History of Math

In the beginning…

• Humans noticed and tried to make sense of patterns.

• What types of things do you think humans noticed that they needed to keep track of?– Seasons– Migration– Estimating sizes of animal herds– Geography

Egyptians

• 3200-343 BC - formal dynasty

• Flooding of Nile - tracking for agriculture

• Measuring land for taxes

• Dividing harvest to offer to gods

• Knotted ropes 3, 4, 5

• Pyramids, Sphinx

Sumerians

• Height 2000 BC

• Mesopotamia (now Iraq)

• Numbers were the first written language

• To keep track of payments in trade system in city

• Base 60

Babylonians

• 1500 BC - also Mesopotamia

• Practiced math to build skill

• Base 60 system

• Used place value (used a space for ‘zero’)

• Studied astronomy, quadratic equations

Ancient Greece

• 700 BC - 600 AD

• Base 10, used letters as numbers

• No place value

• All geometry

• Math was scholarly pursuit, more focused on abstraction and proof

• Ended by Roman invasion

Greek Accomplishments

• Pythagorean Theorem• Discovery of irrational numbers• Platonic solids• Archimedes’ approximation of pi• Euclid’s Elements• Hypatia• Anyone else?

China

• The Nine Chapters, written by Chinese scholars from 10th - 2nd centuries BC;

• Training in math important for government workers - utilitarian;

• The Great Wall - started in 7th century BC, most built during Ming Dynasty in 14th century AD;

China

• Used rods with place value for computation, but recorded numbers as characters;

• Abstract mathematics studied by scholars, e.g. Chinese Remainder Theorem, Magic Squares

• Qin JiuShao (13th century AD) - military mathematician who made breakthroughs in volume and cubic equations

India

• Zero as the concept of nothing, not just a placeholder, cultural relevance of 0;

• Origin of Hindu-Arabic numerals (8th century AD) we use today - Brahmi numerals (from 300 BC);

• Developed trigonometry to measure distance to objects in sky (5th century AD);

India

• Brahmagupta (598-668) - rules for arithmetic with 0, first to write abstract equations with letters - algebra;

• Spread of Islam (8th century) - pursuit of knowledge is key to fulfilling life’s purpose for God;

• House of Wisdom (8th century) - center for teaching mathematics & science;

• Al Khwarizmi (780-850) - important scholar at H of W - developed and taught algebra and more;

Pre-Renaissance Europe

• Fibonacci (1170-1220) - brought Hindu-Arabic numerals to Italy;

• University of Bologna (founded in 1088) held mathematical contests - drew many spectators;

• Printing press - 1440 - Fibonacci’s Liber Abaci spread Hindu-Arabic numerals to rest of Europe;

Early Renaissance Europe

• Piero della Francisca (1415-1492) mathematician & artist who developed perspective;

• Leonardo da Vinci (1452-1519)• Tartaglia vs. Cardano (15th century) - solved

cubic equations;• Galileo (1564-1642) major advancements in

astronomy;

Late Renaissance Europe

• Rene Descartes (1596-1650) - invented Cartesian coordinate plane which bridged Geometry & Algebra, key thinker in Rationalism school of philosophy “I think, therefore I am”

• Marin Mersenne (1588-1648) - monk, music theorist, mathematician, described Mersenne Primes

• Pierre de Fermat (1601-1665) - famous for Fermat’s Last Theorem

18th-19th century Europe

• Isaac Newton (1642-1727) vs. Gottfried Liebniz (1646-1716) - Calculus;

• Leonard Euler (1707-1783) - number e;• Maria Agnesi (1718-1799) - first female math

professor, book on calculus;• Sophie Germain (1776-1831) - laid foundation for

data encryption later used to solve Fermat’s Last Theorem;

• Henri Poincare (1854-1912) - furthered Hyperbolic Geometry;

18th-19th Century

• Carl Friedrich Gauss (1777-1855) - Number Theory, Magnetism, questions Euclid’s 5th postulate;

• Janos Bolyai (1802-1860) - developed Non-Euclidean Geometry;

• Bernhard Riemann (1826-1866) - Riemann sums in Calculus, number theory.

20th Century and Beyond

• Georg Cantor (1845-1918) - crazy for infinity;• Albert Einstein (1879-1955) - equation pulled

together others’ theorems;• Emmy Noether (1882-1935) - abstract

algebra, Einstein wrote her eulogy;• John von Neumann (1903-1957) - started

Game Theory;• Benoit Mandelbrot (1924-2010) - father of

Fractal Geometry.