3rd century BC Greek mathematician Euclid (holding calipers), as imagined by Raphael in this detail from The School of Athens (1509–1511)
Charles Babbage, sometimes referred to as the "father of computing".
Efficient solutions to the vehicle routing problem require tools from combinatorial optimization and integer programming.
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.
Ada Lovelace published the first algorithm intended for processing on a computer.
A numerical solution to the heat equation on a pump casing model using the finite element method.
The quadratic formula expresses concisely the solutions of all quadratic equations
Fluid mechanics is often considered a branch of applied mathematics and mechanical engineering.
Rubik's cube: the study of its possible moves is a concrete application of group theory
Mathematical finance is concerned with the modelling of financial markets.
The Babylonian mathematical tablet Plimpton 322, dated to 1800 BC.
The Brown University Division of Applied Mathematics is the oldest applied math program in the U.S.
Archimedes used the method of exhaustion, depicted here, to approximate the value of pi.
Applied mathematics has substantial overlap with statistics.
The numerals used in the Bakhshali manuscript, dated between the 2nd century BC and the 2nd century AD.
A page from al-Khwārizmī's Algebra
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.
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".

Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry.

- Applied mathematics

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

- Mathematics

Some areas of mathematics, such as statistics and game theory, are developed in close correlation with their applications and are often grouped under applied mathematics.

- Mathematics

Computer science research also often intersects other disciplines, such as cognitive science, linguistics, mathematics, physics, biology, Earth science, statistics, philosophy, and logic.

- Computer science

From its origins in cybernetics and in the Dartmouth Conference (1956), artificial intelligence research has been necessarily cross-disciplinary, drawing on areas of expertise such as applied mathematics, symbolic logic, semiotics, electrical engineering, philosophy of mind, neurophysiology, and social intelligence.

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

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