21st-Century Mathematics

Chaos theory is a mathematical theory that studies the behavior of complex systems that are highly sensitive to initial conditions.

A fractal is a mathematical object that exhibits self-similarity, meaning that it has the same pattern at different scales.

Graph theory is a mathematical theory that studies the structure and properties of networks, which are collections of nodes and edges.

Quantum mechanics is a mathematical theory that studies the behavior of quantum systems, which are systems that exhibit wave-particle duality and quantization of energy.

Number theory is a mathematical theory that studies the properties of prime numbers and other integers.

Differential geometry is a mathematical theory that studies the properties of smooth manifolds, which are spaces that are locally Euclidean.

Topology is a mathematical theory that studies the properties of topological spaces, which are sets of points that are equipped with a notion of closeness.

Analysis is a mathematical theory that studies the properties of functions, limits, derivatives, and integrals.

Algebra is a mathematical theory that studies the properties of algebraic structures, such as groups, rings, and fields.

Geometry is a mathematical theory that studies the properties of geometric objects, such as points, lines, and planes.

Probability theory is a mathematical theory that studies the properties of probability distributions, which are functions that assign probabilities to events.

Statistics is a mathematical theory that studies the properties of statistical data, which is data that is collected from a population.

Bayesian inference is a mathematical theory that studies the properties of Bayesian inference, which is a method of statistical inference that uses Bayes' theorem to update beliefs in the light of new evidence.

Machine learning is a mathematical theory that studies the properties of machine learning algorithms, which are algorithms that can learn from data.

Optimization theory is a mathematical theory that studies the properties of optimization problems, which are problems of finding the best solution to a given problem.