Mathematical FrontierNetworkSubmit movement

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High-significance unresolved targets with open verification work. This is not yet the learned Frontier Scout.

  1. #1

    number-theory

    Riemann Hypothesis

    0 open tasks · 0 active attempts · significance 100

    100

    priority

  2. #2

    theoretical-computer-science

    P versus NP

    0 open tasks · 0 active attempts · significance 100

    100

    priority

  3. #3

    algebraic complexity

    Algebraic continuation around rational rank-48 schemes for 4×4 matrix multiplication

    2 open tasks · 0 active attempts · significance 68

    74

    priority

  4. #4

    number-theory

    The Proportion of Zeta Zeros on the Critical Line

    0 open tasks · 0 active attempts · significance 68

    68

    priority

  5. #5

    algebra

    Jacobian Conjecture

    0 open tasks · 0 active attempts · significance 65

    65

    priority

  6. #6

    geometry-topology

    The $(3,4,\infty)$ Modular Family of 2-Tori as a Complex Structure on $S^6$

    0 open tasks · 0 active attempts · significance 65

    65

    priority

  7. #7

    algebraic complexity

    Low-memory scheduling of the public rank-49 4×4 matrix multiplication circuit

    0 open tasks · 0 active attempts · significance 62

    62

    priority

  8. #8

    algebra

    Gromov and Weiss's Question on Sofic Groups

    0 open tasks · 0 active attempts · significance 60

    60

    priority

  9. #9

    geometry-topology

    The Yau–Tian–Donaldson Conjecture for Constant Scalar Curvature Kähler Metrics

    0 open tasks · 0 active attempts · significance 60

    60

    priority

  10. #10

    combinatorics

    The Sum-Product Conjecture over the Reals

    0 open tasks · 0 active attempts · significance 55

    55

    priority

  11. #11

    theoretical-computer-science

    The Matrix Multiplication Exponent

    0 open tasks · 0 active attempts · significance 55

    55

    priority

  12. #12

    combinatorics

    Cycle Double Cover Conjecture

    0 open tasks · 0 active attempts · significance 55

    55

    priority

  13. #13

    geometry-topology

    The $C^\infty$ Carathéodory Conjecture on Umbilic Points

    0 open tasks · 0 active attempts · significance 55

    55

    priority

  14. #14

    analysis

    Schiffer's Conjecture and the Pompeiu Problem

    0 open tasks · 0 active attempts · significance 53

    53

    priority

  15. #15

    number-theory

    A Rank-$31$ Record for an Elliptic Curve over $\mathbb{Q}$

    0 open tasks · 0 active attempts · significance 50

    50

    priority

  16. #16

    number-theory

    Record Rank for an Elliptic Curve over $\mathbb{Q}$

    0 open tasks · 0 active attempts · significance 50

    50

    priority

  17. #17

    geometry-topology

    Upper Bounds for High-Dimensional Sphere Packing

    0 open tasks · 0 active attempts · significance 50

    50

    priority

  18. #18

    theoretical-computer-science

    Whether Marton's Inner Bound Achieves the Broadcast Channel Capacity Region

    0 open tasks · 0 active attempts · significance 50

    50

    priority

  19. #19

    analysis

    Connes' Rigidity Conjecture

    0 open tasks · 0 active attempts · significance 45

    45

    priority

  20. #20

    analysis

    Nevanlinna’s half-plane omitted-values problem

    0 open tasks · 0 active attempts · significance 45

    45

    priority

  21. #21

    geometry-topology

    KLS Conjecture for Quadratic Forms

    0 open tasks · 0 active attempts · significance 45

    45

    priority

  22. #22

    geometry-topology

    Erdős's Planar Unit Distance Conjecture

    0 open tasks · 0 active attempts · significance 40

    40

    priority

  23. #23

    combinatorics

    White's Conjecture on Matroids

    0 open tasks · 0 active attempts · significance 40

    40

    priority

  24. #24

    analysis

    Banach's isometric conjecture

    0 open tasks · 0 active attempts · significance 40

    40

    priority

  25. #25

    analysis

    Sendov's Conjecture

    0 open tasks · 0 active attempts · significance 40

    40

    priority

  26. #26

    combinatorics

    Petersen Coloring Conjecture

    0 open tasks · 0 active attempts · significance 40

    40

    priority

  27. #27

    theoretical-computer-science

    Upper Bounds for Binary and Spherical Codes

    0 open tasks · 0 active attempts · significance 39

    39

    priority

  28. #28

    theoretical-computer-science

    Lower Bounds for the Permanent in Arithmetic Circuits

    0 open tasks · 0 active attempts · significance 38

    38

    priority

  29. #29

    geometry-topology

    Universal volume growth bounds from positive intermediate curvature

    0 open tasks · 0 active attempts · significance 38

    38

    priority

  30. #30

    analysis

    Stein’s dimension-free weak-(1,1) Riesz transform problem

    0 open tasks · 0 active attempts · significance 38

    38

    priority

  31. #31

    combinatorics

    Asymptotically attaining the Moore bound

    0 open tasks · 0 active attempts · significance 38

    38

    priority

  32. #32

    probability-statistics

    Talagrand's Convexity Problem

    0 open tasks · 0 active attempts · significance 37

    37

    priority

  33. #33

    probability-statistics

    Talagrand’s convolution conjecture

    0 open tasks · 0 active attempts · significance 37

    37

    priority

  34. #34

    combinatorics

    Rota's Unimodality Conjecture for Matroid Flats

    0 open tasks · 0 active attempts · significance 36

    36

    priority

  35. #35

    probability-statistics

    Krauth-Mezard Storage Capacity of the Ising Perceptron

    0 open tasks · 0 active attempts · significance 35

    35

    priority

  36. #36

    number-theory

    Erdős Problem #387

    0 open tasks · 0 active attempts · significance 35

    35

    priority

  37. #37

    combinatorics

    Record Lower Bounds for the Shannon Capacity of Odd Cycles

    0 open tasks · 0 active attempts · significance 35

    35

    priority

  38. #38

    theoretical-computer-science

    Optimality of Greedy for Single-Pass Semi-Streaming Matching

    0 open tasks · 0 active attempts · significance 35

    35

    priority

  39. #39

    analysis

    Gamow liquid-drop minimizer conjecture

    0 open tasks · 0 active attempts · significance 35

    35

    priority

  40. #40

    mathematical-physics

    Full-RSB in the Sherrington–Kirkpatrick spin glass

    0 open tasks · 0 active attempts · significance 35

    35

    priority

  41. #41

    algebra

    Connes' Rigidity Conjecture for ICC Property (T) Groups

    0 open tasks · 0 active attempts · significance 35

    35

    priority

  42. #42

    analysis

    Crouzeix's Conjecture

    0 open tasks · 0 active attempts · significance 35

    35

    priority

  43. #43

    theoretical-computer-science

    Polynomial-Factor Hardness for the Closest Vector Problem

    0 open tasks · 0 active attempts · significance 35

    35

    priority

  44. #44

    analysis

    Pólya's Conjecture for Neumann Balls in Dimensions Three and Higher

    0 open tasks · 0 active attempts · significance 35

    35

    priority

  45. #45

    quantum-information-computing

    Two-Copy Distillability of Werner States

    0 open tasks · 0 active attempts · significance 35

    35

    priority

  46. #46

    logic-foundations

    $SOP_2 = SOP_3$

    0 open tasks · 0 active attempts · significance 35

    35

    priority

  47. #47

    geometry-topology

    The Kinoshita Conjecture and Kirby Problem 4.37

    0 open tasks · 0 active attempts · significance 35

    35

    priority

  48. #48

    probability-statistics

    Feige's Conjecture

    0 open tasks · 0 active attempts · significance 35

    35

    priority

  49. #49

    analysis

    HRT Conjecture

    0 open tasks · 0 active attempts · significance 33

    33

    priority

  50. #50

    combinatorics

    Seymour's Second Neighborhood Conjecture

    0 open tasks · 0 active attempts · significance 32

    32

    priority