History of Mathematics
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
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
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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
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.