare conjecturePoincare; Smale; Stallings✭✭✭✭0Topologyrybu
Slice-ribbon problemFox✭✭✭✭0Topologyrybu
Realisation problem for the space of knots in the 3-sphereBudney✭✭0Topologyrybu
Which homology 3-spheres bound homology 4-balls?Ancient/folklore✭✭✭✭0Topologyrybu
Fundamental group torsion for subsets of Euclidean 3-spaceAncient/folklore✭✭0Topologyrybu
Which compact boundaryless 3-manifolds embed smoothly in the 4-sphere?Kirby✭✭✭0Topologyrybu
What is the homotopy type of the group of diffeomorphisms of the 4-sphere?Smale✭✭✭✭0Topologyrybu
Is there an algorithm to determine if a triangulated 4-manifold is combinatorially equivalent to the 4-sphere?Novikov✭✭✭0Topologyrybu
Unsolvability of word problem for 2-knot complementsGordon✭✭✭0Topologyrybu
The 4x5 chessboard complex is the complement of a link, which link? David Eppstein✭✭0Topologyrybu
Outer reloid of restricted funcoidPorton✭✭0Topologyporton
Sticky Cantor sets✭✭0Topologyporton
Nonseparating planar continuum✭✭0Topologyporton
Hilbert-Smith conjectureDavid Hilbert; Paul A. Smith✭✭0Topologyporton
Strict inequalities for products of filtersPorton✭0Topologyporton
Funcoidal products inside an inward reloidPorton✭✭0Topologyporton
Upgrading a completary multifuncoidPorton✭✭0Topologyporton
Atomicity of the poset of completary multifuncoidsPorton✭✭0Topologyporton
Atomicity of the poset of multifuncoidsPorton✭✭0Topologyporton
Graph product of multifuncoidsPorton✭✭0Topologyporton
A conjecture about direct product of funcoidsPorton✭✭0Topologyporton
Closing Lemma for Diffeomorphism (Dynamical Systems)Charles Pugh✭✭✭✭0TopologyJailton Viana
Jacob Palis Conjecture(Finitude of Attractors)(Dynamical Systems)✭✭✭✭0TopologyJailton Viana
Decomposition of completions of reloidsPorton✭✭0Topologyporton
Every metamonovalued funcoid is monovaluedPorton✭✭0Topologyporton
Every metamonovalued reloid is monovaluedPorton✭✭0Topologyporton

Imp.¹: Importance (Low ✭, Medium ✭✭, High ✭✭✭, Outstanding ✭✭✭✭)
Rec.²: Recommended for undergraduates.

Note: Resolved problems from this section may be found in Solved problems.

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