History of Algebra Timeline

(c. 2000 BCE - Present)

The history of algebra traces the development of one of mathematics' most fundamental branches, from ancient Babylonian and Egyptian methods for solving equations, through the symbolic innovations of Diophantus and al-Khwarizmi (whose work gave algebra its name), to the Renaissance breakthroughs in solving polynomial equations and the 19th-century emergence of abstract algebra with groups, rings, and fields. More Less

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Ancient and Medieval Algebra

Plimpton 322 tablet created

1900 BC - 1600 BC

One of the most famous Babylonian mathematical tablets, Plimpton 322 was created around 1900–1600 BC. It gives a table of Pythagorean triples and represents some of the most advanced mathematics prior to Greek mathematics.

Image source: Plimpton 322

Rhetorical algebra developed by Babylonians

1800 BC

Rhetorical algebra, in which equations are written in full sentences without symbols, was first developed by the ancient Babylonians. It remained dominant up to the 16th century.

Ahmes transcribes the Rhind Mathematical Papyrus

1650 BC

In 1650 BC, the Egyptian scribe Ahmes transcribed a mathematical papyrus from an earlier work that he dated to between 2000 and 1800 BC, preserving some of the earliest known algebraic problem-solving.

Image source: Rhind Mathematical Papyrus

Earliest Indian mathematical documents

600 BC

The earliest known Indian mathematical documents are dated to around the middle of the first millennium BC (around the 6th century BC), marking the beginning of a rich tradition of mathematics in India.

Image source: Indian mathematics

Diophantus writes Arithmetica

250 AD

Diophantus' Arithmetica, dated to about 250 AD (though the uncertainty of this date is so great it may be off by more than a century), introduced syncopated algebraic expressions, using abbreviations for unknowns and operations.

Image source: Diophantus

Brahmagupta writes Brahma Sphuta Siddhanta

628 AD

Syncopated algebraic expression first appeared in Diophantus' Arithmetica in the 3rd century AD, followed by Brahmagupta's Brahma Sphuta Siddhanta in the 7th century, which advanced algebraic methods in India.

Image source: Brahmagupta

Islamic Golden Age

Early Islamic Empire sees few scientific achievements

650 AD - 750 AD

The first century of the Islamic Arab Empire saw almost no scientific or mathematical achievements, since the Arabs, with their newly conquered empire, had not yet gained any intellectual drive, and research elsewhere in the world had faded.

Image source: Islamic Golden Age

Early Islamic Empire sees few scientific achievements

Cultural awakening in the Islamic world

750 AD - 800 AD

In the second half of the 8th century, Islam experienced a cultural awakening, and research in mathematics and the sciences increased dramatically across the Islamic world.

Al-Khwarizmi founds algebra as a discipline

820 AD

Al-Khwarizmi's Al-Jabr established algebra as an independent discipline devoted to the theory of equations. He most likely did not know of Diophantus's Arithmetica, which became known to the Arabs sometime before the 10th century.

Image source: Al-Khwarizmi

Al-Uqlidisi uses decimal fractions

950 AD

The Baghdadi mathematician Abu'l-Hasan al-Uqlidisi used decimal fractions as early as the 10th century, five centuries before later mathematicians who were once credited with their invention.

Image source: Abu'l-Hasan al-Uqlidisi

$Al-Uqlidisi uses decimal fractions$

Al-Karaji introduces theory of algebraic calculus

1000 AD

Al-Karaji was praised by Woepcke in his 1853 Extrait du Fakhri for being 'the first who introduced the theory of algebraic calculus', freeing algebra from geometrical operations.

Image source: Al-Karaji

Omar Khayyam writes book on Algebra

1070 AD

Omar Khayyam (1050–1123) wrote a book on Algebra that went beyond Al-Jabr to include equations of the third degree, advancing the geometric solution of cubic equations.

Image source: Omar Khayyam

Al-Hassār develops modern fractional notation

1150 AD

Al-Hassār, a Moroccan mathematician specializing in Islamic inheritance jurisprudence during the 12th century, developed the modern symbolic notation for fractions, separating numerator and denominator with a horizontal bar.

Image source: History of algebra

$Al-Hassār develops modern fractional notation$

Sharaf al-Dīn al-Tūsī writes Treatise on Equations

1200 AD

In the 12th century, Sharaf al-Dīn al-Tūsī (1135–1213) wrote the Al-Mu'adalat (Treatise on Equations), dealing with eight types of cubic equations with positive solutions and five types which may not have positive solutions.

Image source: Sharaf al-Din al-Tusi

Ibn al-Banna develops symbolic algebra

1300 AD

The Arabs did not adopt or develop a syncopated or symbolic algebra until the work of Ibn al-Banna, who developed a symbolic algebra in the 13th century — the first such attempt since Diophantus and Brahmagupta.

Al-Qalasādī creates algebraic notation

1450 AD

Abū al-Hasan ibn Alī al-Qalasādī (1412–1486), the last major medieval Arab algebraist, made the first attempt at creating an algebraic notation since Ibn al-Banna two centuries earlier.

Renaissance and Early Modern Europe

Fibonacci adopts fractional notation

1202 AD

The same horizontal-bar fractional notation developed by Al-Hassār appeared soon after in the work of Fibonacci in the 13th century, transmitting Islamic mathematics to Europe.

Image source: Fibonacci sequence

$Fibonacci adopts fractional notation$

Fall of Constantinople ends medieval period

1453 AD

The end of the medieval period is set as the fall of Constantinople to the Turks in 1453. As the Islamic world declined after the 15th century, the European world ascended.

Image source: Fall of Constantinople

Modern arithmetic notation introduced

1489 AD - 1525 AD

Modern notation for arithmetic operations was introduced between the end of the 15th century and the beginning of the 16th century by Johannes Widmann and Michael Stifel, including the plus and minus signs.

Image source: Johannes Widmann

General solution of cubic and quartic equations

1540 AD - 1560 AD

Another key event in the development of algebra was the general algebraic solution of the cubic and quartic equations, developed in the mid-16th century by Italian mathematicians.

Image source: Cubic equation

Cardano publishes Ars Magna

1545 AD

In 1545, Gerolamo Cardano published Ars Magna, covering many topics in algebra, discussing imaginary numbers, and presenting general methods for solving cubic and quartic equations.

Image source: Ars Magna (Cardano book)

Viète introduces symbols for variables

1591 AD

At the end of the 16th century, François Viète introduced symbols, now called variables, for representing indeterminate or unknown numbers, developing fully symbolic algebra.

Image source: François Viète

Failed attempts to solve quintic equations

1600 AD - 1799 AD

In the 17th and 18th centuries, numerous attempts were made to find general solutions to polynomials of degree five and higher, but all proved unsuccessful.

Image source: Quintic function

Descartes publishes La Géométrie

1637 AD

René Descartes introduced modern algebraic notation, first published in La Géométrie (1637), including the use of x, and showed that problems in geometry can be expressed and solved in terms of algebra (Cartesian geometry).

Image source: La Géométrie

Seki Kowa develops idea of determinant

1683 AD

The idea of a determinant was developed by Japanese mathematician Kowa Seki in the 17th century, followed by Gottfried Leibniz ten years later, for solving systems of simultaneous linear equations using matrices.

Image source: Seki Takakazu

Leibniz employs notion of function explicitly

1692 AD - 1694 AD

Gottfried Leibniz was the first, in 1692 and 1694, to employ the notion of function explicitly, denoting geometric concepts derived from a curve such as abscissa, ordinate, tangent, chord, and perpendicular.

Image source: Function (mathematics)

Cramer works on matrices and determinants

1750 AD

Gabriel Cramer did important work on matrices and determinants in the 18th century, culminating in Cramer's rule for solving linear systems.

Image source: Gabriel Cramer

Chinese Algebra

Li Zhi writes Sea-Mirror of the Circle Measurements

1248 AD

Ts'e-yuan hai-ching, or Sea-Mirror of the Circle Measurements, is a collection of some 170 problems written by Li Zhi (or Li Ye) (1192–1279 AD), showcasing advanced Chinese algebraic techniques.

Image source: Li Ye (mathematician)

Yang Hui works with magic squares of order ten

1261 AD - 1275 AD

Yang Hui (c. 1238–1298), working between 1261 and 1275, studied magic squares of order as high as ten, contributing to combinatorial and algebraic mathematics in China.

Image source: Yang Hui

Chu Shih-chieh writes Precious Mirror of the Four Elements

1303 AD

Ssy-yüan yü-chien, or Precious Mirror of the Four Elements, was written by Chu Shih-chieh in 1303 and marks the peak in the development of Chinese algebra, dealing with systems of polynomial equations in four unknowns.

Image source: Zhu Shijie

Abstract Algebra

Gauss proves fundamental theorem of algebra

1799 AD

At the end of the 18th century, Carl Friedrich Gauss proved the fundamental theorem of algebra, describing the existence of zeros of polynomials of any degree without providing a general solution.

Image source: Fundamental theorem of algebra

Gauss proves fundamental theorem of algebra

Ruffini and Abel show quintics unsolvable

1799 AD - 1824 AD

At the beginning of the 19th century, Paolo Ruffini and Niels Henrik Abel showed that no general algebraic solution exists for polynomials of degree five and higher.

Image source: Abel–Ruffini theorem

Emergence of abstract algebra

1850 AD

Starting in the mid-19th century, interest shifted from the study of polynomials toward a more general inquiry into algebraic structures, marking the emergence of abstract algebra, largely a product of the 19th and 20th centuries.

Image source: Abstract algebra

Lagarde theorizes origin of algebra term

1884 AD

The theory on the etymology of the word 'algebra' originated in 1884 with German orientalist Paul de Lagarde, shortly after he published a 1505 Spanish/Arabic bilingual glossary pairing Spanish 'cosa' with Arabic 'shayʔ'.

Image source: Paul de Lagarde

Whitehead conceives universal algebra

1898 AD

The idea of the even more general approach associated with universal algebra was conceived by English mathematician Alfred North Whitehead in his 1898 book A Treatise on Universal Algebra.

Topological algebra arises

1900 AD - 1950 AD

Topological algebra arose in the early 20th century, studying algebraic structures such as topological groups and Lie groups, blending algebra with topology.

Image source: Topological group

Key Facts

Ancient Babylonians around 2000 BCE solved quadratic equations using rhetorical methods, without symbols, recorded on clay tablets.
The Persian mathematician al-Khwarizmi wrote 'Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala' around 820 CE, whose title gave us both the words 'algebra' and 'algorithm'.
Diophantus of Alexandria (c. 250 CE) introduced early symbolic notation in his 'Arithmetica', earning him the title 'father of algebra'.
In the 16th century, Italian mathematicians Cardano, Tartaglia, and Ferrari discovered general solutions to cubic and quartic equations, a major advance over classical algebra.
In the 19th century, mathematicians like Évariste Galois and Niels Henrik Abel founded modern abstract algebra through group theory, shifting focus from solving equations to studying algebraic structures.

Source

This History of Algebra timeline was generated with the help of AI, using information found on the internet.

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