Johann Gutenberg became the first in Europe to print with movable type cast in molds.

Jamestown, Virginia, is settled as what would become the first permanent English colony in North America.

Salem witch trials in Massachusetts.

American Civil War between the Union and seceding Confederacy.

The Bakhshali manuscript is written by Jaina mathematicians, which describes a theory of the infinite containing different levels of infinity, shows an understanding of indices[disambiguation needed], as well as logarithms to base 2, and computes square roots of numbers as large as a million correct to at least 11 decimal places

Aryabhata writes the “Aryabhata-Siddhanta”, which first introduces the trigonometric functions and methods of calculating their approximate numerical values. It defines the concepts of sine and cosine, and also contains the earliest tables of sine and cosine values (in 3.75-degree intervals from 0 to 90 degrees)

Law of sines is discovered by Muslim mathematicians

Leonardo Fibonacci demonstrates the utility of Hindu-Arabic numerals in his Liber Abaci (Book of the Abacus).

Luca Pacioli: first codification of the Double-entry bookkeeping system, which slowly developed in previous centuries

Gerolamo Cardano learns Tartaglia's method for solving depressed cubics and discovers a method for depressing cubics, thereby creating a method for solving all cubics.

John Napier discusses Napierian logarithms in Mirifici Logarithmorum Canonis Descriptio,

René Descartes discovers analytic geometry

First use of the term imaginary number by René Descartes; it was meant to be derogatory.

Blaise Pascal and Pierre de Fermat create the theory of probability,

Isaac Newton works on the fundamental theorem of calculus and develops his version of infinitesimal calculus,

Gottfried Leibniz develops his version of infinitesimal calculus,

Jacob Bernoulli discovered this constant by studying a question about compound interest:

An account starts with $1.00 and pays 100 percent interest per year. If the interest is credited once, at the end of the year, the value of the account at year-end will be $2.00. What happens if the interest is computed and credited more frequently during the year?

Jakob Bernoulli and Johann Bernoulli solve brachistochrone problem, the first result in the calculus of variations,

Abraham de Moivre introduces the normal distribution to approximate the binomial distribution in probability,

Leonhard Euler introduces the integrating factor technique for solving first-order ordinary differential equations,

Nikolai Lobachevsky created Non-Euclidean geometry

George Boole formalizes symbolic logic in The Mathematical Analysis of Logic, defining what is now called Boolean algebra,

Bernhard Riemann introduces Riemannian geometry,

August Ferdinand Möbius invents the Möbius strip,

Charles Hermite solves the general quintic equation by means of elliptic and modular functions,

John von Neumann begins devising the principles of game theory and proves the minimax theorem,

Benoît Mandelbrot publishes Les objets fractals, forme, hasard et dimension,

During the second half of the thirteenth century, gunpowder became known in Europe, perhaps introduced from China through the Mongols. "Knowledge of the explosive properties of salpetre, sulphur, and charcoal seems to have been perfected [in China] about 1000 " (Crombie 1952:192). The evolution of the gun in China appears to have been, first, bamboo flame throwers, then metal tubed flame throwers, then arrow throwers, and, after 1280, ball throwers (O'Connell 2002:113)

1512, Nikolaus Kopérnik, better known as Copernicus, circulated a manuscript, the Commentariolus, which hypothesized that the Earth was a planet and planets revolved in circles and epicircles around the Sun, that the Earth rotated daily, and regressions in planetary orbits were explained by the Earth's motions (Park 1990:143). The problem, as he saw it, was to save the appearance of the phenomena with an hypothsis which was compatible with the principle of physics that hypotheses be founded in the truth of nature, and to demonstrate that to reject this hypothesis meant that the appearances were not saved.

Johannes Kepler: first two laws of planetary motion

Robert Hooke discovers the Cell

Robert Boyle: Boyle's law of ideal gas

Anton van Leeuwenhoek Observes Microorganisms by Microscope

Newton discovers laws of motion, law of universal gravitation, basis for classical physics

Rudolf Clausius: Definition of Entropy

Gregor Mendel: Mendel's laws of inheritance, basis for genetics

Dmitri Mendeleev: Periodic table

James Clerk Maxwell: Theory of electromagnetism

Wilhelm Conrad Röntgen discovers x-rays

Henri Becquerel discovers radioactivity

Max Planck: Planck's law of black body radiation, basis for quantum theory

Henry Moseley: defined atomic number

Niels Bohr: Model of the atom

Albert Einstein: theory of general relativity

Erwin Schrödinger: Schrödinger equation (Quantum mechanics)

James Chadwick: Discovery of the neutron