Fields

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.

41 missions · 40 completed

Optimization

20 missions · 20 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.

19 missions · 19 completed

Bandit Algorithms

16 missions · 16 completed

Linear Optimization

13 missions · 13 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.

11 missions · 2 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.

7 missions · 4 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.

6 missions · 6 completed

Convex Optimization

6 missions · 6 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.

6 missions · 6 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.

5 missions · 3 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.

3 missions · 2 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.

3 missions · 2 completed

Graph Theory

2 missions · 2 completed

Probability

2 missions · 0 completed

Computational Geometry

1 mission · 1 completed

Markov Chain

1 mission · 0 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.

1 mission · 1 completed

Optimal Transport

1 mission · 1 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.

1 mission · 1 completed