3400 BC – Sumerian clay characters for counting
3000 BC – Hieroglyphic numerals in Egypt
2700 BC – Egyptians use Pythagorean triangle to measure right angle
2000 BC – Pythagorean theorem recorded in several cultures
2000 BC – The Babylonians introduced the system of the sixties (still valid for counting time and angles)
1300 BC – the first quadratic equation on the „Berlin Papyrus“ from Egypt
1000 BC – Fragments are used in ancient Egypt
518 BC – Pythagoreans – description and proof of the theorem on a right triangle
1. The crisis of mathematics – ignorance of irrational numbers – solved by the geometrization of mathematics
360 BC – Plato – Platonic solids – proof that there are only 5 regular polyhedra
350 BC – Aristotle of Strageira – defines logical argumentation, thanks to which mathematical proofs are created
300 BC – Euclid of Alexandria – described all known mathematics, Euclidean geometry
240 BC – Eratosthenes – Measured the size of the Earth using geometry
230 BC – Archimedes of Syracuse – approximates the number Pi using the method of polygons inside a circle
225 BC – Apollonios – described conic sections and curves
50 BC – In India laid the foundations of a decimal system with nine digits
46 BC – Julian calendar (365 days instead of 446 ☺)
100 n.l. – Heron of Alexandria – mentions imaginary numbers for the first time
After the end of antiquity in Europe, mathematics declined and the golden age of the Arab world began
595 – Indo-Arabic number system introduced
800 – Al-Khvarizmi Muhammad ibn Musa ibn Abdullah – describes the principle of the algorithm (functional step-by-step solution of problems) and introduces the concept of algebra
876 – Zero ranked among the numbers in India
1202 – Leonardo of Pisan called Fibonacci – Fibonacci sequence, algebra introduces symbols into mathematics
1435 – use of geometry in art – naturalistic representation of space and distance
1581 – Nonlinear equations discovered (thanks to lute string tension and pitch analysis)
1545 – Gerolamo Cardano – Cardano formulas as solutions of cubic equations (x3) and 4th degree equations (x4)
1591 – Francois Viéte – introduces x and y into algebra
1614 John Napier – develops logarithm – complex multiplication and division can be converted to simple addition and subtraction
1621 – Pierre de Fermat – Fermat’s great theorem
1622 – Logarithmic ruler as the forerunner of calculators
1629 – Albert Girard – Describes complex numbers
1636 – Pierre de Fermat and René Descartes – Fundamentals of analytical geometry
1637 – René Descartes – creates a Cartesian coordinate system
1642 – Blaise Pascal – The first extended mechanical calculator
1653 – Pacal’s triangle – a tool for finding binomial coefficients
1654 – Pascal and Fermat – Laws of probability theory – to predict the possibility of winning
1665 – Principle of induction – progression from known to unknown
1666 – Isaac Newton and Gottfried Wilhem von Leibnitz – discover the infinitesimal calculus (independently)
1703 – Gottfried Wilhem von Leibnitz – Examines in detail binary numbers as the basis of the digital revolution
1736 – Leonhard Euler – Euler’s number e and Euler’s equation – relation between basic numbers 1, e, i, and π
1788 – Joseph-Louis Lagrange – Basics of calculus of variations
1799 – Carl Johan Friedrich Gauss – basic theorem of algebra (every polynomial equation has a solution)
1799 – Gaspard Monge – establishes descriptive geometry. Describes Monge’s screening
1817 – Bernard Bolzano – dealt with mathematical analysis and formulated Bolzano’s theorem (theorem on the mean value of a function)
1820 – Augustin Louis Cauchy – Limit of function
1822 – Joseph Fourier – Fourier transform (conversion of complex waves (music, light) to simple sine waves)
1829 – Non-Euclidean geometry discovered (Gauss, Bolyai, Lobachevsky)
1831 – Évariste Galois – Foundations of group theory
1835 – Adolphe Quetelet – Defines the average person (applies mathematics to the human population)
1837 Siméon Denis Poisson – distribution of random events (eg lightning strike) Poisson distribution
1843 William Hamilton – real numbers are a subset of complex numbers, complex numbers are a subset of quaternions
1847 – Boolean Algebra – Converts everyday problems into mathematical form
1858 – Augustus Möbius – tape with one side – Möbius tape
1859 – Bernhard Riemann – Riemann hypothesis
1871 – Maxwell-Boltzman velocity distribution of molecules in a gas
1872 – Richard Dedeking – Defines irrational numbers
1873 – Georg Cantor- Set Theory (infinite number of infinite sets)
1889 – Francis Galton – Random deviations from the mean form a Gaussian curve
1900 – David Hilbert – Mathematics is to be first clearly defined and presents 23 mathematical problems for the next century.
1905 – Albert Einstein – Mathematical expression of the relationship between energy and mass
1908 – Population genetics uses the work of Řehoř Mendel for the human species
1913 – Bertrand Russell – reduction of mathematics to a set of logical principles (logical atomism)
1926 – Quantum mechanics – mathematical description of the subatomic world
1930 – Kurt Gödel – an incompleteness theorem of mathematics
1944 – Game Theory – Mathematics in competition, military strategy and politics
1948 – Binary numbers are used for data transmission
1961 – Edward Lorenz – Chaos Theory
1972 – Disaster Theory -René Thom
1972 – Benoit Mandelbrot – defines a fractal
1977 – RSA public key cipher algorithm for secure data exchange over the Internet
1987 – Self-organized critical state
1995 – Andrew Wiles – proves Fermat’s theorem
1996 – The first mathematical proof performed by a computer
2000 – The Clay Mathematical Institute publishes 7 Millennium Problems. He offers a million dollars for solving each.