# Algebra: A History

## Algebra: A History

Algebra is one of the main areas of pure mathematics that uses mathematical statements such as term, equations, or expressions to relate relationships between objects that change over time. Here is a list of names who have contributed to the specific field of algebra.

**Cuthbert Tunstall**

- Cuthbert Tunstall (1474 -1559) was born in Hackforth, Yorkshire, England and died in Lambeth, London, England.
- He was a significant royal advisor, diplomat, and administrator, and he gained two degrees with great proficiency in Greek, Latin, and mathematics.
- In 1522, he wrote his first printed work that was devoted to mathematics, and this arithmetic book ‘De arte supputandi libri quattuor’ was based on Pacioli’s “Suma”.

**Robert Recorde**

- Robert Recorde (1510-1558) was born in Tenby, Wales and died in London, England.
- He was a Welsh mathematician and physician and in 1557, he introduced the equals sign (=).
- In 1540, Recorde published the first English book of algebra ‘The Grounde of Artes’.
- In 1557, he published another book ‘The Whetstone of Witte’ in which the equals sign was introduced.

**John Widman**

- John Widman (1462-1498) was born in Eger, Bohemia, currently called Czech Republic and died in Leipzig, Germany.
- He was a German mathematician who first introduced + and – signs in his arithmetic book ‘Behende und hupsche Rechnung auf Allen kauffmanschafft’.

**Thomas Harriot**

- Thomas Harriot (1560 -1621) was born in Oxford, London and died in London England.
- He was an astronomer and mathematician, and founder of the English school of algebra.

**William Oughtred**

- William Oughtred (1575-1660) was born in Eton, Buckinghamshire, England and died in Albury, Surrey, England.
- He was one of the world’s great and formally trained mathematicians.
- Oughtred, in his book Clavis Mathematicae included Hindu-Arabic notation, decimal fractions and experimented on many new symbols such as ×,::, >, and <.

**John Pell**

- John Pell (1611-1685) was born in Southwick, Sussex, England, and died in Westminster, London, England.
- Pell’s work was mostly based on number theory and algebra.
- Pell published many books on mathematics such as Idea of Mathematics in 1638 and the two page ‘A Refutation of Longomontanus’s Pretended Quadrature of the Circle’ in 1644.

**Reverend John Wallis**

- John Wallis (1616-1703) was born in Ashford, Kent, England and died in Oxford, England.
- In 1656, Wallis published his most famous book Arithmetica Infinitorum in which he introduced the formula /2 = (2.2.4.4.6.6.8.8.10…)/ (1.3.3.5.5.7.7.9.9…).
- In another of his works, ‘Treatise on Algebra’, Wallis gives a wealth of information on algebra.

**John Herschel**

- John Frederick William Herschel (1792-1871) was born in Slough, England and died in Kent, England.
- He was a great astronomer who discovered Uranus.
- In 1822, he published his first work on astronomy, a small work to calculate the eclipses of the moon.
- In 1824, he published his first major work on double stars in the Transactions of the Royal Society.

**Charles Babbage**

- Charles Babbage (1791 -1871) was born in London, England and died in London, England.
- In 1821, Babbage made the Difference engine to compile tables of mathematics.
- In 1856, he invented Analytical Engine, which is a general symbol manipulator and similar to today’s computers.

**Sir Isaac Newton**

- Sir Isaac Newton (1643-1727) was born in Lincolnshire, England and died in London, England.
- He was a great physicist, mathematician, and one of the greatest scientific intellects of all time.
- In 1672, he published his first work on light and color in the Philosophical Transactions of the Royal Society.
- In 1704, Newton’s works on pure mathematics was published and in 1707, his Cambridge lectures from 1673 to 1683 were published.

**George Boole**

- George Boole (1815-1864) was born in Lincolnshire, England and died in County Cork, Ireland.
- He invented the Boolean logic, which is now the basis of modern digital computers.
- He published his first paper on symbolic logic on calculus in the Royal Society of London for which he was awarded the Royal Medal in 1844.
- In 1847, he published his major work ‘The Mathematical Analysis of Logic’.

**Charles Dodgson**

- Charles Lutwidge Dodgson (1832-1898) was born in Daresbury, England and died in Guilford, England.
- He was a famous mathematician, but he was most famous for his children books ‘Alice’s Adventures in Wonderland’ and ‘Through the Looking Glass’.
- He wrote many books on mathematics including ‘Two Books of Euclid’, ‘The Formulae of Plane’, ‘Trigonometry’, ‘Condensation of Determinants”, ‘Elementary Treatise on Determinants’, ‘Examples in Arithmetic’, ‘Euclid and His Modern Rivals’, ‘Curiosa Mathematica: Part I’, and ‘Curiosa Mathematica: Part II’.

**Leslie Fox**

- Leslie Fox (1918 – 1992) was born in Yorkshire, England and died in Oxford, England.
- He was the first professor to teach Numerical analysis at Oxford University.
- He was an active member and an editor of the Institute of Mathematics.

**Alan Turing**

** **

- Alan Turing (1912 – 1954) was born in London, England and died in Cheshire, England.
- In 1936, he published a paper ‘On Computable Numbers, with an application to the ‘Entscheidungsproblem’ in which he introduced the Turing machine.
- In 1950, he published a paper ‘Computing Machinery and Intelligence’ on computer and artificial intelligence.

**Christopher Strachey**

- Christopher Strachey (1916-1975) was born in Hampstead, England and died in Oxford, England.
- He introduced the Combined Programming Language (CPL) and defined the term Currying.
- He took the active part in designing the Ferranti PEGASUS computer.

**Stephan Wolfram**

- Stephen Wolfram was born in London in 1959.
- He is famous for his work in cosmology, cellular automata, particle physics, computer algebra, complexity theory, and Wolfram Alpha computational engine.

**Tony Hoare**

- Tony Hoare was born in Sri Lanka in 1934 and he is a famous British computer scientist.
- He is very famous for developing Quicksort, one of the famous sorting algorithms.
- He also developed Hoare logic and Communicating Sequential Processes (CSP).

For additional resources on mathematicians refer to the following sites:

- Recorde
- History of Signs
- Thomas Harriot
- Thomas Harriot, Renaissance Scholar
- William Oughtred
- Oughtred
- Pell Biography
- John Pell
- Wallis
- John Herschel
- Herschel
- Charles Babbage
- Babbage Biography
- Newton’s Life
- Sir Isaac Newton
- Boole
- George Boole
- Charles Dodgson
- Leslie Fox
- Turing
- Christopher Strachey
- Stephan Wolfram
- Hoare