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Field Atlas

Atlas / Toolkit

Toolkit

Some fields become tools for everyone else. This page ranks fields by how far their ideas travelled in the atlas: directly into other threads, where a new field grew from them, and into other domains, where their results were put to use. The count of fields downstream includes indirect descendants too. It is a rough proxy for influence, built only from the lineage and crossings recorded on each field's page, and it undercounts anything the atlas has not yet surveyed.

  1. 01
    Probability Theory

    Mathematics · Analysis

    5 other threads reached directly · 2 other domains · 7 fields downstream

    Grew intoBayesian Statistics, Information Theory, Monte Carlo Methods, Probabilistic Combinatorics, Statistical Inference, Stochastic Processes

    Used inPopulation Genetics, Kinetic Theory of Gases

  2. 02
    Electromagnetism

    Physics · Relativity

    5 other threads reached directly · 1 other domain · 23 fields downstream

    Grew intoAstronomical Spectroscopy, Crystallography, Old Quantum Theory, Radioactivity

    Used inMolecular Biology

  3. 03
    Calculus

    Mathematics · Analysis

    4 other threads reached directly · 1 other domain · 32 fields downstream

    Grew intoDifferential Equations, Differential Geometry of Surfaces, Numerical Analysis

    Used inClassical Mechanics

  4. 04
    Real Analysis

    Mathematics · Analysis

    4 other threads reached directly · 16 fields downstream

    Grew intoContinuous Optimisation, Ergodic Theory, Set Theory, Stochastic Processes

  5. 05
    Quantum Mechanics

    Physics · Quantum

    4 other threads reached directly · 1 other domain · 13 fields downstream

    Grew intoNuclear Structure, Solid-State Physics, Stellar Astrophysics

    Used inMolecular Biology

  6. 06
    Computational Complexity

    Mathematics · Foundations

    4 other threads reached directly · 1 other domain · 3 fields downstream

    Grew intoCombinatorial Optimisation, Public-Key Cryptography, Statistical Learning Theory

    Used inGenomics

  7. 07
    Statistical Mechanics

    Physics · Entropy

    3 other threads reached directly · 1 other domain · 19 fields downstream

    Grew intoMagnetism, Old Quantum Theory

    Used inMolecular Biology

  8. 08
    Complex Analysis

    Mathematics · Analysis

    3 other threads reached directly · 1 other domain · 4 fields downstream

    Grew intoAnalytic Number Theory, Complex Dynamics

    Used inQuantum Mechanics

  9. 09
    Geometric Topology

    Mathematics · Geometry

    3 other threads reached directly · 2 other domains · 0 fields downstream

    Used inPhysical Cosmology, Molecular Biology, Quantum Information

  10. 10
    Phase Transitions

    Physics · Entropy

    2 other threads reached directly · 1 other domain · 2 fields downstream

    Grew intoSuperconductivity, Topological Matter

    Used inMolecular Biology

  11. 11
    Euclidean Geometry

    Mathematics · Geometry

    2 other threads reached directly · 42 fields downstream

    Grew intoCalculus, Elementary Number Theory

  12. 12
    Evolutionary Biology

    Biology · Heredity

    2 other threads reached directly · 8 fields downstream

    Grew intoBiogeography, Evolutionary Developmental Biology

  13. 13
    Biochemistry

    Biology · Cell

    2 other threads reached directly · 7 fields downstream

    Grew intoMolecular Biology, Synaptic Transmission

  14. 14
    Non-Euclidean Geometry

    Mathematics · Geometry

    2 other threads reached directly · 1 other domain · 6 fields downstream

    Grew intoGroup Theory

    Used inSpecial Relativity

  15. 15
    Differential Equations

    Mathematics · Dynamics

    2 other threads reached directly · 1 other domain · 5 fields downstream

    Grew intoNumerical Methods for PDEs

    Used inClassical Mechanics

  16. 16
    Crystallography

    Physics · Matter

    2 other threads reached directly · 2 other domains · 4 fields downstream

    Used inBiochemistry, Euclidean Geometry

  17. 17
    Radioactivity

    Physics · Nuclear

    2 other threads reached directly · 2 other domains · 4 fields downstream

    Used inProbability Theory, Molecular Biology

  18. 18
    Electrophysiology

    Biology · Brain

    2 other threads reached directly · 2 other domains · 3 fields downstream

    Used inElectromagnetism, Dynamical Systems

  19. 19
    Graph Theory

    Mathematics · Combinatorics

    2 other threads reached directly · 2 other domains · 3 fields downstream

    Used inElectromagnetism, Genomics

  20. 20
    Stellar Astrophysics

    Physics · Stars

    2 other threads reached directly · 1 other domain · 3 fields downstream

    Grew intoFusion Energy

    Used inEvolutionary Biology

  21. 21
    Algebraic Geometry

    Mathematics · Geometry

    2 other threads reached directly · 1 other domain · 2 fields downstream

    Grew intoArithmetic Geometry

    Used inEvolutionary Biology

  22. 22
    Enumerative Combinatorics

    Mathematics · Combinatorics

    2 other threads reached directly · 2 other domains · 2 fields downstream

    Used inEvolutionary Biology, Statistical Mechanics

  23. 23
    Population Genetics

    Biology · Heredity

    2 other threads reached directly · 1 other domain · 2 fields downstream

    Grew intoConservation Biology

    Used inProbability Theory

  24. 24
    Information Theory

    Mathematics · Statistics

    2 other threads reached directly · 2 other domains · 1 field downstream

    Used inStatistical Mechanics, Molecular Biology

  25. 25
    Bayesian Statistics

    Mathematics · Statistics

    2 other threads reached directly · 2 other domains · 0 fields downstream

    Used inEvolutionary Biology, Physical Cosmology

  26. 26
    Monte Carlo Methods

    Mathematics · Computation

    2 other threads reached directly · 2 other domains · 0 fields downstream

    Used inStatistical Mechanics, Evolutionary Biology

  27. 27
    Radiometric Dating

    Physics · Nuclear

    2 other threads reached directly · 1 other domain · 0 fields downstream

    Used inEvolutionary Biology, Cell Biology

  28. 28
    Statistical Learning Theory

    Mathematics · Statistics

    2 other threads reached directly · 2 other domains · 0 fields downstream

    Used inMolecular Biology, Phase Transitions

  29. 29
    Stochastic Processes

    Mathematics · Statistics

    2 other threads reached directly · 2 other domains · 0 fields downstream

    Used inKinetic Theory of Gases, Cell Biology

  30. 30
    Population Ecology

    Biology · Ecology

    1 other thread reached directly · 1 other domain · 3 fields downstream

    Used inDifferential Equations, Chaos Theory

  31. 31
    Statistical Inference

    Mathematics · Statistics

    1 other thread reached directly · 1 other domain · 2 fields downstream

    Used inPopulation Genetics, Genomics

  32. 32
    Numerical Methods for PDEs

    Mathematics · Computation

    1 other thread reached directly · 1 other domain · 0 fields downstream

    Used inClassical Mechanics, General Relativity

  33. 33
    Representation Theory

    Mathematics · Algebra

    1 other thread reached directly · 1 other domain · 0 fields downstream

    Used inQuantum Mechanics, Particle Physics

  34. 34
    Classical Mechanics

    Physics · Relativity

    1 other thread reached directly · 24 fields downstream

    Grew intoKinetic Theory of Gases

  35. 35
    Thermodynamics

    Physics · Entropy

    1 other thread reached directly · 1 other domain · 21 fields downstream

    Used inMolecular Biology

  36. 36
    Fourier Analysis

    Mathematics · Analysis

    1 other thread reached directly · 1 other domain · 17 fields downstream

    Used inMolecular Biology

  37. 37
    Old Quantum Theory

    Physics · Quantum

    1 other thread reached directly · 16 fields downstream

    Grew intoAstronomical Spectroscopy

  38. 38
    Cell Theory

    Biology · Cell

    1 other thread reached directly · 12 fields downstream

    Grew intoNeuroanatomy

  39. 39
    Theory of Equations

    Mathematics · Algebra

    1 other thread reached directly · 9 fields downstream

    Grew intoComplex Analysis

  40. 40
    Genetics

    Biology · Heredity

    1 other thread reached directly · 6 fields downstream

    Grew intoDevelopmental Genetics

  41. 41
    Special Relativity

    Physics · Relativity

    1 other thread reached directly · 5 fields downstream

    Grew intoQuantum Field Theory

  42. 42
    Algebraic Number Theory

    Mathematics · Number Theory

    1 other thread reached directly · 4 fields downstream

    Grew intoAbstract Algebra

  43. 43
    Algebraic Topology

    Mathematics · Geometry

    1 other thread reached directly · 1 other domain · 4 fields downstream

    Used inTopological Matter

  44. 44
    Numerical Analysis

    Mathematics · Computation

    1 other thread reached directly · 1 other domain · 4 fields downstream

    Used inClassical Mechanics

  45. 45
    Dynamical Systems

    Mathematics · Dynamics

    1 other thread reached directly · 1 other domain · 3 fields downstream

    Used inClassical Mechanics

  46. 46
    Experimental Embryology

    Biology · Development

    1 other thread reached directly · 1 other domain · 3 fields downstream

    Used inDifferential Equations

  47. 47
    Solid-State Physics

    Physics · Matter

    1 other thread reached directly · 1 other domain · 3 fields downstream

    Used inGenomics

  48. 48
    Cell Biology

    Biology · Cell

    1 other thread reached directly · 2 fields downstream

    Grew intoStem Cell Biology

  49. 49
    Community Ecology

    Biology · Ecology

    1 other thread reached directly · 1 other domain · 2 fields downstream

    Used inProbability Theory

  50. 50
    General Relativity

    Physics · Relativity

    1 other thread reached directly · 2 fields downstream

    Grew intoCompact Objects

  51. 51
    Nuclear Structure

    Physics · Nuclear

    1 other thread reached directly · 1 other domain · 2 fields downstream

    Used inBiochemistry

  52. 52
    Riemannian Geometry

    Mathematics · Geometry

    1 other thread reached directly · 1 other domain · 2 fields downstream

    Used inGeneral Relativity

  53. 53
    Developmental Genetics

    Biology · Development

    1 other thread reached directly · 1 other domain · 1 field downstream

    Used inKinetic Theory of Gases

  54. 54
    Quantum Field Theory

    Physics · Quantum

    1 other thread reached directly · 1 other domain · 1 field downstream

    Used inGeometric Topology

  55. 55
    Chaos Theory

    Mathematics · Dynamics

    1 other thread reached directly · 1 other domain · 0 fields downstream

    Used inPopulation Ecology

  56. 56
    Combinatorial Optimisation

    Mathematics · Combinatorics

    1 other thread reached directly · 1 other domain · 0 fields downstream

    Used inStatistical Mechanics

  57. 57
    Computational Neuroscience

    Biology · Brain

    1 other thread reached directly · 1 other domain · 0 fields downstream

    Used inComputability Theory

  58. 58
    Conservation Biology

    Biology · Ecology

    1 other thread reached directly · 1 other domain · 0 fields downstream

    Used inProbability Theory

  59. 59
    Continuous Optimisation

    Mathematics · Computation

    1 other thread reached directly · 1 other domain · 0 fields downstream

    Used inMolecular Biology

  60. 60
    Ecosystem Ecology

    Biology · Ecology

    1 other thread reached directly · 1 other domain · 0 fields downstream

    Used inThermodynamics

  61. 61
    Ergodic Theory

    Mathematics · Dynamics

    1 other thread reached directly · 1 other domain · 0 fields downstream

    Used inStatistical Mechanics

  62. 62
    Exoplanetary Science

    Physics · Stars

    1 other thread reached directly · 1 other domain · 0 fields downstream

    Used inEvolutionary Biology

  63. 63
    Magnetism

    Physics · Matter

    1 other thread reached directly · 1 other domain · 0 fields downstream

    Used inCombinatorial Optimisation

  64. 64
    Non-Equilibrium Physics

    Physics · Entropy

    1 other thread reached directly · 1 other domain · 0 fields downstream

    Used inMolecular Biology

  65. 65
    Numerical Linear Algebra

    Mathematics · Computation

    1 other thread reached directly · 1 other domain · 0 fields downstream

    Used inQuantum Mechanics

  66. 66
    Quantum Information

    Physics · Quantum

    1 other thread reached directly · 1 other domain · 0 fields downstream

    Used inPublic-Key Cryptography

  67. 67
    Stem Cell Biology

    Biology · Development

    1 other thread reached directly · 1 other domain · 0 fields downstream

    Used inProbability Theory

  68. 68
    Topological Matter

    Physics · Matter

    1 other thread reached directly · 1 other domain · 0 fields downstream

    Used inAlgebraic Topology