3rd century BC Greek mathematician Euclid (holding calipers), as imagined by Raphael in this detail from The School of Athens (1509–1511)
Onion (Allium) cells in different phases of the cell cycle. Growth in an 'organism' is carefully controlled by regulating the cell cycle.
The distribution of prime numbers is a central point of study in number theory. This Ulam spiral serves to illustrate it, hinting, in particular, at the conditional independence between being prime and being a value of certain quadratic polynomials.
This structural formula for molecule caffeine shows a graphical representation of how the atoms are arranged.
The quadratic formula expresses concisely the solutions of all quadratic equations
The orbitals of the hydrogen atom are descriptions of the probability distributions of an electron bound to a proton. Their mathematical descriptions are standard problems in quantum mechanics, an important branch of physics.
Rubik's cube: the study of its possible moves is a concrete application of group theory
Uncrewed and crewed spacecraft missions have been used to image distant locations within the Solar System, such as this Apollo 11 view of Daedalus crater on the far side of the Moon.
The Babylonian mathematical tablet Plimpton 322, dated to 1800 BC.
The materials paradigm represented as a tetrahedron
Archimedes used the method of exhaustion, depicted here, to approximate the value of pi.
Aristotle's view of inheritance, as a model of the transmission of patterns of movement of the body fluids from parents to child, and of Aristotelian form from the father.
The numerals used in the Bakhshali manuscript, dated between the 2nd century BC and the 2nd century AD.
Plato (left) and Aristotle in a 1509 painting by Raphael. Plato rejected inquiry into natural philosophy as against religion, while his student, Aristotle, created a body of work on the natural world that influenced generations of scholars.
A page from al-Khwārizmī's Algebra
Isaac Newton is widely regarded as one of the most influential scientists of all time.
Leonardo Fibonacci, the Italian mathematician who introduced the Hindu–Arabic numeral system invented between the 1st and 4th centuries by Indian mathematicians, to the Western World.
The Michelson–Morley experiment was used to disprove that light propagated through a luminiferous aether. This 19th-century concept was then superseded by Albert Einstein's special theory of relativity.
Leonhard Euler created and popularized much of the mathematical notation used today.
Carl Friedrich Gauss, known as the prince of mathematicians
The front side of the Fields Medal
Euler's identity, which American physicist Richard Feynman once called "the most remarkable formula in mathematics".

As empirical sciences, natural sciences use tools from the formal sciences, such as mathematics and logic, converting information about nature into measurements which can be explained as clear statements of the "laws of nature".

- Natural science

Mathematics is essential in many fields, including natural sciences, engineering, medicine, finance, computer science and social sciences.

- Mathematics
3rd century BC Greek mathematician Euclid (holding calipers), as imagined by Raphael in this detail from The School of Athens (1509–1511)

4 related topics

Alpha

Various examples of physical phenomena

Physics

Various examples of physical phenomena
Ancient Egyptian astronomy is evident in monuments like the ceiling of Senemut's tomb from the Eighteenth Dynasty of Egypt.
Ibn al-Haytham (c. 965–c. 1040), Book of Optics Book I, [6.85], [6.86]. Book II, [3.80] describes his camera obscura experiments.
The basic way a pinhole camera works
Galileo Galilei showed a modern appreciation for the proper relationship between mathematics, theoretical physics, and experimental physics.
Sir Isaac Newton (1643–1727), whose laws of motion and universal gravitation were major milestones in classical physics
Max Planck (1858–1947), the originator of the theory of quantum mechanics
Albert Einstein (1879–1955), whose work on the photoelectric effect and the theory of relativity led to a revolution in 20th century physics
The basic domains of physics
Solvay Conference of 1927, with prominent physicists such as Albert Einstein, Werner Heisenberg, Max Planck, Hendrik Lorentz, Niels Bohr, Marie Curie, Erwin Schrödinger and Paul Dirac
This parabola-shaped lava flow illustrates the application of mathematics in physics—in this case, Galileo's law of falling bodies.
Mathematics and ontology are used in physics. Physics is used in chemistry and cosmology.
The distinction between mathematics and physics is clear-cut, but not always obvious, especially in mathematical physics.
Classical physics implemented in an acoustic engineering model of sound reflecting from an acoustic diffuser
Archimedes' screw, a simple machine for lifting
Experiment using a laser
The astronaut and Earth are both in free fall.
Lightning is an electric current.
Physics involves modeling the natural world with theory, usually quantitative. Here, the path of a particle is modeled with the mathematics of calculus to explain its behavior: the purview of the branch of physics known as mechanics.
A simulated event in the CMS detector of the Large Hadron Collider, featuring a possible appearance of the Higgs boson.
Velocity-distribution data of a gas of rubidium atoms, confirming the discovery of a new phase of matter, the Bose–Einstein condensate
The deepest visible-light image of the universe, the Hubble Ultra-Deep Field
Feynman diagram signed by R. P. Feynman.
A typical phenomenon described by physics: a magnet levitating above a superconductor demonstrates the Meissner effect.

Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.

Over much of the past two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the Scientific Revolution in the 17th century these natural sciences emerged as unique research endeavors in their own right.

Chronology of the universe as deduced by the prevailing Big Bang theory, a result from science and obtained knowledge

Science

Systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.

Systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.

Chronology of the universe as deduced by the prevailing Big Bang theory, a result from science and obtained knowledge
The first diagram of an evolutionary tree made by Charles Darwin in 1837
First global view of the ozone hole in 1983, using a space telescope
Radio light image of M87* black hole, made by the earth-spanning Event Horizon Telescope array in 2019
Supply and demand curve in economics, crossing over at the optimal equilibrium
A steam turbine with the case opened, such turbines produce most of the electricity used today
A diagram variant of scientific method represented as an ongoing process
Cover of the first issue of Nature, 4 November 1869
For Kuhn, the addition of epicycles in Ptolemaic astronomy was "normal science" within a paradigm, whereas the Copernican revolution was a paradigm shift.
Marie Curie was the first person to be awarded two Nobel Prizes: Physics in 1903 and Chemistry in 1911.
Picture of scientists in 200th anniversary of the Prussian Academy of Sciences, 1900
Medal of the Nobel Prize, one of the most well-known science awards
Budget of NASA as percentage of United States federal budget, peaking at 4.4% in 1966 and slowly decline since
Dinosaur exhibit in the Houston Museum of Natural Science
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Their contributions to mathematics, astronomy, and medicine entered and shaped Greek natural philosophy of classical antiquity, whereby formal attempts were made to provide explanations of events in the physical world based on natural causes.

Modern science is typically divided into three major branches: natural sciences (e.g., biology, chemistry, and physics), which study the physical world; the social sciences (e.g., economics, psychology, and sociology), which study individuals and societies; and the formal sciences (e.g., logic, mathematics, and theoretical computer science), which study formal systems, governed by axioms and rules.

The Paranal Observatory of European Southern Observatory is shooting a laser guide star to the Galactic Center

Astronomy

The Paranal Observatory of European Southern Observatory is shooting a laser guide star to the Galactic Center
Astronomical Observatory, New South Wales, Australia 1873
19th-century Quito Astronomical Observatory is located 12 minutes south of the Equator in Quito, Ecuador.
A celestial map from the 17th century, by the Dutch cartographer Frederik de Wit
The Suryaprajnaptisūtra, a 6th-century BC astronomy text of Jains at The Schoyen Collection, London. Above: its manuscript from c. 1500 AD.
Greek equatorial sundial, Alexandria on the Oxus, present-day Afghanistan 3rd–2nd century BC
Galileo's sketches and observations of the Moon revealed that the surface was mountainous.
An astronomical chart from an early scientific manuscript, c. 1000
The Very Large Array in New Mexico, an example of a radio telescope
ALMA Observatory is one of the highest observatory sites on Earth. Atacama, Chile.
The Subaru Telescope (left) and Keck Observatory (center) on Mauna Kea, both examples of an observatory that operates at near-infrared and visible wavelengths. The NASA Infrared Telescope Facility (right) is an example of a telescope that operates only at near-infrared wavelengths.
X-ray jet made from a supermassive black hole found by NASA's Chandra X-ray Observatory, made visible by light from the early Universe
Star cluster Pismis 24 with a nebula
Astrophysics applies physics and chemistry to understand the measurements made by astronomy. Representation of the Observable Universe that includes images from Hubble and other telescopes.
Hubble Extreme Deep Field
This image shows several blue, loop-shaped objects that are multiple images of the same galaxy, duplicated by the gravitational lens effect of the cluster of yellow galaxies near the middle of the photograph. The lens is produced by the cluster's gravitational field that bends light to magnify and distort the image of a more distant object.
Observed structure of the Milky Way's spiral arms
Mz 3, often referred to as the Ant planetary nebula. Ejecting gas from the dying central star shows symmetrical patterns unlike the chaotic patterns of ordinary explosions.
An ultraviolet image of the Sun's active photosphere as viewed by the TRACE space telescope. NASA photo
Solar observatory Lomnický štít (Slovakia) built in 1962
The black spot at the top is a dust devil climbing a crater wall on Mars. This moving, swirling column of Martian atmosphere (comparable to a terrestrial tornado) created the long, dark streak.
Amateur astronomers can build their own equipment, and hold star parties and gatherings, such as Stellafane.

Astronomy is a natural science that studies celestial objects and phenomena.

It uses mathematics, physics, and chemistry in order to explain their origin and evolution.

The School of Athens (1509–1511) by Raphael, depicting famous classical Greek philosophers in an idealized setting inspired by ancient Greek architecture.

Philosophy

Systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language.

Systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language.

The School of Athens (1509–1511) by Raphael, depicting famous classical Greek philosophers in an idealized setting inspired by ancient Greek architecture.
The Vinegar Tasters (Japan, Edo period, 1802-1816) by Kanō Isen'in, depicting the three main philosophical figures in East Asian thought: Buddha, Confucius and Laozi.
Statue of Aristotle (384–322 BCE), a major figure of ancient Greek philosophy, in Aristotle's Park, Stagira.
A painting of the influential modern philosopher Immanuel Kant (in the blue coat) with his friends. Other figures include Christian Jakob Kraus, Johann Georg Hamann, Theodor Gottlieb von Hippel and Karl Gottfried Hagen.
A page of The Maxims of Ptahhotep, traditionally attributed to the Vizier Ptahhotep (c. 2375–2350 BCE).
An Iranian portrait of Avicenna on a Silver Vase. He was one of the most influential philosophers of the Islamic Golden Age.
Adi Shankara is one of the most frequently studied Hindu philosophers.
The parable of the blind men and the elephant illustrates the important Jain doctrine of anēkāntavāda.
Statue of the Neo-Confucian scholar Zhu Xi at the White Deer Grotto Academy in Lushan Mountain.
Kitaro Nishida, considered the founder of the Kyoto School of philosophical thought, c. 1943.
Painting of Zera Yacob from Claude Sumner's Classical Ethiopian Philosophy.
A Tlamatini (Aztec philosopher) observing the stars, from the Codex Mendoza.
Depiction of Pachacuti worshipping Inti (god Sun) at Coricancha, in the 17th century second chronicles of Martín de Murúa. Pachacuti was a major Incan ruler, author and poet.
Mary Wollstonecraft (1759-1797) was an English writer and philosopher.
The Beijing imperial college was an intellectual center for Confucian ethics and classics during the Yuan, Ming and Qing dynasties.
Dignaga founded a school of Buddhist epistemology and logic.
The beginning of Aristotle's Metaphysics in an incunabulum decorated with hand-painted miniatures.
Thomas Hobbes, best known for his Leviathan, which expounded an influential formulation of social contract theory.
Martin Luther King Jr.

Before the modern age, the term was used in a very wide sense, which included the individual sciences, like physics or mathematics, as its sub-disciplines, but the contemporary usage is more narrow.

Many of them differ significantly from the methods used in the natural sciences in that they do not use experimental data obtained through measuring equipment.