The History of Mathematics and Its Applications

The Map of Mathematics

The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BCE the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by <a href="https://history-maps.com/story/History-of-Egypt" rel="noopener noreferrer" target="_blank">Ancient Egypt</a> and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars. The earliest mathematical texts available are from <a href="https://history-maps.com/story/History-of-Iraq" rel="noopener noreferrer" target="_blank">Mesopotamia</a> and Egypt – Plimpton 322 (Babylonian c. 2000 – 1900 BCE),[1] the Rhind Mathematical Papyrus (Egyptian c. 1800 BCE)[2] and the Moscow Mathematical Papyrus (Egyptian c. 1890 BCE). All of these texts mention the so-called Pythagorean triples, so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. The study of mathematics as a "demonstrative discipline" began in the 6th century BCE with the Pythagoreans, who coined the term "mathematics" from the ancient <a href="https://history-maps.com/story/History-of-Greece" rel="noopener noreferrer" target="_blank">Greek</a> μάθημα (mathema), meaning "subject of instruction".[3] Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics.[4] Although they made virtually no contributions to theoretical mathematics, the ancient Romans used applied mathematics in surveying, structural engineering, mechanical engineering, bookkeeping, creation of lunar and solar calendars, and even arts and crafts. <a href="https://history-maps.com/story/History-of-China" rel="noopener noreferrer" target="_blank">Chinese</a> mathematics made early contributions, including a place value system and the first use of negative numbers.[5] The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today evolved over the course of the first millennium CE in <a href="https://history-maps.com/story/History-of-India" rel="noopener noreferrer" target="_blank">India</a> and were transmitted to the Western world via Islamic mathematics through the work of Muḥammad ibn Mūsā al-Khwārizmī.[6] <a href="https://history-maps.com/story/History-of-Iran" rel="noopener noreferrer" target="_blank">Islamic</a> mathematics, in turn, developed and expanded the mathematics known to these civilizations.[7] Contemporaneous with but independent of these traditions were the mathematics developed by the Maya civilization of <a href="https://history-maps.com/story/History-of-Mexico" rel="noopener noreferrer" target="_blank">Mexico</a> and Central America, where the concept of zero was given a standard symbol in Maya numerals. Many Greek and Arabic texts on mathematics were translated into Latin from the 12th century onward, leading to further development of mathematics in Medieval Europe. From ancient times through the Middle Ages, periods of mathematical discovery were often followed by centuries of stagnation.[8] Beginning in Renaissance <a href="https://history-maps.com/story/History-of-Italy" rel="noopener noreferrer" target="_blank">Italy</a> in the 15th century, new mathematical developments, interacting with new scientific discoveries, were made at an increasing pace that continues through the present day. This includes the groundbreaking work of both Isaac Newton and Gottfried Wilhelm Leibniz in the development of infinitesimal calculus during the course of the 17th century.

Visual Timelines

Story of Mathematics Timeline

Story of Mathematics Timeline

Ancient Egyptian Mathematics

Sumerian Mathematics

Abacus

Old Babylonian Mathematics

Thales's Theorem

Pythagoras

Discovery of Irrational Numbers

Plato

Chinese Geometry

Chinese Decimal System

Hellenistic Greek Mathematics

Euclid

Archimedes

Apollonius's Parabola

Nine Chapters on the Mathematical Art

Hipparchus & Trigonometry

Almagest of Ptolemy

Chinese Remainder Theorem

Diophantine Analysis

Story of Zero

Hypatia

Indian Trigonometry

Indian Decimal System

Muhammad ibn Musa al-Khwarizmi

Abu Kamil

Mayan Mathematics

Al-Karaji

Chinese Algebra

Hindu-Arabic Numerals

Leonardo Fibonacci

Infinite Series

Probability Theory

Logarithms

Cartesian Coordinate System

Calculus

Graph Theory

Normal Distribution

Euler's Formula

Bayes' Theorem

Gauss's Law

Group Theory

Fourier Analysis

Maxwell's Equations

Set Theory

Game Theory

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