Cultural Perspectives on Mathmematics

By 16PINECONES
  • Period: 4000 BCE to 2334 BCE

    Sumerian City-States

    Tokens and tokens in clay envelops were found with their impressions on the outside. These tokens were probably used for accounting to claim resources. This eventually created the need for a written number system where symbols were used to represent numbers.
  • Period: 2334 BCE to 2250 BCE

    Akkadian Empire

    Sargon of Akkad conquers Mesopotamia including Sumer. The Sexagesimal Place-value system (SPVS) with base 60 was developed during this time and would be used throughout Mesopotamia and Greece
  • Period: 2112 BCE to 1792 BCE

    Sumerian-City States

    Gutians invade Akkadian Empire in 2250BC, but Sumerians defeat the Gutians around 2112BC. They develop City States that are each ruled mini-empires.
  • Period: 2112 BCE to 2004 BCE

    Ur III

    Ur III is one of the strongest Sumerian city state. Scribes are the people learning to do mathematics at this time. They focus on applied problems with very recipe like procedures in the context of real world problems. Ur-Namma, the last king of Ur III establishes equity by standardizing weight and measurement.
  • Period: 2040 BCE to 1500 BCE

    Egyptian Middle Kingdom Period

    During this period, scribes are trained in school like in Mesopotamia. There are many Egyptian mathematical texts with writing in hieroglyphs. They developed a system of symbols to represent numbers, and they developed a way to express fractions in the form of reciprocals.
  • Period: 2017 BCE to 1763 BCE

    Isin and Larsa

    Isin: 2017-1763BC. Larsa 1897-1763BC. These are two more strong Sumerian city states. A tablet by the name of Pimplton 322 which uses the SPVS base 60 number system was found to have probably come from this time.
  • Period: 1900 BCE to 1595 BCE

    Babylon

    Babylon started as an Akkadian town and then became another Sumerian City State. Hammurabi ruled as king until 1749BC for what is now known as Old Babylonian Empire. He created a code known as Hammurabi's Law Code which helped develop administration of empires. Eventually, the Hittites took over the Old Babylonian Empire.
  • Period: 1600 BCE to 1050 BCE

    Shang Dynasty China

    Oracle Bones have been found from this time period which show evidence for a Chinese decimal, positional number system.
  • Period: 1500 BCE to 500 BCE

    Vedic Period India

    Indo-Aryan Nomads settling in Northern India and establishing small kingdoms. They established the Caste System. Brahmanas (priests) are doing math handed down from father to son. They have math texts like Sulbusutras on understanding the sacred Vedas. They also have texts on mathematics relating to building fire alters using geometry.
  • Period: 1050 BCE to 250 BCE

    Zhou Dynasty China

    Counting mats first appear as a way to do basic arithmetic. Private schools are string to appear.
  • Period: 900 BCE to 636 BCE

    Neo-Assyrian Empire

    At this time, there is a lot of conquest of empires. This is the Neo-Assyrian Empire. People come in and out of rule at this time
  • 800 BCE

    Thales

    Thales is a Greek philosopher who had a larger impact on the development of mathematics. He is known as the father of deductive reasoning or deductive proofs. He used this in his theorems for geometry.
  • Period: 800 BCE to 400 BCE

    Greece Archaic Period

    This period births many Greek philosophers. They focus on natural philosophy like substance and change. Most philosophers deduce conclusions with models and did not use experiments.
  • Period: 800 BCE to 400 BCE

    Pythagoras and the Pythagoreans

    Pythagoras is a cult leader who established rules for living which could influence one's fate of death. He tales a lot of stories that modernly we don't believe. The pythagoreans were followers of Pythagoras who more definitely studied math.
  • Period: 636 BCE to 539 BCE

    Neo-Babylonian Empire

    During this time, the land was under rule of Neo-Babylonian Empire.
  • Period: 539 BCE to 330 BCE

    Persian Empire

    This is a Babylonian center of astronomy and math. We start to see the rise of Babylonian astronomy where people make connections to things in the heavens to on Earth. Procedural texts and lists begin to be created of the heavens in which people will study patterns and use arithmetic to try and predict what will happen.
  • Period: 530 BCE to 450 BCE

    Hippasus

    He is one of the people of this time to actually perform experiments to prove harmonic correspondences. He describes ratios in music with whole numbers.
  • Period: 500 BCE to 200 BCE

    Pre-Classical India

    This time period started the rise of larger Kingdoms in India amd the first empire, Mauryan Empire. There is a rise of Buddhism and Jainism religions. Ashoka introduces Brahmi Script which is an additive/decimal numerical system. Pengala does work on combinatorics with poetic meter. These texts are in sutra style. Brahmanas or priests, Buddhist monks, and merchants perform most of the mathematics for commerce, religious study, and exploration.
  • Period: 480 BCE to 323 BCE

    Classical Greece

    This time period is the birth of more philosophers in Greece like Plato, Aristotle, and Eudoxus.
  • Period: 470 BCE to 385 BCE

    Philolaus

    He was a philosopher who believed the world is the product og harmonious things fitting together. He describes the unlimited with the limited
  • Period: 428 BCE to 347 BCE

    Archytas

    Archytas was a philosopher who believed every magnitude to be whole number ratios known as commensurability. He showed it is impossible to divide basic musical intervals "in half."
  • Period: 427 BCE to 337 BCE

    Eudoxus

    Eudoxus applies a lot of Aristotle's thoughts to mathematics. He comes up with a resolution for the crisis of incommensurability with his work in ratios. He uses a method of exhaustion that enables different proofs in geometry. Eudoxus also creates a geocentric model of the universe.
  • 425 BCE

    Plato

    Plato was an aristocrat philosopher who works with only perfect world theoretical mathematics. He describes the world of forms and the world of materials. Plato believes knowledge comes from remembering forms.
  • Period: 348 BCE to 323 BCE

    Aristotle

    Aristotle was a student of Plato who, unlike Plato, believes knowledge comes from experience and the abstraction from those experiences via reason. He uses reasoning via deductive reasoning and makes claims based on "earlier" claims on top a foundation of claims. He also explains the difference between potential and actual infinity.
  • 335 BCE

    Ptolemaic Kingdom

    Ptolemy is one of Alexander the Great's friends that rules part of his land after he dies. In this land is the capital, Alexandria. This is the city of economic, political, and cultural power. It houses a museum and library of Alexandria with many texts that scholars go to to study mathematics.
  • Period: 323 BCE to 149 BCE

    Seleucid Empire

    Alexander the Great rules the land under the Greeks until death in 323BC. After the his death, his friends each rule different parts of his land. Seleucus rules the Seleucid Empire. They continue to study astronomy through the use of texts and lists. They use the base 60 system to measure time of day, and they use the zodiac to measure time of year.
  • Period: 323 BCE to 31 BCE

    Hellenistic Period

    This is a period in Greece after the death of Alexander the Great
  • 300 BCE

    Euclid

    Euclid studied in Alexandria and his goal was to organize and unite all known theoretical mathematics. His most famous work was the book, "The Elements" which include principles or geometry, proportions, number theory, and 3D geometry.
  • 220 BCE

    Aristarchus

    Aristarchus is a mathematician and astronomer from the island of Samos. He used hypotheses to measure the distance of the sun and moon via geometry.
  • 220 BCE

    Eratosthenes

    Eratosthenes uses Euclid's ideas in "The Elements" to measure. For example, he used similar triangle to measure the Earth. He then combines the size of the Earth and travel logs to create maps.
  • Period: 206 BCE to 220

    Han Dynasty China

    The period has an extensive use of bureaucracy. There is an establishment of an extensive Academy and other provincial schools. This time period marks the beginnings of trade with the west which evolves into the Silk Road. Zhou bi is an anonymous author texts written on calendrical astronomy. Suan Shu Shu is a text on basic calculations. Nine Chapters is a manual of bureaucratic math. Bureaucrats are mostly doing math now for accounting, assessment, astronomy, and calendars.
  • Period: 200 BCE to 650

    Classical India

    There is a continuation of large kingdoms including rise of Gupta Empire. The Silk Road, a trade route, starts to flourish. Astronomical texts by Siddhantas, trigonometrical sine tables by Aryabhata, systems of congruences called pulverizer by Brahmagupta are all developed. The first solid evidence for zero is found with a positional system in Bakshali Manuscript. Royally Patronized scholars and Buddist monks are doing mathematics and are teaching others in universities.
  • Period: 190 BCE to 120 BCE

    Hipparchus

    Hipparchus is from modern day Turkey. He studies mathematics with astronomy. He used theoretical based mathematics to do applied math.
  • Period: 149 BCE to 220

    Parthian Empire

    Still under Greek rule, they continue to study Babylonian Astronomy and use arithmetic to create texts and predict what will happen. They believe there is a connection between the things in the sky to things on Earth.
  • Period: 110 to 190 BCE

    Claudius Ptolemy

    Claudius Ptolemy used Hipparchus' and Euclid's work in the Roman Period (31BC to 395AD) to measure things. He is credited to using parts of circles and measuring its chord length. This was the first trigonometric function: the chord of an angle.
  • Period: 220 to 580

    Post-Han Dynasty China

    This is a very complicated time period for Ancient China as many people come in and out of power. Mathematical developments during this period include Liu Hui's adds commentating to Nine Chapters wit explanations to the problems. Zu Chongzhi creates a daming calendar, makes an approximation on pi and volume of sphere
  • Period: 580 to 907

    Sui and Tang Dynasty China

    This time period includes the establishing of institution of civil service exams for placement in the bureaucracy. A major math text studied during this time is the Ten Mathematical Manuals. Math is used for bureaucratic work like assessment, measurement, astronomy, and calendar making.
  • Period: 750 to 1258

    Abbasid Caliphate

    The Abbasids conquered the Umayyad Caliphate in 750. The Abbasids rule for a long time. They establish a new capital, Baghdad, with access to trade routes and encourage scholarly work. In 900s, the power of caliphs starts to erode from powerful families in provinces establishing Dynasties. 1258 is the end of the end of Abbasid Caliphate when Helugu Khan in the Mongol Invasion kills the last caliphs.
  • Period: 762 to 847

    House of Wisdom

    Under the Abbasid Caliphate, the The House of Wisdom, a cultural and scholarly center, was established in 762 and flourishes under the rule of al-ma'mun. Many mathematicians study and do work in the House of Wisdom.
  • Period: 800 to 850

    al-Kindi

    Al-Kindi works at the House of Wisdom under Abbasid Caliphate. He does work with mathematical cryptology and language studies by inventing frequency analysis.
  • Period: 800 to 850

    al-Kharizmi

    Al-Khwarizmi is a mathematician studying in House of Wisdom. He does work in equation solving, translated many Indian texts, he introduce Hindu numbers, and work in classifying the quadratics. He is also appointed by al-Ma'mun to measure the Earth in which he leads a team into desert to measuring one degree.
  • Period: 850 to 900

    Thabit ibn Qurra

    Thabit ibn Qurra works at the House of Wisdom. He is a translator of Greek mathematical works (Euclid, Ptolemy, etc.) He also does work in trigonometry with translating chord tables into sines and paved the way to real numbers by writing Hellenistic Greek ratios as fractions.
  • Period: 900 to 950

    Abu al-Wafa

    Abu al-Wafa works at House of Wisdom. He is associated with work in trigonometry and spherical trigonometry (spherical law of sines). He made a handbook for artisans on dissections with tiling.
  • Period: 929 to 1050

    Caliphate of Cordoba

    When the Abbasids overthrew Umayyads, one prince made to Spain and establishes the Emirate of Cordoba. In 929, this is renamed to the CALIPHATE OF CORDOBA. Abd al-Rahman III is the ruler/patron, and he establishes the University of Cordoba.
  • Period: 950 to 1000

    Al-Uqlidisi

    Al-Uqlidisi works at House of Wisdom. He works with base ten system and decimal fractions. He also does development with inheriting and using Hindu-Arabic system
  • Period: 950 to 1050

    Fatmid Caliphate

    Egypt is part of the Abbasid Caliphate for a long time until it is taken over by the FATIMID CALIPHATE. This Caliphate found a capital, the city of Cairo where there is established the Al-Azhar University. Ibn
  • Period: 1000 to 1050

    al-Haytham

    al-Haytham is a mathematician under the Fatmid Caliphate. He does work in physics, optics, geometry of reflections, and volume of paraboloids. He also participates in the critiques of Ptolemy saying that his data measurements and model don't agree. al-Haytham solves the fourth degree polynomial by using two conic sections in a way that proceeds Omar Khayyam.
  • Period: 1000 to 1050

    GHAZNAVID EMPIRE

    GHAZNAVID EMPIRE is part of the Abbasid Caliphate.
    The Mahmud of Ghazni is the ruler/patron. al-Biruni is a notable mathematician doing wok in this empire. He shows interests in geography, measures circumference of Earth using mountains and law of sines, and is famous for the qibla problem to find direction of Mecca using spherical trigonometry.
  • Period: 1050 to 1100

    Fall of Caliphate of Cordoba

    The Caliphate fractures into small kingdoms called Taifas due to Al-Hakem's death leaving his young son to rule. It is seized power of Almonzor who orders al-Hakem's library to be expunged of all objectionable material. The land then goes back and fourth between being run by a bunch of small kingdoms and then overrun by Dynasties from the south.
  • Period: 1100 to 1150

    SELJUK EMPIRE and Omar Khayyam

    SELJUK EMPIRE is one of the empires to start to taker over the Abbasid Caliphate. Malik Shah I is the ruler/patron. Omar Khayyam is a mathematician working in this empire. He does work in algebra and geometry especially with cubic equations. He is also famous for his work in classifying cubics.
  • Period: 1100 to 1150

    Al-Samawal

    Al-Samawal is a mathematician who works still under the Abassid Caliphate but while the region is under Seljuks rule. He does work with decimal fractions, polynomials, and systematizing exponents includes negative exponents.
  • Period: 1100 to 1350

    Western Europe

    Europeans are less interested in scholarly work. They had large churches in big cities with schools attached, but math is largely overlooked. Merchants are large driving force of mathematics with focus of practical math for commercial work where they picked up new ideas and techniques. The influx of Greek and Arabic texts renewed interest in math. Frederick II is an outlier with his weird science but also believes in doing similar things with universities and translators.
  • 1202

    Leonardo of Pisa

    Leonardo of Pisa, also known as Fibonacci, was a merchant in Western Europe who encountered various systems of numbers and arithmetic. He, after 3 prior fails, was an advocate for the Hindu-Arabic System. In 1202, he wrote a book, Liber Abaci. This book helped adopt the Hindu-Arabic numeral system and laid how how to use it. He is also known for the Rabbits problem, an example from his book, that derives the Fibonacci Sequence.
  • Period: 1205 to 1220

    Mongol Invasion

    MONGOL INVASION is a full scale invasion of Central Asia. This creates giant empire, but eventually breaks up into 4 Khanates.
  • Period: 1250 to 1300

    CHAGATAI KHANATE

    CHAGATAI KHANATE is 1/4 khanates as result from Mongol Invasion. They are not as conducive to mathematics as other Khanates because Central Asia was so destroyed. They are not as interested in Urban centers, Persian or Islamic cultures, and they kept to their nomadic ways and religion.
  • Period: 1250 to 1300

    ILKHANATE

    ILKHANATE is another 1/4 khanates as result of Mongol Invasion.
    al-Tusi is a mathematician doing work at this time period. He is credited with the creation of observatory at Maragha which brings together scholars from Islamic World. This is done under the patronage of Helugu Khan.
  • Period: 1400 to 1450

    Timurid Empire

    Ulugh Beg is the ruler/patron of the TIMURID EMPIRE. This empire established power shortly after the Mongol Invasion when conditions were unstable. Al-Kashi is a major mathematician in this empire. He does work in trigonometry like producing similar version of law of cosines useful for surveying. He also created many indigenous devices for measurement and calculation and created precise sine tables.