The following list of 800 math subjects grew out of my embedding space research regarding proximity of mathematical texts in LLMs.
I discussed that research in a youtube video talk here:
- Axioms
- Naive set theory
- Set theory
- Axiomatic set theory
- Zermelo-Fraenkel set theory
- ZFC
- Axiom of choice
- Set operations
- Relations
- Equivalence relations
- Functions
- Families of sets
- Infinity
- Ordinal numbers
- Ordinal arithmetic
- Cardinal numbers
- Cardinal arithmetic
- Continuum hypothesis
- Large cardinals
- Forcing
- Descriptive set theory
- Well-foundedness
- Order theory
- Partial orders
- Well-orders
- Lattice theory
- Boolean algebra
- Formal languages
- Syntax
- Semantics
- Logical connectives
- Inference
- Logical consequence
- Classical logic
- Propositional logic
- Predicate logic
- First-order logic
- Second-order logic
- Higher-order logic
- Mathematical logic
- Logical calculi
- Natural deduction
- Sequent calculus
- Tableau methods
- Completeness theorem
- Compactness theorem
- Löwenheim-Skolem theorem
- Proof theory
- Model theory
- Formal theories of arithmetic
- Peano arithmetic
- Gödel incompleteness theorems
- Induction
- Rewriting systems
- Lambda calculus
- Type theory
- Dependent type theory
- Homotopy type theory
- Curry-Howard correspondence
- Constructivism
- Intuitionism
- Non-classical logic
- Many-valued logic
- Paraconsistent logic
- Relevance logic
- Substructural logic
- Modal logic
- Temporal logic
- Linear logic
- Fuzzy logic
- Term logic
- Provability logic
- Proof complexity
- Logical paradoxes
- Program logic
- Automated theorem proving
- Proof assistants
- Theory of computation
- Models of computation
- Turing machines
- Lambda calculus models of computation
- Register machines
- Finite automata
- Pushdown automata
- Automata theory
- Formal grammars
- Regular languages
- Context-free languages
- Computability theory
- Recursion theory
- Computable functions
- Computably enumerable sets
- Turing degrees
- Decidability
- Undecidability
- Halting problem
- Limits of computation
- Complete problems
- Computational complexity theory
- Complexity classes
- P versus NP problem
- NP-completeness
- PSPACE
- Circuit complexity
- Randomized complexity
- Quantum complexity theory
- Communication complexity
- Descriptive complexity
- Computational hardness
- Kolmogorov complexity
- Algorithmic randomness
- Logic in computer science
- Logic programming
- Logic gates
- Transition systems
- Process calculi
- Concurrency theory
- Type systems
- Semantics of programming languages
- Discrete mathematics
- Combinatorics
- Enumerative combinatorics
- Generating functions
- Combinatorial species
- Permutations
- Combinations
- Binomial coefficients
- Integer partitions
- Young tableaux
- Recurrence relations
- Finite differences
- Extremal combinatorics
- Probabilistic combinatorics
- Algebraic combinatorics
- Analytic combinatorics
- Additive combinatorics
- Design theory
- Block designs
- Finite incidence structures
- Latin squares
- Packing problems
- Discrete geometry
- Matroid theory
- Posets
- Graph theory
- Trees
- Directed graphs
- Planar graphs
- Graph families
- Graph distance
- Graph connectivity
- Graph coloring
- Graph minors
- Graph minor theory
- Extremal graph theory
- Random graphs
- Spectral graph theory
- Algebraic graph theory
- Geometric graph theory
- Graph embeddings
- Graph isomorphism
- Ramsey theory
- Network theory
- Elementary arithmetic
- Natural numbers
- Integers
- Rational numbers and fractions
- Irrational numbers
- Congruences
- Modular arithmetic
- Prime numbers
- Square numbers
- Fibonacci numbers
- Arithmetic progressions
- Arithmetic functions
- Integer sequences
- Elementary number theory
- Number theory
- Sieve methods
- Sieve theory
- Integer factorization
- Primality testing
- Continued fractions
- Diophantine equations
- Diophantine approximation
- Quadratic forms
- Cyclotomic polynomials
- Fermat's Last Theorem
- Geometry of numbers
- Transcendental numbers
- p-adic numbers
- Local fields
- Global fields
- Adeles and ideles
- Valuation theory
- Algebraic number theory
- Class field theory
- Analytic number theory
- Prime number theorem
- Zeta functions
- L-functions
- Modular forms
- Automorphic forms
- Arithmetic combinatorics
- Computational number theory
- Algorithms for π
- Geometry
- Points
- Lines
- Angles
- Circles
- Curves
- Spirals
- Surfaces
- Coordinate geometry
- Plane geometry
- Solid geometry
- Euclidean geometry
- Euclidean constructions
- Classical geometry
- Elementary geometry
- Synthetic geometry
- Transformation geometry
- Trigonometry
- Spherical trigonometry
- Trigonometric functions
- Geometric configurations
- Polyhedra
- Polytopes
- Tessellations
- Honeycombs
- Finite geometry
- Affine geometry
- Projective geometry
- Analytic geometry
- Convex geometry
- Metric geometry
- Incidence geometry
- Hyperbolic geometry
- Spherical geometry
- Inversive geometry
- Conformal geometry
- Klein geometry
- Integral geometry
- Geometric measure theory
- Manifold theory
- Differential manifolds
- Differential geometry
- Curves and surfaces
- Riemannian geometry
- Pseudo-Riemannian geometry
- Lorentzian geometry
- Symplectic geometry
- Contact geometry
- Finsler geometry
- Sub-Riemannian geometry
- Complex geometry
- Kähler geometry
- Poisson geometry
- Cartan geometry
- Discrete differential geometry
- Integration on manifolds
- Diffeomorphisms
- Multidimensional geometry
- Four-dimensional geometry
- Systolic geometry
- Foundations of geometry
- Fractals
- Fractal geometry
- Mathematical morphology
- Digital geometry
- Morse theory
- Map projections
- Linear algebra
- Vector spaces
- Subspaces
- Linear combinations
- Span
- Linear independence
- Bases
- Dimension
- Linear maps
- Kernels and images
- Rank
- Systems of linear equations
- Matrices
- Matrix theory
- Matrix decompositions
- Gaussian elimination
- Determinants
- Trace
- Eigenvalues and eigenvectors
- Diagonalization
- Jordan normal form
- Canonical forms
- Inner product spaces
- Orthogonality
- Projections
- Spectral theorem
- Bilinear forms
- Sesquilinear forms
- Multilinear algebra
- Multilinear maps
- Tensors
- Tensor algebra
- Exterior algebra
- Symmetric algebra
- Clifford algebras
- Hilbert spaces
- Elementary algebra
- Abstract algebra
- Algebraic structures
- Universal algebra
- Algebras
- Algebraic properties of elements
- Morphisms
- Isomorphism theorems
- Semigroup theory
- Monoid theory
- Group theory
- Group actions
- Permutation groups
- Subgroups
- Finite groups
- Finite group theory
- Nilpotent groups
- Solvable groups
- Topological groups
- Lie groups
- Quaternions
- Ring theory
- Ideals
- Noetherian rings
- Local rings
- Dedekind domains
- Commutative algebra
- Module theory
- Exact sequences
- Projective modules
- Injective modules
- Field theory
- Field extensions
- Finite fields
- Galois theory
- Polynomial algebra
- Non-associative algebra
- Associative algebras
- Composition algebras
- Lie algebras
- Algebraic groups
- Algebraic homogeneous spaces
- Bialgebras
- Hopf algebras
- Diagram algebras
- Ockham algebras
- Relational algebra
- Computational algebra
- Computer algebra
- Representation theory
- Invariant theory
- Duality theories
- Geometric algebra
- Spinors
- Fréchet algebras
- Banach algebras
- C*-algebras
- Von Neumann algebras
- Category theory
- Categories
- Functors
- Natural transformations
- Limits and colimits
- Adjunctions
- Yoneda lemma
- Monads
- Monoidal categories
- Enriched categories
- Abelian categories
- Derived categories
- Triangulated categories
- Higher category theory
- Topos theory
- Homological algebra
- Chain complexes
- Homology
- Cohomology
- Spectral sequences
- Sheaf cohomology
- Group cohomology
- K-theory
- Real numbers
- Calculus
- Sequences and series
- Power series
- Derivatives
- Integrals and integration
- Integration theory
- Lebesgue integration
- Exponential and logarithmic functions
- Special functions
- Gamma functions
- Mathematical analysis
- Real analysis
- Metric spaces
- Normed vector spaces
- Topological vector spaces
- Locally convex spaces
- Measure theory
- Measure spaces
- Functional equations
- Inequalities
- Smooth functions
- Lipschitz maps
- Ordinary differential equations
- Partial differential equations
- Differential equations
- Boundary value problems
- Initial value problems
- Elliptic partial differential equations
- Parabolic partial differential equations
- Hyperbolic partial differential equations
- Differentiable structures
- Differential forms
- Complex analysis
- Riemann surfaces
- Several complex variables
- Fourier series
- Fourier analysis
- Fourier transform
- Laplace transform
- Harmonic analysis
- Functional analysis
- Banach spaces
- Hilbert space methods
- Sobolev spaces
- Distribution theory
- Generalized functions
- Operator theory
- Functional calculus
- Spectral theory
- Approximation theory
- Fixed point theory
- Convex analysis
- Calculus of variations
- Variational analysis
- Geometric analysis
- Asymptotic analysis
- Asymptotic geometric analysis
- Summability theory
- Tauberian theorems
- Potential theory
- Integral equations
- Dynamical systems
- Nonlinear systems
- Optimal transport
- Limit sets
- Stability theory
- Perturbation theory
- Ergodic theory
- Chaos theory
- Chaotic maps
- Bifurcation theory
- Control theory
- Wavelets
- Microlocal analysis
- Algebraic analysis
- Nonstandard analysis
- Fractional calculus
- Topology
- General topology
- Point-set topology
- Topological spaces
- Open and closed sets
- Continuity
- Homeomorphisms
- Compactness
- Connectedness
- Separation axioms
- Product topology
- Quotient topology
- Compact-open topology
- Nets and filters
- Manifolds
- Topological manifolds
- Differential topology
- Geometric topology
- Low-dimensional topology
- Knot theory
- Vector bundles
- Fiber bundles
- Covering spaces
- Fundamental group
- CW complexes
- Simplicial complexes
- Homotopy theory
- Algebraic topology
- Homology theory
- Cohomology theory
- Characteristic classes
- Cobordism theory
- Sheaf theory
- Surgery theory
- Events
- Probability theory
- Measure-theoretic probability
- Random variables
- Probability distributions
- Conditional probability
- Conditional expectation
- Independence
- Randomness
- Expected value
- Means
- Moments
- Covariance
- Correlation
- Statistical deviation and dispersion
- Law of large numbers
- Central limit theorem
- Limit theorems
- Probabilistic methods
- Random walks
- Markov chains
- Markov processes
- Martingales
- Branching processes
- Brownian motion
- Stochastic processes
- Stochastic calculus
- Stochastic differential equations
- Large deviations theory
- Percolation theory
- Queueing theory
- Monte Carlo methods
- Markov chain Monte Carlo
- Probability paradoxes
- Statistics
- Statistical inference
- Sampling theory
- Point estimation
- Estimation theory
- Confidence intervals
- Hypothesis testing
- Likelihood theory
- Maximum likelihood estimation
- Sufficiency
- Exponential families
- Least squares
- Linear models
- Generalized linear models
- Mixed models
- Regression analysis
- Analysis of variance
- Multivariate statistics
- Nonparametric statistics
- Robust statistics
- Bayesian statistics
- Bayesian inference
- Decision theory
- Causal inference
- Survival analysis
- Econometrics
- Spatial statistics
- Resampling methods
- Bootstrap methods
- Statistical approximations
- Statistical algorithms
- Time series
- Time-series models
- Design of experiments
- Information geometry
- Mathematical optimization
- Optimization theory
- Convex optimization
- Nonlinear programming
- Integer programming
- Combinatorial optimization
- Stochastic optimization
- Variational methods
- Optimal control
- Operations research
- Linear programming
- Network optimization
- Scheduling theory
- Decision analysis
- Game theory
- Mechanism design
- Choice theory
- Social choice theory
- Public choice theory
- Algorithms
- Algorithms and data structures
- Analysis of algorithms
- Data structures
- Computer arithmetic
- Positional numeral systems
- Binary arithmetic
- Hexadecimal numeral system
- Linked lists
- Stacks and queues
- Heaps
- Hash tables
- Search algorithms
- Sorting algorithms
- Selection algorithms
- Parsing algorithms
- Pattern matching
- String matching algorithms
- Algorithms on strings
- String metrics
- Divide-and-conquer algorithms
- Greedy algorithms
- Dynamic programming
- Approximation algorithms
- Randomized algorithms
- Probabilistic algorithms
- Heuristic algorithms
- Optimization algorithms
- Automatic differentiation
- Numerical analysis
- Numerical linear algebra
- Numerical optimization
- Root-finding algorithms
- Interpolation
- Numerical integration
- Finite difference methods
- Finite volume methods
- Finite element method
- Spectral methods
- Numerical methods for partial differential equations
- Fast Fourier transform algorithms
- Graph algorithms
- Computational geometry
- Geometric algorithms
- Geometry processing
- Convex hull algorithms
- Voronoi diagrams
- Delaunay triangulations
- Triangulation algorithms
- Polygon clipping algorithms
- Number-theoretic algorithms
- Symbolic computation
- Classification algorithms
- Streaming algorithms
- Online algorithms
- Distributed algorithms
- Scheduling algorithms
- Analysis of parallel algorithms
- Quantum algorithms
- Travelling salesman problem
- Information theory
- Entropy
- Mutual information
- Conditional entropy
- Kullback-Leibler divergence
- Shannon theory
- Source coding
- Channel coding
- Coding theory
- Error detection
- Error-correcting codes
- Block codes
- Convolutional codes
- Algebraic coding theory
- Checksum algorithms
- Data compression
- Signal processing
- Signal estimation
- Filter frequency response
- Nonlinear filters
- Image processing
- Cryptography
- Hash functions
- Pseudorandomness
- Symmetric-key cryptography
- Public-key cryptography
- Encryption
- Ciphers
- Asymmetric-key algorithms
- Elliptic-curve cryptography
- Lattice-based cryptography
- Post-quantum cryptography
- Zero-knowledge proofs
- Secure multiparty computation
- Secret sharing
- Encryption standards
- Differential privacy
- Algebraic geometry
- Algebraic sets
- Algebraic varieties
- Affine varieties
- Projective varieties
- Algebraic curves
- Algebraic surfaces
- Schemes
- Scheme theory
- Sheaves in algebraic geometry
- Geometry of divisors
- Intersection theory
- Étale cohomology
- Motives
- Elliptic curves
- Abelian varieties
- Arithmetic geometry
- Toric geometry
- Tropical geometry
- Moduli spaces
- Stacks
- Deformation theory
- Birational geometry
- Rational varieties
- Singularities
- Resolution of singularities
- Real algebraic geometry
- Complex algebraic geometry
- Enumerative geometry
- Noncommutative geometry
- Derived algebraic geometry
- Classical mechanics
- Rigid body mechanics
- Lagrangian mechanics
- Hamiltonian mechanics
- Geometric mechanics
- Symplectic mechanics
- Noether's theorem
- Conservation laws
- Conservation equations
- Fluid mechanics
- Fluid dynamics
- Continuum mechanics
- Kinetic theory
- Thermodynamic equations
- Equations of state
- Statistical mechanics
- Electromagnetism
- Maxwell equations
- Special relativity
- General relativity
- Spacetime geometry
- Theories of gravitation
- Quantum mechanics
- Mathematical quantization
- Operator algebras in quantum theory
- Scattering theory
- Gauge theory
- Quantum field theory
- Conformal field theory
- Integrable systems
- Solitons
- Quantum gravity
- String theory
- Applied mathematics
- Mathematical modeling
- Computational science
- Simulation
- Inverse problems
- Parameter estimation
- Systems theory
- Complex systems theory
- Network science
- Population models
- Mathematical epidemiology
- Mathematical ecology
- Evolutionary computation
- Computational phylogenetics
- Bioinformatics
- Mathematical biology
- Mathematical chemistry
- Molecular geometry
- Crystallography
- Computational neuroscience
- Financial mathematics
- Actuarial mathematics
- Mathematical economics
- Belief revision
- Data analysis
- Machine learning
- Statistical learning theory
- Supervised learning
- Unsupervised learning
- Reinforcement learning
- Regression algorithms
- Cluster analysis
- Dimensionality reduction
- Principal component analysis
- Kernel methods
- Support vector machines
- Gaussian processes
- Graphical models
- Bayesian networks
- Decision trees
- Random forests
- Ensemble methods
- Neural networks
- Deep learning
- Representation learning
- Optimization in machine learning
- Data mining algorithms
- Evolutionary algorithms
- Genetic algorithms