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 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 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. Solving Equations, Chinese Remainder Theorem, Magic Squares, applications to astronomy 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 ( ) - rules for arithmetic with 0, first to write abstract equations with letters – algebra, as well as negative numbers; 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 ( ) - important scholar at H of W - developed and taught algebra and more;

Pre-Renaissance Europe Fibonacci ( ) - brought Hindu- Arabic numerals to Italy; University of Bologna (founded in 1088) held mathematical contests - drew many spectators; Printing press Fibonacci’s Liber Abaci spread Hindu-Arabic numerals to rest of Europe;

Early Renaissance Europe Piero della Francisca ( ) mathematician & artist who developed perspective; Leonardo da Vinci ( ) Tartaglia vs. Cardano (15th century) - solved cubic equations; Galileo ( ) major advancements in astronomy;

Late Renaissance Europe Rene Descartes ( ) - invented Cartesian coordinate plane which bridged Geometry & Algebra, key thinker in Rationalism school of philosophy “I think, therefore I am” Marin Mersenne ( ) - monk, music theorist, mathematician, described Mersenne Primes Pierre de Fermat ( ) - famous for Fermat’s Last Theorem

18th-19th century Europe Isaac Newton ( ) vs. Gottfried Liebniz ( ) – Calculus; Bernoulli Family (late 1600’s to mid 1700’s) – family of mathematicians, artists, found applications for Calculus as well as probability and other areas of math and science. Leonard Euler ( ) - number e; pi, i Maria Agnesi ( ) - first female math professor, book on calculus; Sophie Germain ( ) - laid foundation for data encryption later used to solve Fermat’s Last Theorem;

18th-19th Century Carl Friedrich Gauss ( ) - Number Theory, Magnetism, questions Euclid’s 5th postulate, 2D representation of imaginary numbers; Janos Bolyai ( ) - developed Non- Euclidean Geometry; Bernhard Riemann ( ) - Riemann sums in Calculus, number theory, higher dimensions; Georg Cantor ( ) - crazy for infinity; Henri Poincare ( ) - furthered Hyperbolic Geometry, Chaos Theory, Topology;

20th Century and Beyond David Hilbert ( ) – 23 problems of Hilbert at International Congress of Mathematicians in Paris 1900; Albert Einstein ( ) - equation pulled together others’ theorems; Emmy Noether ( ) - abstract algebra, Einstein wrote her eulogy; John von Neumann ( ) - started Game Theory; Benoit Mandelbrot ( ) - father of Fractal Geometry.