Maths Research Through Time – A Timeline of Significant Mathematical Advances
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.
