Proved
Analysis
Kakeya Conjecture (3D)
Any set in R³ containing a unit segment in every direction must have Hausdorff dimension 3.
D
B
V
JZ
Reviewed 2026-04Open ->
Proved
Algebra
Geometric Langlands Conjecture
The 'grand unification' connecting number theory, algebraic geometry, and representation theory.
D
B
V
SR
Reviewed 2026-04Open ->
Resolved
Math Physics
Hilbert's Sixth Problem
Rigorously derived Euler and Navier-Stokes equations from hard-sphere particle dynamics.
D
B
V
YD
ZH
Reviewed 2026-04Open ->
Disproved
Analysis
Mizohata-Takeuchi Conjecture
17-year-old found a counterexample to the 40-year-old conjecture about Fourier restriction estimates.
D
B
V
HC
Reviewed 2026-04Open ->
Disproved
Geometry
The Noperthedron
First convex polyhedron (90 vertices) proven to NOT have Rupert's property — cannot pass through itself.
D
B
V
JS
SY
Reviewed 2026-04Open ->
Resolved
AI × Math
AlphaEvolve × Strassen
AI broke Strassen's 56-year record for 4×4 matrix multiplication: 48 vs 49 scalar ops.
D
B
V
AN
MB
Reviewed 2026-04Open ->
Open
Number Theory
Riemann Hypothesis
All nontrivial zeros of the zeta function should lie on the critical line Re(s) = 1/2.
D
B
V
BR
Reviewed 2026-04Open ->
Open
Computer Science
P vs NP
Asks whether every efficiently verifiable solution can also be efficiently found.
D
B
V
SC
Reviewed 2026-04Open ->
Open
Analysis
Navier-Stokes Regularity
Asks whether smooth 3D incompressible fluid flows can develop singularities.
D
B
V
CN
GS
Reviewed 2026-04Open ->
Open
Geometry
Hodge Conjecture
Predicts which cohomology classes on projective varieties come from algebraic cycles.
D
B
V
WV
Reviewed 2026-04Open ->
Open
Number Theory
Birch-Swinnerton-Dyer
Relates rational points on elliptic curves to the behavior of their L-functions at s = 1.
D
B
V
BB
PS
Reviewed 2026-04Open ->
Open
Math Physics
Yang-Mills Mass Gap
Asks for a rigorous quantum Yang-Mills theory with a positive mass gap.
D
B
V
CY
RM
Reviewed 2026-04Open ->
Open
Number Theory
Collatz Conjecture
Repeatedly apply n/2 for even n and 3n+1 for odd n; every path should reach 1.
D
B
V
LC
Reviewed 2026-04Open ->
Open
Number Theory
Goldbach's Conjecture
Every even integer greater than 2 should be expressible as a sum of two primes.
D
B
V
CG
Reviewed 2026-04Open ->
Partial
Number Theory
Twin Prime Conjecture
Predicts infinitely many prime pairs separated by 2, such as 11 and 13.
D
B
V
Ad
Reviewed 2026-04Open ->
Open
Number Theory
abc Conjecture
Controls how often a + b = c can have c much larger than the radical of abc.
D
B
V
JO
DM
Reviewed 2026-04Open ->
Resolved
Logic
Continuum Hypothesis
Asks whether there is a set size strictly between the integers and the real numbers.
D
B
V
GC
PC
Reviewed 2026-04Open ->
Proved
Topology
Poincare Conjecture
Every simply connected closed 3-manifold is homeomorphic to the 3-sphere.
D
B
V
HP
GP
Reviewed 2026-04Open ->