• 3500 BCE

# Earliest Known Use of Math 35,000 BC

The Lebombo bone was found in the mountains of Switzerland, with a dating of around 35,000 BC, It has 29 distinct notches, used presumably as some sort of tally. The picture shows the Ishango bone, from around 20,00 BC
• Period: 3500 BCE to 3000 BCE

## Prehistoric Discoveries

The rudiments of mathematics first appeared in the prehistoric era. The mere distinction between “one” and “many” was sufficient for early people. The next number needed was “two.” Thus, we arrive at “one-two-many”, a system sufficient for hunter-gatherers; The influence of trade & agriculture leads to a need for higher numbers; small isolated hunter-gatherer tribes with no trade still use “one-two-many”. A few ancient bones with tally marks show how early man began the use of math.
• 3000 BCE

# Ist Recorded use of Natural Numbers

Around this time the Greeks started using their Ionic system , which uses the Greek alphabet and a ciphered system. The Egyptians also had a system of hieroglyphic numerals at this time.
• Period: 3000 BCE to 332 BCE

## Ancient Babylonian / Egyptian Civilizations

Babylonian math-Mesopotamia: Earliest evidence of written math dates to ancient Sumerians, developed a complex system of metrology from 3000 BC, multiplication tables, geometric exercises & division on clay tablets
Egyptian math texts: papyri from -c.1890 to 1650 BC show use of area, multiplication, division, unit fractions,composite & prime; Sieve of Eratosthenes, 1st order linear equations, arithmetic & geometric series, word problems volume of frustum, 2nd order algebraic equation
• 2500 BCE

# Babylonian Numeration System

The Babylonians were first recorded as using the natural numbers and rationals: this is the earliest known decimal system allows indefinite counting by way of introducing new symbols. Over 400 clay tablets have been found, starting in the 1850's, showing the work of clerks, teachers and even students.
• 1650 BCE

# Rhund Papyrus written

Much of our knowledge of Egyptian mathematics comes from a roll of papyrus measuring 18 ft by 13 in. It was discovered in a shop in Luxor, Egypt, in 1858 by Henry Rhind, a Scottish lawyer turned archaeologist. The Rhind Papyrus has inscribed on it 85 mathematical problems and solutions involving addition, subtraction, multiplication, division, and geometry. [https://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus]
• Period: 1000 BCE to 1300

## Indian Mathematics

Earliest civilization is the Indus Valley Civilization ~2600-1900 BC cities were laid out with geometric regularity
Oldest extant math records are the Sulba Sutras-appendices to religious texts- give methods for constructing a circle, several approximations of π, square root of 2, Pythagorean triples, Pythagorean theorem
5th c AD, Aryabhata wrote the Aryabhatiya to supplement rules of calculation in astronomy & mathematics; here the decimal place-value system 1st appears.
• Period: 1000 BCE to 1300

## Chinese Mathematics

Early Chinese math show unique & independent development. The oldest text from China is the Zhoubi Suanjing, (~300 BC) The Tsinghua Bamboo Slips, with earliest known decimal multiplication table is dated ~305 BC
Chinese mathematics used decimal positional notation, the "rod numerals" with distinct ciphers for numbers 1-10, & ciphers for powers of 10. The most advanced system in the world, it allowed numbers as large as desired; calculations could be done on the suan pan, or Chinese abacus.
• Period: 600 BCE to 529

## Greek Era

Greek mathematics- from the time of Thales of Miletus (~600 BC) to the closure of the Academy of Athens in 529 AD. in cities spread over the entire Eastern Mediterranean, from Italy to North Africa. The period following Alexander the Great is often called Hellenistic mathematics.
All surviving pre-Greek mathematics show inductive reasoning. Greek mathematicians, by contrast, used logic to derive conclusions from definitions and axioms, and used mathematical rigor to prove them.
• 518 BCE

# Pythagorean Arithmetic & Geometry

Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and putative founder of the Pythagoreanism movement. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem which bears his name.
• 300 BCE

# Euclid's Elements

Little is known about Euclid, 300BC, author of The Elements. He taught & wrote at the Museum and Library at Alexandria, founded by Ptolemy I.
Proclus' Commentary, 4th c. AD. states that Euclid collected, perfected and completed fragmentary works of others.
The Elements-- Basic facts
Written about 2300 years ago, No copies extant,
A few potsherds dating from 225 BC contain notes about some propositions, Many new editions issued, Earliest copy from 888AD
• 230 BCE

# Seive of Eratosthenes

The sieve of Eratosthenes is one of the most efficient ways to find all of the smaller primes. It is named after Eratosthenes of Cyrene, a Greek mathematician; although none of his works have survived, the sieve was described and attributed to Eratosthenes in the Introduction to Arithmetic by Nicomachus.
• 200 BCE

# The Nine Chapters on the Mathematical Art

a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BC, ending at the building of the Great Wall of China, the period of Han Dynasty - about 206 to 220 AD. The Nine Chapters sums up contemporary mathematical knowledge in China. Not for beginners, it contains assumptions of preexisting knowledge
The problems given are general, and can be applied in various situations, from surveying and engineering to taxation and administration.
• 250

# Mayan Number System

he Mayan civilisation had settled in the region of Central America from about 2000 BCE, although the so-called Classic Period stretches from about 250 CE to 900 CE.
The Mayan and other Mesoamerican cultures used a vigesimal number system based on base 20 (and, to some extent, base 5), The numerals consisted of only three symbols: zero, represented as a shell shape; one, a dot; and five, a bar. [http://www.storyofmathematics.com/mayan.html]
• 250

# Diophantus' Arithmetica

Arithmetica (Greek: Ἀριθμητικά) is an Ancient Greek text on mathematics written by the mathematician Diophantus in the 3rd century AD.[1] It is a collection of 130 algebraic problems giving numerical solutions of determinate equations (those with a unique solution) and indeterminate equations. Introduces symbols for powers of a number.
• Period: 400 to 1350

## Medieval Period

Medieval European interest in mathematics was driven by concerns quite different from modern mathematicians. One was belief that math provided the key to understanding the created order of nature "God had ordered all things in measure, and number, and weight"
In 12th c, European scholars traveled to Spain & Sicily seeking scientific Arabic texts,
14th century saw the rise of new mathematical concepts to investigate a wide range of problems, such as the mathematics of local motion.
• 415

# Death of Hypatia of Alexandria

Hypatia, (born c. 355 ce—died March 415, Alexandria), mathematician, astronomer, and philosopher who lived in a very turbulent era in Alexandria’s history. A scholar and teacher with a large following, she was caught up in the politics of the day, which led to her tragic death.
• 641

# Great Library of Alexandria Destroyed?

largest, most significant library of the ancient world. Flourished under the patronage of the Ptolemys, Major center of scholarship Constructed in 3rd c BC, til Roman conquest of Egypt 30 BC. Part of the Musaeum of Alexandria, where many of the most famous thinkers of the ancient world studied.
Created by Ptolemy I Soter, successor of Alexander the Great. Mostly papyrus scrolls, from 40,000 to 400,000 at its height.
[https://en.wikipedia.org/wiki/Library_of_Alexandria]
• Period: 820 to 1400

## Islamic Mathematics

The Islamic Empire- 8th century made significant contributions towards mathematics. In 9th c the Persian Muḥammad ibn Mūsā al-Khwārizmī wrote several books on Hindu–Arabic numerals & methods for solving equations; instrumental in spreading Indian mathematics to the West. He was the first to teach algebra in an elementary form for its own sake.
Other achievements of Muslims- adding the decimal point to Arabic numerals, discovery of trigonometric functions, algebraic & analytic geometry
• 1000

# Pope Sylvester II

Pope Sylvester II (c.946–12 May 1003) was Pope from 2 April 999 to his death in 1003. Originally known as Gerbert of Aurillac, a prolific scholar & teacher, he endorsed & promoted study of Arab & Greco-Roman arithmetic, mathematics, & astronomy, reintroduced to Europe the abacus & armillary sphere, lost to Latin Europe since the end of the Greco-Roman era. He is said to be the first to introduce in Europe the decimal numeral system using Arabic numerals. But Europe wasn't ready.
• 1070

# Omar Khayyam

Persian mathematician, astronomer & poet best known for the Rubaiyat; Measured length of the year as 365.24219858156 days. Wrote "Problems of Arithmetic", a book on music, & algebra before age 25
Later wrote "Treatise on Demonstration of Problems of Algebra" containing a complete classification of cubic equations w/ geometric solutions found by means of intersecting conic sections. Another achievement in this text is his realizing that a cubic equation can have more than 1 solution.
• 1202

The publication of Fibonacci's work introduced the Western world to the Hindu-Arabic numerals and calculation methods.
• 1298

# Zero Banned in Italy

For many years, account books were still
kept in Roman numerals. It was believed that the Hindu-Arabic numerals could be altered
too easily, and thus it was risky to depend on them alone in recording large commercial
transaction.
In 1298, the city council of Florence, Italy, banned the use of zero entirely
• Period: 1350 to

## Renaissance

The development of math & of accounting were linked; Books for children of merchants, sent to reckoning schools (in Flanders & Germany) or abacus schools (in Italy), taught skills for trade and commerce. For complex bartering operations or calculating compound interest, arithmetic was mandatory & algebra was useful.
In Summa Arithmetica, Pacioli introduced symbols for plus & minus in a printed book
Navigation & the need for accurate maps made trigonometry a major branch of mathematics
• 1535

# 16TH CENTURY MATHEMATICS - TARTAGLIA, CARDANO & FERRARI

n the Renaissance Italy of the early 16th Century, Bologna University in particular was famed for its intense public mathematics competitions. It was in just such a competition, in 1535, that the unlikely figure of the young Venetian Tartaglia first revealed a mathematical finding hitherto considered impossible, and which had stumped the best mathematicians of China, India and the Islamic world. [http://www.storyofmathematics.com/16th_tartaglia.html]
• 1545

# 1st Appearance of Complex Numbers

Tartaglia’s secret method of solving cubics was leaked to Gerolamo Cardano, who published it in his 1545 book "Ars Magna" along with work of his student Ferrari. Ferrari, realized he could use a similar method to solve quartics. In the Ars, Tartaglia, Cardano & Ferrari showed the 1st uses of complex numbers, a + bi, where i is imaginary unit √-1. Rafael Bombelli in the late1560's, showed exactly what imaginary numbers are & how to use them. [http://www.storyofmathematics.com/16th_tartaglia.html]
• Period: to

## Scientific Revolution

17th century saw an unprecedented increase of mathematical and scientific ideas across Europe. René Descartes' analytic geometry allowed Galileo & Kepler's planetary orbits to be plotted. Isaac Newton discovered the laws of physics & brought together the concepts of calculus. Pascal and Fermat stage for probability theory & the rules of combinatorics in their discussions over gambling. Leonard Euler (standardizing many modern math terms), Lagrange & Laplace dominated the 17th century
• # Napier's Bones

Napier's bones is a calculating device created by John Napier of Merchiston. Based on Arab mathematics & lattice multiplication, and Fibonacci's work in Liber Abaci. Napier published his work in 1617, Edinburgh, Scotland. Using the tables embedded in the rods, multiplication can be reduced to addition operations and division to subtractions. More advanced use of the rods can even extract square roots. Napier is also credited with the first use of the decimal point, and inventing logarithms.
• # June 8, 1637: Descartes Codifies Scientific Method

Descartes Discourse on the Method outlines his rules for understanding the natural world through reason & skepticism, forming the foundation of the scientific method still used. The 1st part was published 1662, 12 years after his death.
Descartes expressed his preference for mathematics as the basis & language of his new method. His essays on Geometry introduced the Cartesian coordinate system, still in use.
[https://www.wired.com/2010/06/0608descartes-publishes-scientific-method/]
• # Metric System Invented in France

The metric system, featuring meters, liters and kilograms, was adopted following the French Revolution and devised by a group of French scientists in an effort to create a system of standard measurements (at the time, thanks to local and regional practices, there were nearly 400 different ways to measure areas of land in France).
• # Rosetta Stone discovered

The Rosetta stone was an ancient inscription of an Egyptian decree, that was written in two forms of Egyptian hieroglyphics and in ancient Greek. This cracked the code to understanding hieroglyphics.
• Period: to

## Modern Era

19th century mathematics became increasingly abstract. It saw the development of 2 forms of non-Euclidean geometry, where the parallel postulate no longer holds. Abstract algebra began: Boole's algebra is the start of mathematical logic & has important use in computer science. In the later 19th century, Georg Cantor established the first foundations of set theory, which enabled the rigorous treatment of the notion of infinity & became the common language of nearly all mathematics
• Period: to

## Post Modern Era

The 20th century saw mathematics become a major profession. Every year, 1000's of new Ph.D.s in mathematics were awarded, jobs were available in both teaching & industry. David Hilbert set a list of 23 unsolved problems in mathematics. These problems, spanning many areas of math, formed a central focus for much of 20th-century mathematics. Today, 10 have been solved, 7 are partially solved, and 2 are still open. The remaining 4 are too loosely formulated to be stated as solved or not.
• # Introduction of Fractals

Fractals are the geometry of nature, they describe the texture of reality! This idea was introduced by French mathematician, Benoit Mandelbrot. In 1975 he coined the word ‘fractal’ to describe shapes that are detailed at all levels of scale. What started as an investigation into an obscure area of math led to the field of fractal geometry. “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line”
• # 1st Computer Aided Proof

Kenneth Appel and Wolfgang Haken use a computer to prove the Four color theorem,
• # Poincare Conjecture Proven

Grigori Perelman proved the Poincare Conjecture, one of the seven famous unsolved Millennium Prize Problems.