# History of Mathematics

### Algebra

## Babylonian Mathematics

**1800-1600 B.C. Clay tablets with fractions, algebra, and equations.**

## Diophantus 200-284 A.D.

**Greek mathematician****Found rational solutions to equations with several unknowns****Some claim he should be called "The Father of Algebra"****Wrote a collection of 13 books called***Arithmetica***The series included over 100 algebraic problems with solutions****He used three types of quadratic equations, instead of one, because he did not have notation for zero****He thought out the solutions to problems concerning linear and quadratic equations, using only positive rational solutions****There is no evidence that he found two solutions to the quadratic equations****He thought negative or irrational square roots were useless**

## LIU HUI 220-280 A.D.

**Chinese mathematician that solved linear equations using matrices.****Edited and published The Nine Chapters on Mathematical Art in 263 A.D.****The contents of the chapters included arithmetic, algebraic and geometric algorithms.****He approximated pi as 3.14014 and suggested 3.14 was a practical approximation.**

## THE NINE CHAPTERS ON MATHEMATICAL ART

## ARYABHATA 476-550 A.D.

**Indian mathematician and astronomer.****Published his first book,***Aryabhatiya*, at age 23**The mathematical part of the book covered arithmetic, algebra, plane trigonometry, and spherical trigonometry.****He wrote important observations on 4 types of equations. Equations with one variable, quadratic equations, simultaneous equations, and indeterminate equations.**

## BRAHMAGUPTA 598-550 A.D.

**Indian mathematician and astronomer****His understanding of the number system went far beyond that of other mathematicians of this period****He established rules for zero****For example, one plus zero equals zero, one minus zero equals zero, and one times zero equals zero****His understanding of the division of zero was not complete****He thought positive and negative numbers divided by zero equaled zero or expressed as a fraction and zero divided by zero equaled zero**

## AL-HAITHAM (ALHAZEN) 965-1040 A.D.

**Considered the father of modern optics****Alhazen's problem, lead to an equation of the fourth degree****He developed analytical geometry by establishing a link between algebra and geometry**

**(Al h ai z in n)**

http://images.rapgenius.com/a474212330aa50e11894253a602afc94.187x227x1.jpg

## 1100 THE SPREAD OF MATHEMATICS

**Arabic and Hindu mathematics spread throughout the Western Europe**

## BHASKARA II (1114-1185)

**Indian mathematician****Had an understanding of the number system and solving equations that was not achieved for several centuries****He knew that x^2 = 9 had two solutions**

## ROBERT RECORDE (1510-1558)

**Welch mathematician who published the first English book of Algebra,**

*The Ground of Artes*## RENE DESCARTES (1596-1650)

**French philosopher and mathematician****Created the Cartesian coordinate system with axes label x, y, and z (later extended to negative numbers)****Algebra could now be linked with geometry**

## ISAAC NEWTON (1642-1727)

**Polish philosopher, scientist, astronomer, and mathematician credited for the generalized binomial theorem**

## LEONARD EULER (1701-1783)

**Swiss mathematician****Wrote***The Elements of Algebra***f(x) functions****The symbol, e, for the base of natural logarithms****Sometimes called Euler's number**

*leonhard-euler-source.jpg*

## CARL FRIEDRICH GAUSS (1777-1825)

**German mathematician who was credited for the Fundamental Theorem of Algebra****The theorem states, if we have an n-th degree polynomial, we will have n-roots****Example: A second degree parabola has exactly two roots****Note: Complex non-real root are always in pairs**

## 1827 ALGEBRA EDUCATION

**Massachusetts passed a law requiring algebra to be taught in the high school of any town with at least 500 families.**