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Statement (48)
- Abhyankar's two points at infinity proved · V3
- Alpöge's map
- The cubic reduction of Bass–Connell–Wright and Yagzhev proved · V3
- Campbell's theorem: Galois Keller maps are automorphisms proved · V3
- Cubic-homogeneous counterexamples
- The Jacobian conjecture for cubic-homogeneous maps refuted · V3
- The symmetric reduction proved · V3
- The degree spectrum of ℂ³ proved · V4
- DC₁: Dixmier's problem for the first Weyl algebra open
- DC₂: the Dixmier conjecture for the second Weyl algebra open
- The Dixmier conjecture in rank n refuted · V3
- Drużkowski's reduction to cubic-linear maps proved · V3
- Is torus symmetry forced? (O5) open
- Generators of the étale monoid of ℂ³ (O1) refuted · V4
- The formal inverse and its tree formula proved · V3
- Gallagher's family
- The Gaussian moments conjecture refuted · V0
- The generalized vanishing conjecture refuted · V3
- Graded Keller maps proved · V4
- Gradient counterexamples
- Harish's map of ℂ⁴
- The Hessian conjecture in dimension n refuted · V1
- HC₄: the Hessian conjecture in four variables open
- The image conjecture refuted · V3
- JC₃: the Jacobian conjecture in dimension three refuted · V0
- The Jacobian conjecture in dimension n refuted · V0
- JC₂: the Jacobian conjecture in the plane open
- The non-properness set proved · V3
- Jung–van der Kulk: automorphisms of the plane are tame proved · V3
- Keller's birational theorem proved · V3
- Xavier's dichotomy for the Keller locus proved · V4
- The master equation proved · V4
- The Mathieu conjecture refuted · V3
- Meng–Yang's five-variable potential Ψ
- Moh's theorem: no plane counterexample of degree ≤ 100 proved · V3
- Pinchuk's non-injective local diffeomorphisms of the plane
- Degree and gcd constraints on a plane counterexample proved · V3
- The Poisson conjecture in rank n refuted · V3
- No plane Keller map has prime field degree proved · V4
- For a Keller map, invertible, injective and proper are the same proved · V3
- The real Jacobian question in dimension n refuted · V0
- Are there native counterexamples in higher dimensions? open
- The strong real Jacobian conjecture refuted · V3
- Tangent sweeps proved · V4
- The stable equivalence of the Jacobian and Dixmier conjectures proved · V3
- Wang's theorem: quadratic Keller maps are invertible proved · V3
- Zhao's vanishing conjecture refuted · V3
- Zyskind's factory
Problem (176)
- abc conjecture open
- The age of the Earth solved · V3
- The causes of aging open
- AI alignment open
- Alzheimer's disease partial
- Ammonia at ambient conditions open
- Atlantic overturning circulation tipping point open
- Antimicrobial resistance open
- ARC-AGI open
- A fair voting rule refuted · V3
- The arrow of time open
- Artificial photosynthesis open
- Autonomous driving partial
- Matter–antimatter asymmetry open
- Local realism (Bell's theorem) refuted · V3
- The structure of benzene solved · V3
- Bieberbach conjecture solved · V3
- Big Bang or steady state solved · V3
- Birch and Swinnerton-Dyer conjecture open
- Imaging a black hole solved · V3
- Black hole information paradox partial
- Boolean Pythagorean triples problem solved · V3
- Bounded gaps between primes solved · V3
- Is language localized in the brain? solved · V3
- Burnside problem refuted · V3
- Busy Beaver BB(5) solved · V3
- Busy Beaver BB(6) open
- The Cambrian explosion open
- Cancer partial
- Carbon removal at gigaton scale open
- Catalan's conjecture solved · V3
- Reversing cell differentiation solved · V3
- Chronic pain open
- Classification of finite simple groups solved · V3
- Equilibrium climate sensitivity partial
- Collatz conjecture open
- Cooperation on global commons open
- The complete human genome solved · V3
- Complete brain wiring diagrams partial
- Continuum hypothesis independent · V3
- Cosmic inflation partial
- What dark energy is open
- What dark matter is open
- What killed the dinosaurs solved · V3
- Early supermassive black holes open
- Earthquake prediction open
- Egyptian hieroglyphs solved · V3
- Einstein problem (aperiodic monotile) solved · V3
- The origin of complex cells partial
- Planets around other stars solved · V3
- Is the universe expanding? solved · V3
- Fault-tolerant quantum computing partial
- Fermat's Last Theorem solved · V3
- The Fermi paradox open
- Four color theorem solved · V3
- Free will open
- What sleep is for open
- Fusion as a power plant partial
- General-purpose robots open
- Why deep networks generalize open
- Cracking the genetic code solved · V3
- The genotype–phenotype map open
- The geodynamo and magnetic reversals partial
- Geometric Langlands conjecture solved · V3
- What causes infectious disease solved · V3
- The Gettier problem open
- The nature of the glass transition open
- Goldbach's conjecture open
- Graph isomorphism complexity partial
- Direct detection of gravitational waves solved · V3
- Why some nations grow rich open
- Hadwiger–Nelson problem partial
- The hard problem of consciousness open
- Reading the Herculaneum scrolls partial
- The hierarchy problem open
- The Higgs boson solved · V3
- Mechanism of high-temperature superconductivity open
- Hilbert's second problem: consistency of arithmetic refuted · V3
- Hilbert's tenth problem refuted · V3
- A cure for HIV partial
- Hodge conjecture open
- The Hubble tension open
- The Indus script open
- Mechanistic interpretability open
- Invariant subspace problem open
- Inverse Galois problem open
- The is–ought problem open
- The island of stability open
- Jacobian conjecture, n ≥ 3 refuted · V0
- Kadison–Singer problem solved · V3
- Kahn–Kalai conjecture solved · V3
- Kakeya conjecture in three dimensions solved · V3
- Kakeya set conjecture, all dimensions open
- The Jacobian conjecture in the plane open
- Kepler conjecture solved · V3
- Langlands reciprocity (general) open
- How children learn language open
- The liar paradox partial
- Linear A open
- Linear B solved · V3
- Cheap long-duration energy storage open
- Longitude at sea solved · V3
- Can artificial systems be conscious? open
- A malaria vaccine partial
- Drawing the map of knowledge open
- The exponent of matrix multiplication open
- The measurement problem open
- How memories are stored partial
- The precession of Mercury solved · V3
- Metallic hydrogen open
- MLC: the Mandelbrot set is locally connected open
- Modularity theorem solved · V3
- Molyneux's problem partial
- Moving sofa problem partial
- How species arise solved · V3
- Navier–Stokes existence and smoothness open
- Neural correlates of consciousness open
- The neuron doctrine solved · V3
- Neutrino masses partial
- Newcomb's problem open
- Fixing nitrogen from the air solved · V3
- Existence of one-way functions open
- The origin of language open
- The origin of life open
- Where Earth's water came from open
- The ozone hole solved · V3
- P versus NP open
- What causes stomach ulcers solved · V3
- The order of the elements solved · V3
- Continental drift solved · V3
- Poincaré conjecture solved · V3
- Polio eradication partial
- Post-quantum cryptography partial
- Heavier-than-air powered flight solved · V3
- PRIMES is in P solved · V3
- The problem of induction open
- The productivity slowdown open
- Designing proteins with arbitrary function partial
- Protein structure prediction solved · V3
- A quantum theory of gravity open
- Solving the quintic by radicals refuted · V3
- Ramsey number R(5,5) open
- Limb regeneration open
- Resolution of singularities in characteristic p open
- Reusable orbital rockets solved · V3
- Riemann hypothesis open
- Room-temperature, ambient-pressure superconductor open
- Sato–Tate conjecture solved · V3
- Scurvy solved · V3
- Sensitivity conjecture solved · V3
- Smallpox eradication solved · V3
- Smooth 4-dimensional Poincaré conjecture open
- Snowball Earth partial
- The solar neutrino problem solved · V3
- Selling the airwaves solved · V3
- Sphere packing in dimensions 8 and 24 solved · V3
- Spontaneous generation refuted · V3
- Squaring the circle refuted · V3
- The strong CP problem open
- The structure of DNA solved · V3
- High-efficiency thermophotovoltaics open
- The three-body problem refuted · V3
- A solid-state amplifier solved · V3
- Turbulence open
- Can machines think? (the imitation game) partial
- Twin prime conjecture open
- The ultraviolet catastrophe solved · V3
- Union-closed sets conjecture partial
- The sorites paradox open
- The Voynich manuscript open
- Weak Goldbach conjecture solved · V3
- Weil conjectures solved · V3
- Whitehead problem independent · V3
- Why there is something rather than nothing open
- Yang–Mills existence and mass gap open
- Zeno's paradoxes of motion partial
Space (45)
- Algebra and groups
- Algebraic geometry
- Algorithms
- Analysis and PDE
- Chronic disease
- Climate
- Collective choice
- Combinatorics
- Complexity classes
- Computing hardware
- Consciousness
- Cryptography
- The dark sector
- The deep Earth
- Development and aging
- Dynamical systems
- Early Earth
- Wealth and growth
- Energy
- Energy and catalysis
- Geometry and topology
- Gravity and the quantum
- Heredity and the code
- Infectious disease
- Knowledge
- The Langlands program
- Language
- Learning and AI
- Life beyond Earth
- Logic and foundations
- Machine minds
- Machines that move
- Materials
- Fluids and many bodies
- Being and self
- Molecules of life
- The brain
- Number theory
- Origins of the universe
- Origins
- Quantum foundations
- Scripts and the past
- The Standard Model's loose ends
- Stars and black holes
- Value and reason
Continent (12)
- Chemistry and matter
- Computation
- Cosmos
- Earth
- Engineering
- Life
- Mathematics
- Medicine
- Mind
- Philosophy
- Physics
- Society