The world's unsolved problems
993 open questions across 14 fields, gathered from Wikipedia. Pick one and start thinking.
Showing all 993 problems · surprise me
-
Capacity of the broadcast channel
The capacity of the broadcast channel, or the case in which a single transmitter is sending information to many receivers, is unknown in general, though it is known for several specific cases.
Read on Wikipedia → -
Capacity of the interference channel (Two User)
The capacity of the interference channel, in the case where there are two transmitter and receiver pairs that interfere among each other, is unknown in general. Capacity is known in special cases: strong interference regime, injective-deterministic....
Read on Wikipedia → -
Capacity of the two-way channel
The capacity of the two-way channel (a channel in which information is sent in both directions simultaneously) is unknown. Capacity is known in special cases: for the two-way channel with additive white Gaussian noise, capacity is achieved without using...
Read on Wikipedia → -
Capacity of Aloha
The ALOHAnet used a very simple access scheme for which the capacity is still unknown, though it is known in a few special cases.
Read on Wikipedia → -
Capacity of the queue channel
Under a FIFO policy, whether the feedback capacity of the queue channel is strictly greater than the capacity without feedback is unknown for general service time distributions though it is known that the two quantities are equal when the service time...
Read on Wikipedia → -
Quantum capacity
The capacity of a quantum channel is in general not known.
Read on Wikipedia → -
Lossy distributed source coding
The best way to compress correlated information sources using encoders that do not communicate with each other, preserving each source to within its distortion metric, is not known.
Read on Wikipedia → -
Birch and Swinnerton-Dyer conjecture
Read on Wikipedia → -
Hodge conjecture
Read on Wikipedia → -
Navier–Stokes existence and smoothness
Read on Wikipedia → -
P versus NP
Read on Wikipedia → -
Riemann hypothesis
Read on Wikipedia → -
Yang–Mills existence and mass gap
Read on Wikipedia → -
The Poincaré conjecture can be formulated in terms of the generalized Poincaré conjecture for different categories of manifolds. In the…
The Poincaré conjecture can be formulated in terms of the generalized Poincaré conjecture for different categories of manifolds. In the category of piecewise linear manifolds, the generalized conjecture is still an open problem for 4-dimensional manifolds....
Read on Wikipedia → -
The Birch and Swinnerton-Dyer conjecture can be formulated for elliptic curves over any number field, and generalizations for more general…
The Birch and Swinnerton-Dyer conjecture can be formulated for elliptic curves over any number field, and generalizations for more general arithmetic objects have been proposed. The Millennium Prize is offered for resolving the conjecture for elliptic...
Read on Wikipedia → -
The Navier–Stokes equations have a general form that can take into account many physical phenomena including the difference between volume…
The Navier–Stokes equations have a general form that can take into account many physical phenomena including the difference between volume viscosity and dynamic viscosity, compressible flow, change of viscosities in the flow, and an external force. The...
Read on Wikipedia → -
The Riemann hypothesis has many generalizations for different types of L-functions that are expected to be true. The Millennium Prize…
The Riemann hypothesis has many generalizations for different types of L-functions that are expected to be true. The Millennium Prize problem is offered for showing the original Riemann hypothesis for the Riemann zeta function.
Read on Wikipedia → -
The Kourovka Notebook () is a collection of unsolved problems in group theory, first published in 1965 and updated many times since.
Read on Wikipedia → -
The Sverdlovsk Notebook () is a collection of unsolved problems in semigroup theory, first published in 1965 and updated every 2 to 4 years…
The Sverdlovsk Notebook () is a collection of unsolved problems in semigroup theory, first published in 1965 and updated every 2 to 4 years since.
Read on Wikipedia → -
The Dniester Notebook () lists several hundred unsolved problems in algebra, particularly ring theory and modulus theory.
Read on Wikipedia → -
The Erlagol Notebook () lists unsolved problems in algebra and model theory.
Read on Wikipedia → -
Birch–Tate conjecture on the relation between the order of the center of the Steinberg group of the ring of integers of a number field to…
Birch–Tate conjecture on the relation between the order of the center of the Steinberg group of the ring of integers of a number field to the field's Dedekind zeta function.
Read on Wikipedia → -
Casas-Alvero conjecture
if a polynomial of degree d defined over a field K of characteristic 0 has a factor in common with its first through d - 1-th derivative, then must f be the d-th power of a linear polynomial?
Read on Wikipedia → -
Connes embedding problem in Von Neumann algebra theory
Read on Wikipedia → -
Determinantal conjecture on the determinant of the sum of two normal matrices.
Read on Wikipedia → -
Eilenberg–Ganea conjecture
a group with cohomological dimension 2 also has a 2-dimensional Eilenberg–MacLane space K(G, 1).
Read on Wikipedia → -
Farrell–Jones conjecture on whether certain assembly maps are isomorphisms.
Read on Wikipedia → -
Finite lattice representation problem
is every finite lattice isomorphic to the congruence lattice of some finite algebra?
Read on Wikipedia → -
Goncharov conjecture on the cohomology of certain motivic complexes.
Read on Wikipedia → -
Green's conjecture
the Clifford index of a non-hyperelliptic curve is determined by the extent to which it, as a canonical curve, has linear syzygies.
Read on Wikipedia →
Data last refreshed 2026-10-20 03:01 UTC.