# History of Mathematics

## Babylonian Mathematics

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

## THE RHIND PAPYRUS OR AHMES PAPYRUS

This document dates back to 1650 B.C. Copied by a scribe, Ahmes, from a copied document that may have been written as far back as 2650 B.C. The written material included simple equations and simple algebra problems.

## 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.

## 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

http://economictimes.indiatimes.com/slideshows/people/indian-maths-wizards-and-their-ideas/brahmagupta-598-670/slideshow/40354409.cms

## 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)

## 1100 THE SPREAD OF MATHEMATICS

Arabic and Hindu mathematics spread throughout the Western Europe

http://etc.usf.edu/maps/pages/6800/6866/6866.jpg

• 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.