• 5000 BCE

# Earliest evidence of emergence of math in Mesopotamia and Egypt

"As societies adopted various forms of centralized government, they needed ways of keeping track of what was produced, how much was owed in taxes, and so on" (Berlinghoff & Gouvea, 2015, pp.7)
• 3000 BCE

# Earliest artifacts showing numeration system using symbols in royal Egypt.

(Berlinghoff & Gouvea, 2015)
• Period: 1900 BCE to 1600 BCE

## Old Babylonian Period: Mesopotamian Math

"The history of ancient Iraq spans thousands of years and a number of cultures, including Sumerian Babylonian, Assyrian, Persian, and eventually Greek. All of these cultures knew and used mathematics but there was a lot of variety. Most of our information about the mathematics of Mesopotamia comes from tablets produced between 1900 and 1600 B.C., sometimes called the Old Babylonian period" (Berlinghoff and Gouvea, 2015, pp. 10). Also referred to as Babylonian mathematics.
• Period: 1900 BCE to 1600 BCE

## Babylonian math seems to have arisen from the everyday needs of running a central government.

Math (computation/multiplication) tablets from this period provide the following about Mesopotamian math: place-value system based on sixty, symbols for 1s and 10s that (based on position) represent powers of 60, fractions in sexigesimal format, solving of linear equations, hints of solving quadratic equations, geometry devoted to measurement, formulas for area and volume, driven by methods, and the occurrence of non-practical, recreational problems (Berlinghoff and Gouvea, 2015).
• 1650 BCE

# Rhind Papyrus: most extensive source of Egyptian math.

Named after Henry A. Rhind. Contains, on one side, tables that were used to aide computation (multiplication) and, on the other side, a collection of problems used to train scribes. The examples cover a wide range of ideas. Math highlights from papyrus: 2 numeration systems based on grouping by tens, symbols for powers of 10, adding, doubling, unit fractions, area, volume, and solving linear equations (Berlinghoff & Gouvea, 2015).
• 1650 BCE

# Rhind Papyrus from Acient Egypt approximates area of a unit circle as 4(8/9)6^2.

4 is the earliest approximation of Pi (Berlinghoff & Gouvea, 2015).
• 600 BCE

# Most significant early Indian texts are the Vedas and supplementary texts the Sulbasutras.

Mostly focuses on the rules for building altars which requires math. Math found: statement of the Pythagorean Theorem, approximating the length of the diagonal, discussions about surface areas and volumes of solids, very large numbers, and a workable number system used for astronomy and elementary geometry (Berlinghoff & Gouvea, 2015).
• 600 BCE

# First Greek mathematician was said to be Thales.

First person to attempt to prove some geometrical theorems (Berlinghoff & Gouvea, 2015).
• Period: 600 BCE to 400

## Greek math is developed.

Greek math refers to the language in which it was written. Not all Greek mathematicians were born in Greece. The dominant form of Greek mathematics is Geometry but they also studied theory of ratios and properties of whole numbers. Euclid's Elements contains squaring the circle, trisecting the angle, and duplicating the cube (Berlighoff & Gouvea, 2015).
• 500 BCE

# Second known Greek mathematician is Pythagoras.

Stories about Pythagoras center around the Pythagorean Brotherhood which believed in number mysticism, the belief that numbers are the secret principal of reality. They study mathematike, "that which is learned". The achievements of the brotherhood were later attributed to Pythagoras.Pythagoras may not have been a mathematician but may have believed in number mysticism. They studied: properties of whole numbers, study of ratios, and the Pythagorean Theorem (Berlinghoff & Gouvea, 2015).
• 400 BCE

# Greek flourished in northern Egypt in Alexandria named for Alexander the Great.

"By the end of the 4th century B.C., Alexandria was the real center of Greek Mathematics" (Berlinghoff & Gouvea, 2015, pp.20). Euclid probably lived in Alexandria in 300 B.C. Elements lists definitions, postulates, common notions, propositions, proofs, diagrams, plane and solid geometry, divisibility rules of whole numbers, ratios, and quadratic irrational ratios. This topics cover the main accomplishments of Greek math up to this period (Berlinghoff & Gouvea, 2015).
• 300 BCE

• 240 BCE

# Archimedes shows that Pi is between 3 10/71 and 10/70.

3 1/7 (Berlinghoff & Gouvea, 2015).
• 220 BCE

# Emperor at the beginning of Qin Dynasty ordered all books from earlier periods be destroyed except "useful" documents like official records and medicine books.

This, in addition to natural difficulties which caused the loss of most of the bamboo strips and string that contained early Chinese math texts, erased evidence of earlier Chinese math.
• 100

# Chinese Math and the Invention of Paper.

Chinese wrote on bamboo strips tied together with string. These materials decayed over time which means that earlier evidence of Chinese math was destroyed.
• 120

# Greek Astronomer, Claudius Ptolemy lived in Alexandria. His book is the basis of positional astronomy until the 16th century.

About a century later, lived the most original Greek mathematician, Diophantus. His book, Arithmetica, demonstrates use of a notation for powers, common fractions, and writing squares as the sum of two other squares. Diophantine equations are equations which must be solved in whole numbers or rational numbers (Berlinghoff & Gouvea, 2015)
• 150

# Greek Astronomer, Ptolemy used 377/120 for Pi.

(Berlinghoff & Gouvea, 2015).
• 263

# Liu Hui annotated and supplemented the earliest of the Mathematical Classics, The Nine Chapters on the Mathematical Art. Material in the texts date back to 11th century and 100 B.C.

"The best known mathematical texts from China are The Ten Mathematical Classics, books studied by civil servants who were expected to demonstrate the ability to solve mathematical problems before they could get their jobs" (Beringhoff & Gouvea, 2015, pp.13). Solutions to these problems are presented to solve general problems of that nature. Problems from these books included: recreation, proportionality (in geometry and arithmetic), and solving linear equations.
• Period: 300 to 400

## Math from Alexandria in the 4th century was mostly commentaries on earlier works.

Theon made new editions of Euclid's Elements and Ptolemy's Syntaxis. Theons' daughter, Hypatia, wrote commentaries on Apollonius's Conics, Diophantus's Arithmetica, and her father's work. Proclus also wrote commentaries on Euclid's Elements.
• 480

# Chinese scholar, Zu Chongzhi used 355/113 for Pi.

(Berlinghoff & Gouvea, 2015).
• 500

# Indian mathematician, Aryabhata, used 62832/20000 for Pi.

(Berlinghoff & Gouvea, 2015).
• Period: 500 to

## Math in India: contributions to Trigonometry, combinatorics, methods for computing square and cube roots, sum of arithmetic progressions, quadratic equations, and equations in multiple variables.

Early 6th century, Aryabhata. 7th century, mathematicians are Brahmagupta and Bashkara who were said to be some of the first people to work with negative numbers. In the 12th century, there was another Bashkara. Indian math is responsible for the decimal numeration system with symbols for 1-9 and a small dot for a place holder. Before the year 600, they were using a place-value system based upon powers of 10 (Berlinghoff & Gouvea, 2015).
• 801

# By the 9th century, Indian math recognized sunya, the absence of quantity.

This is when zero began to be treated as a number (Berlinghoff and Gouvea, 2015).
• Period: 801 to 1300

## Arabic Mathematics: solving equations of degree 3, combinatorics, and positive numbers.

Work in Trigonometry led to approximate solutions of equations. Provided a method for approximating the nth root of a number (Berlinghoff & Gouvea, 2015).
• 1145

# Robert of Chester translates Arabic mathematician, al-Khwarzimi's, algebra book from Arabic to Latin.

"al-jabr" turned into algebra. "Dixit Algorismi" is the word algorithm which means recipe for doing something.
• 1489

# In Germany our plus and minus signs appear in print for the first time.

(Berlinghoff & Gouvea, 2015).
• 1557

# First use of + and - in an English book in Recorde's algebra text, The Whetstone of Witte.

He also introduces a symbol for equality (Berlinghoff & Gouvea, 2015).
• # Early 1700s, Parentheses () become the popular grouping notation, x symbol for multiplication is first seen in European text, and use of popular division symbol chosen over subtraction.

Raised dot introduced to avoid confusion between x as multiplication or variable. Johann Rahn responsible for the popular division symbol being used for division and being discontinued for subtraction (Berlingoff & Gouvea, 2015).
• Period: to

## Algebra Comes of Age

English Scholar Robert Recorde with cossic art. In Italy, Girolamo Cardano with solving cubics based upon Tartaglia's methods. French cryptographer Francois Viete using letters to stand for numbers. Rene Descartes in La Geometrie proposed the notion that we use for variable in algebra today. Descartes and Pierre de Fermat linked algebra and geometry in coordinate geometry (Berlinghoff & Gouvea, 2015).
• # British mathematician, William Jones first use the Greek symbol Pi as the name of the number.

Leonhard Euler adopted it in the 1730s and it became the common name/symbol for Pi (Berlinghoff & Gouvea, 2015).
• # Metric System: Bishop Charles Maurice de Talleyrand proposed a measurement system.

Based upon the length of pendulum that would swing once per second. French Academy of Sciences, instead, comes up with a new system based on the length of a sea -level meridian arc from the North Pole's Equator. One ten-millionth of this arc is named the meter. Metric system comes from smaller and larger units of length which are powers of ten and multiples of the meter (Berlinghoff & Gouvea, 2015).
• # Carl Friedrich Gauss published Disquisitiones Arithmeticae which produced Gaussian style.

Dealt with whole numbers and their properties. Spanned pure and applied mathematics (Berlinghoff and Gouvea, 2015).
• # United States passes law making Metric System legal in commerce but not mandatory.

(Berlinghoff & Gouvea, 2015). Metric Conversion Act comes later in 1975 which urged conversion to the metric system but little progress was made.
• # Modern mathematician, John von Neumannm, used a U.S. government computer to workout Pi to 2,035 decimal places.

He did this in 70 hours (Berlinghoff & Gouvea, 2015).
• # Clay Mathematics Institute chooses 7 Millennium Problems.

At the begin of the 21st century (inside "golden age" of mathematics), they chose 7 problems and offer a million dollar prize for the solution of each. The problems cover the full spectrum of mathematics (Berlinghoff & Gouvea, 2015).