[ { "id": 1, "slug": "number-theory", "name": "Number theory", "discipline": "mathematics", "blurb": "Primes, Diophantine equations, L-functions โ€” the field with the highest ratio of easily stated to hopelessly hard.", "sortOrder": 10 }, { "id": 2, "slug": "combinatorics", "name": "Combinatorics", "discipline": "mathematics", "blurb": "Extremal and additive questions about finite structures, where a single clever construction can end a decades-old problem.", "sortOrder": 11 }, { "id": 3, "slug": "graph-theory", "name": "Graph theory", "discipline": "mathematics", "blurb": "Colourings, minors, expansion and the conjectures that organise them.", "sortOrder": 12 }, { "id": 4, "slug": "analysis", "name": "Analysis", "discipline": "mathematics", "blurb": "Harmonic analysis, operator theory and the fine structure of functions and spectra.", "sortOrder": 13 }, { "id": 5, "slug": "partial-differential-equations", "name": "Partial differential equations", "discipline": "mathematics", "blurb": "Regularity, blow-up and long-time behaviour of the equations of physics.", "sortOrder": 14 }, { "id": 6, "slug": "geometry-and-topology", "name": "Geometry and topology", "discipline": "mathematics", "blurb": "Manifolds, knots, packings and the stubborn gap between the smooth and the topological.", "sortOrder": 15 }, { "id": 7, "slug": "algebra", "name": "Algebra", "discipline": "mathematics", "blurb": "Groups, rings and the representation theory that keeps them honest.", "sortOrder": 16 }, { "id": 8, "slug": "probability", "name": "Probability", "discipline": "mathematics", "blurb": "Random walks, percolation and scaling limits โ€” where physics intuition outruns proof by decades.", "sortOrder": 17 }, { "id": 9, "slug": "dynamical-systems", "name": "Dynamical systems", "discipline": "mathematics", "blurb": "Iteration, ergodic theory and the geometry of long-run behaviour.", "sortOrder": 18 }, { "id": 10, "slug": "logic-and-foundations", "name": "Logic and foundations", "discipline": "mathematics", "blurb": "Set theory, model theory and the limits of what axioms decide.", "sortOrder": 19 }, { "id": 11, "slug": "computational-complexity", "name": "Computational complexity", "discipline": "computer-science", "blurb": "What can be computed with bounded resources. Home of the discipline's largest embarrassments.", "sortOrder": 30 }, { "id": 12, "slug": "algorithms", "name": "Algorithms and data structures", "discipline": "computer-science", "blurb": "Upper bounds: the running times we can achieve, and the ones we cannot rule out.", "sortOrder": 31 }, { "id": 13, "slug": "cryptography", "name": "Cryptography", "discipline": "computer-science", "blurb": "Security reductions and the hardness assumptions the modern internet is standing on.", "sortOrder": 32 }, { "id": 14, "slug": "computational-geometry", "name": "Computational geometry", "discipline": "computer-science", "blurb": "Points, distances and arrangements, counted and computed.", "sortOrder": 33 }, { "id": 15, "slug": "learning-theory", "name": "Learning theory", "discipline": "machine-learning", "blurb": "Sample complexity, regret and the formal limits of learning from data. Source of the COLT open-problem track.", "sortOrder": 50 }, { "id": 16, "slug": "optimization", "name": "Optimization", "discipline": "machine-learning", "blurb": "Convergence rates, landscapes and the complexity of finding a good point.", "sortOrder": 51 }, { "id": 17, "slug": "deep-learning-theory", "name": "Deep learning theory", "discipline": "machine-learning", "blurb": "Why the methods that work in practice work at all โ€” the field's largest open questions are still qualitative.", "sortOrder": 52 }, { "id": 18, "slug": "high-dimensional-statistics", "name": "High-dimensional statistics", "discipline": "statistics", "blurb": "Estimation when the number of parameters rivals the number of samples, and the computational price of it.", "sortOrder": 60 }, { "id": 19, "slug": "quantum-information", "name": "Quantum information", "discipline": "physics", "blurb": "Entanglement, channels and the structure of quantum correlations. Unusually rich in crisply stated problems.", "sortOrder": 70 }, { "id": 20, "slug": "mathematical-physics", "name": "Mathematical physics", "discipline": "physics", "blurb": "Rigorous foundations for the models physicists already trust.", "sortOrder": 71 }, { "id": 21, "slug": "condensed-matter", "name": "Condensed matter", "discipline": "physics", "blurb": "Phases of matter, and the many-body models nobody can solve.", "sortOrder": 72 }, { "id": 43, "slug": "mathematics-general", "name": "Mathematics ยท general", "discipline": "mathematics", "blurb": "Mathematical questions awaiting a more specific subject classification.", "sortOrder": 29 }, { "id": 44, "slug": "mathematical-biology", "name": "Mathematical biology", "discipline": "biology", "blurb": "Mathematical models of biological and other natural systems.", "sortOrder": 60 }, { "id": 45, "slug": "mathematical-economics", "name": "Mathematical economics and game theory", "discipline": "economics", "blurb": "Equilibria, games, and mathematical models of social systems.", "sortOrder": 70 }, { "id": 46, "slug": "control-and-information", "name": "Control and information theory", "discipline": "mathematics", "blurb": "Control systems, stability, communication, and information.", "sortOrder": 19 }, { "id": 143, "slug": "astronomy", "name": "Astronomy and solar physics", "discipline": "astronomy", "blurb": "Planet formation, stellar activity and the physical universe.", "sortOrder": 80 }, { "id": 144, "slug": "evolution-and-origins", "name": "Evolution and origins of life", "discipline": "biology", "blurb": "The emergence of living systems and the mechanisms of evolutionary change.", "sortOrder": 81 }, { "id": 145, "slug": "neuroscience", "name": "Neuroscience", "discipline": "biology", "blurb": "Neural mechanisms of perception, learning, memory and behavior.", "sortOrder": 82 }, { "id": 146, "slug": "chemical-sciences", "name": "Chemical sciences", "discipline": "chemistry", "blurb": "Molecular structure, reaction mechanisms and chemical origins.", "sortOrder": 83 }, { "id": 147, "slug": "earth-sciences", "name": "Earth sciences", "discipline": "geoscience", "blurb": "Earth's interior, landscape evolution and climate dynamics.", "sortOrder": 84 }, { "id": 148, "slug": "statistical-inference", "name": "Statistical inference", "discipline": "statistics", "blurb": "Reliable inference, testing and uncertainty under dependence.", "sortOrder": 85 }, { "id": 149, "slug": "economic-theory", "name": "Economic theory and empirical puzzles", "discipline": "economics", "blurb": "Models of decisions and economic observations that challenge them.", "sortOrder": 86 } ]