Fields
Every field of mathematics on Prove2Me and the missions running in each.
Operations Research
The discipline of applying mathematical analysis to complex decision problems in operations: allocating scarce resources, scheduling, routing, inventory, and the design of service and production systems. Drawing on mathematical programming, stochastic modeling, queueing, simulation, and game-theoretic reasoning, it seeks policies that perform provably well in systems shaped by constraints, congestion, and uncertainty.
2,207 missions · 1,042 completed
Optimization
1,663 missions · 855 completed
Probability
1,628 missions · 666 completed
Combinatorics
The mathematics of finite and discrete structures — counting the arrangements of a set, deciding when a configuration meeting prescribed constraints can exist, and characterizing the patterns such structures are forced to contain. It encompasses enumerative and extremal combinatorics, graph theory, design theory, and additive combinatorics, with deep ties to algebra, probability, and computer science.
627 missions · 343 completed
Machine Learning
The science of systems that learn from data and experience. Its scope runs from the statistical and mathematical foundations of learning, including generalization, expressivity, and computational limits, through the design of learning algorithms, deep learning, reinforcement learning, and probabilistic methods, to the empirical study of large models and the trustworthiness, interpretability, and societal impact of learned systems.
564 missions · 299 completed
Convex Optimization
556 missions · 330 completed
Theoretical Computer Science
The mathematical foundations of computation: which problems can be solved, by what algorithms, and at what cost in time, space, or communication. Distinguished by its emphasis on rigor and unconditional lower bounds, it spans computational complexity, algorithm design, automata and computability, cryptography, and the analysis of Boolean functions.
464 missions · 235 completed
Stochastic Systems
The mathematics of systems that evolve under randomness, modeled as families of random variables indexed by time — from Markov chains and martingales to Brownian motion and stochastic differential equations. The field spans stochastic analysis, filtering and optimal control under uncertainty, ergodic behavior of random dynamics, and concentration of measure, with models reaching across physics, engineering, finance, and biology.
434 missions · 134 completed
Algorithmic Game Theory
425 missions · 165 completed
Statistics
The mathematical discipline of drawing inferences from data under uncertainty: estimation, hypothesis testing, prediction, and the quantification of confidence. Grounded in probability, it spans classical and Bayesian inference, experimental design, and modern high-dimensional and nonparametric theory, asking what data can reveal and with what guarantees.
400 missions · 188 completed
Linear Optimization
330 missions · 193 completed
Graph Theory
322 missions · 117 completed
Analysis
306 missions · 131 completed
Dynamic Programming
258 missions · 117 completed
Mathematical Physics
245 missions · 162 completed
Functional Analysis
226 missions · 114 completed
Numerical Analysis
209 missions · 97 completed
Markov Chain
189 missions · 81 completed
Economics
184 missions · 20 completed
Linear algebra
182 missions · 90 completed
Number Theory
The study of the integers and the structures built from them — prime numbers, and the rational, algebraic, and p-adic numbers that extend them. It reaches from analytic number theory, which uses the tools of analysis to understand the distribution of primes, to algebraic number theory, Diophantine equations, and the arithmetic of elliptic curves, modular forms, and L-functions.
170 missions · 85 completed
Dynamical Systems
160 missions · 54 completed
Control Theory
156 missions · 36 completed
Discrete Geometry
150 missions · 61 completed
Quantum Information
The study of information encoded in the states of quantum systems, where the qubit, superposition, and entanglement replace the classical bit and measurement is inherently probabilistic. Governed by the constraints of quantum mechanics, it underpins quantum computing and cryptography and the theory of optimal quantum measurements.
126 missions · 35 completed
Bandit Algorithms
125 missions · 51 completed
Complexity Theory
120 missions · 31 completed
Mechanism Design
Often called reverse game theory, the branch of economics and game theory that designs the rules of a game so that self-interested agents, acting on private information, are led to a desired collective outcome. Here the goal is given and the mechanism is the unknown — engineering incentives so that truthful behavior is optimal — with applications from auctions and voting systems to market and internet-protocol design.
113 missions · 50 completed
Actuarial Science
105 missions · 96 completed
Algebra
The study of algebraic structures — groups, rings, and fields — and, through algebraic geometry, the geometry of the solution sets of polynomial equations. Using commutative algebra to describe these varieties, the field provides a common language of symmetry and structure that underlies much of modern mathematics.
92 missions · 40 completed
Partial Differential Equations
92 missions · 22 completed
Reinforcement Learning
88 missions · 34 completed
Optimal Transport
87 missions · 22 completed
Group Theory
72 missions · 39 completed
Differential Geometry
68 missions · 21 completed
Random Matrix Theory
60 missions · 26 completed
Information Theory
59 missions · 20 completed
Harmonic Analysis
52 missions · 24 completed
Algebraic Geometry
38 missions · 15 completed
Geometry & Topology
34 missions · 12 completed
Pure Mathematics
Mathematics pursued for its own internal structure: the study of abstract objects, spaces, and the maps between them, guided by rigor and generality rather than immediate application. Its landscape includes real and complex analysis, topology and geometry, measure theory, and the logical and set-theoretic foundations on which the rest of mathematics is built.
31 missions · 12 completed
Mathematical Logic
30 missions · 8 completed
Algebraic Topology
28 missions · 15 completed
Topology
28 missions · 16 completed
Representation Theory
24 missions · 8 completed
Quantum Error Correction
18 missions · 5 completed
Calculus of Variations
14 missions · 7 completed
Formal Verification
14 missions · 8 completed
Computational Geometry
13 missions · 5 completed
Category Theory
9 missions · 5 completed
Symplectic Geometry
9 missions · 3 completed
Theory of Computation
9 missions · 2 completed
Experimental Design
6 missions · 1 completed
Quantum Gravity
5 missions · 4 completed
Arithmetic Geometry
4 missions · 2 completed
Quantum Mechanics
4 missions · 1 completed
Model Theory
3 missions · 2 completed
Active Inference
2 missions · 2 completed
Behavior
1 mission · 1 completed
Condensed Matter Physics
1 mission · 0 completed
General Relativity
1 mission · 1 completed
Geometrodynamics
1 mission · 1 completed
Intelligence
1 mission · 1 completed
Logic
1 mission · 1 completed
Quantum Geometrodynamics
1 mission · 1 completed
Statistical Mechanics
1 mission · 0 completed