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Field Atlas

A narrative atlas · 3 domains surveyed

How fields of knowledge branched, and where the map runs out.

Each field here earns a page by answering one question: what forced it to split off from what came before? The atlas follows the dated turning points (proofs, crises, reformulations) that drew each boundary. It also marks, as honestly as it can, the problems no one has solved yet.

fields charted
104
turning points
604
unresolved problems
113
Open the first surveyOr see where domains cross
Plate IGeneral survey, not to scale

The atlas at a glance

Every thread on one circle. Fields rarely stay inside their own thread: a solid line means a field grew from a parent in another thread, and a dashed line means a result from one domain was put to use in another. Select a thread to open its map.

MATHEMATICSPHYSICSBIOLOGYGeometry → Heredity: 2 crossingsGeometry → Matter: 1 crossingStatistics → Heredity: 5 crossingsStatistics → Relativity: 1 crossingAnalysis → Relativity: 1 crossingDynamics → Ecology: 1 crossingCombinatorics → Entropy: 2 crossingsEcology → Analysis: 2 crossingsAnalysis → Quantum: 1 crossingFoundations → Heredity: 1 crossingBrain → Foundations: 1 crossingComputation → Heredity: 2 crossingsMatter → Cell: 1 crossingMatter → Geometry: 2 crossingsDevelopment → Entropy: 1 crossingDynamics → Relativity: 2 crossingsEcology → Entropy: 1 crossingRelativity → Heredity: 1 crossingBrain → Relativity: 1 crossingBrain → Dynamics: 1 crossingCombinatorics → Heredity: 2 crossingsDynamics → Entropy: 1 crossingStars → Heredity: 2 crossingsDevelopment → Dynamics: 1 crossingAnalysis → Heredity: 2 crossingsGeometry → Relativity: 3 crossingsGeometry → Quantum: 1 crossingCombinatorics → Relativity: 1 crossingStatistics → Entropy: 3 crossingsMatter → Combinatorics: 1 crossingComputation → Entropy: 1 crossingEntropy → Heredity: 4 crossingsNuclear → Cell: 2 crossingsComputation → Relativity: 3 crossingsComputation → Quantum: 1 crossingEcology → Dynamics: 2 crossingsHeredity → Analysis: 1 crossingAnalysis → Entropy: 1 crossingQuantum → Geometry: 1 crossingQuantum → Number Theory: 1 crossingQuantum → Heredity: 1 crossingNuclear → Analysis: 1 crossingNuclear → Heredity: 2 crossingsAlgebra → Quantum: 2 crossingsMatter → Heredity: 1 crossingDevelopment → Analysis: 1 crossingStatistics → Cell: 1 crossingNumber Theory → Algebra: 1 field descend across threadsAnalysis → Number Theory: 1 field descend across threadsGeometry → Number Theory: 2 fields descend across threadsRelativity → Stars: 2 fields descend across threadsQuantum → Stars: 2 fields descend across threadsAnalysis → Statistics: 5 fields descend across threadsHeredity → Ecology: 2 fields descend across threadsGeometry → Analysis: 1 field descend across threadsFoundations → Combinatorics: 1 field descend across threadsAlgebra → Analysis: 1 field descend across threadsAnalysis → Dynamics: 3 fields descend across threadsAnalysis → Computation: 3 fields descend across threadsRelativity → Matter: 1 field descend across threadsHeredity → Development: 2 fields descend across threadsAnalysis → Geometry: 1 field descend across threadsStars → Nuclear: 1 field descend across threadsGeometry → Algebra: 1 field descend across threadsRelativity → Entropy: 1 field descend across threadsEntropy → Matter: 3 fields descend across threadsCell → Heredity: 1 field descend across threadsCell → Brain: 2 fields descend across threadsQuantum → Nuclear: 1 field descend across threadsDynamics → Computation: 1 field descend across threadsEntropy → Quantum: 1 field descend across threadsRelativity → Quantum: 2 fields descend across threadsAnalysis → Combinatorics: 1 field descend across threadsFoundations → Number Theory: 1 field descend across threadsRelativity → Nuclear: 1 field descend across threadsAnalysis → Foundations: 1 field descend across threadsQuantum → Matter: 1 field descend across threadsFoundations → Statistics: 1 field descend across threadsCell → Development: 1 field descend across threadsGeometryGeometry: 9 fieldsNumber TheoryNumber Theory: 5 fieldsAnalysisAnalysis: 5 fieldsFoundationsFoundations: 5 fieldsAlgebraAlgebra: 5 fieldsCombinatoricsCombinatorics: 5 fieldsDynamicsDynamics: 5 fieldsStatisticsStatistics: 5 fieldsComputationComputation: 5 fieldsRelativityRelativity: 5 fieldsEntropyEntropy: 5 fieldsQuantumQuantum: 5 fieldsStarsStars: 5 fieldsMatterMatter: 5 fieldsNuclearNuclear: 5 fieldsHeredityHeredity: 5 fieldsCellCell: 5 fieldsBrainBrain: 5 fieldsEcologyEcology: 5 fieldsDevelopmentDevelopment: 5 fields
Lineage: a field whose parent sits in another threadCrossing: a result used in another domainDot size: number of fields. Line width: number of links.

Domains

  1. 01 · ChartedMathematicsHow space split into many geometries and whole numbers into theories of their own, how calculus was made rigorous and mathematics met its own limits, and how solving equations became the study of symmetry. How counting puzzles became the mathematics of networks and equations of motion led to chaos, how reasoning from data and calculating by machine became mathematics of their own, and what forced each split.49 fields276 turning points52 unresolved problems
  2. 02 · ChartedPhysicsHow motion, light and gravity were rebuilt around the speed of light, how heat became the statistics of atoms, and how energy turned out to come in lumps. How starlight revealed what stars are made of, how crystals explained metals and magnets, how a fogged photographic plate led to the nucleus, and what is still dark.30 fields182 turning points34 unresolved problems
  3. 03 · ChartedBiologyHow evolution and heredity, long at odds, merged, and how reading DNA rewrote both. How the cell became the unit of life and disease, how the brain was found to signal with electricity and chemistry, how the study of where species live became the science of ecosystems, and how a single egg builds a body.25 fields146 turning points27 unresolved problems
AcrossCrossingsWhere a result in one domain lands in another: geometry becoming gravity, physics revealing the double helix.73 linked crossings21 reaching unmapped ground
InfluenceToolkitWhich fields became tools for everyone else, ranked by how far their ideas travelled across threads and domains.Lineage and crossings
The fogOpen problemsEvery unsolved problem at the edge of the atlas in one place, by domain and thread, with its status as of 2026.113 unresolved

Reading the map

Charted: settled results
Contested: sources disagree on priority or causation
Unmapped: open problems