Interactive Timeline of Mathematical Discoveries

Pythagorean Theorem

~500 BCE - The theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

Babylonian Base-60 System

~1900 BCE - An early numeral system influencing time and angle measurements.

Euclid’s Elements

~300 BCE - Euclid’s foundational work that laid the principles of geometry.

Chinese Remainder Theorem

~3rd Century BCE - A number theory theorem essential for modular arithmetic.

Aryabhata’s Approximation of Pi

499 CE - Indian mathematician Aryabhata calculated pi as approximately 3.1416.

Islamic Golden Age Algebra

~800 CE - Al-Khwarizmi’s work on algebra introduced systematic solutions for equations.

Fibonacci Sequence

~1202 - A sequence where each number is the sum of the previous two, found in nature.

Pascal’s Triangle

~1653 - Organizes binomial coefficients in a triangular format, useful in probability.

Descartes’ Cartesian Geometry

1637 - Descartes’ coordinate system bridging algebra and geometry.

Newton’s Laws of Motion

1687 - Newton’s laws laid the foundation for classical mechanics.

Bernoulli’s Principle

1738 - Describes the relationship between fluid speed and pressure.

Euler’s Identity

~1748 - Links fundamental mathematical constants in a single equation.

Gaussian Elimination

1798 - A systematic method for solving systems of linear equations.

Non-Euclidean Geometry

19th Century - A geometry diverging from Euclid’s parallel postulate.

Complex Numbers

16th-18th Century - Numbers with real and imaginary components.

Prime Number Theorem

1896 - Describes the distribution of prime numbers.

Group Theory

19th Century - Studies algebraic structures fundamental to modern mathematics.

Boolean Algebra

1854 - George Boole’s work laid the foundation for digital logic.

Matrix Algebra

19th-20th Century - A mathematical framework essential for data analysis and transformations.

Game Theory

20th Century - Studies strategic decision-making in competitive and cooperative settings.

Functional Analysis

20th Century - Studies functions and transformations foundational to quantum mechanics.

Turing Machine

1936 - Alan Turing’s theoretical machine model laid the foundation for computer science.

RSA Cryptography

1977 - Uses large prime numbers to secure digital communication.

Chaos Theory

20th Century - Studies complex systems and their inherent unpredictability.

Quantum Mechanics

20th Century - A fundamental theory explaining particle behaviors at atomic scales.

Fractal Geometry

1970s - A field exploring self-repeating patterns in nature and mathematics.

Linear Programming

20th Century - Optimization technique to maximize or minimize a linear objective.

Category Theory

1940s - A branch linking structures across mathematics.

Differential Geometry

19th-20th Century - Integrates calculus with geometry, vital in physics.

Cryptographic Hash Functions

20th Century - Functions for secure data integrity in digital systems.

Fourier Transform

19th-20th Century - Decomposes functions into frequencies, used in signal processing.

Machine Learning

20th-21st Century - Algorithms that enable computers to learn from data.

Homology Theory

20th Century - Studies topological spaces and transformations.

Wavelet Theory

20th Century - Analyzes signals and data at various scales.

Elliptic Curves in Cryptography

20th Century - Used for secure communication in modern cryptography.

Automata Theory

20th Century - Studies abstract machines and computational problems.

Ergodic Theory

20th Century - Studies statistical properties of dynamic systems.

Lie Groups

19th-20th Century - Studies continuous symmetry, with applications in physics.

Representation Theory

20th Century - Studies abstract algebraic structures as linear transformations.

Mathematical Logic

20th Century - Studies the formal foundations of mathematics and computation.

Bayesian Inference

18th-20th Century - Uses probabilities to update beliefs with new data.

Number Theory Applications in Cryptography

20th Century - Secures digital communication using prime numbers.

Set Theory

Late 19th Century - Studies collections of objects, foundational in modern mathematics.

Probability Theory

1654 - Studies randomness and underpins statistical science.

Calculus

17th Century - Studies change and motion, fundamental in science and engineering.

Algebraic Structures

19th Century - Studies groups, rings, and fields in abstract algebra.

Topology

19th Century - Studies properties of space preserved under continuous transformations.

Artificial Intelligence and Machine Learning Applications

20th-21st Century - Algorithms that enable systems to learn and make decisions.