Presentation on theme: "Lessons from the History of Mathematics"— Presentation transcript:
1Lessons from the History of Mathematics Tom OslerRowan University
2Is Mathematics a Humanity or a Science? HumanitiesThe branch of learning regarded as having primarily a cultural character and use, including languages, literature, history and philosophy.SciencesA branch of study that is concerned with observation and classification of facts, and especially with the establishment or strictly the quantitative formulation of verifiable general laws by induction and by hypothesis,
3Introduction Teaching math history for about 20 years I am not a historianSome of the opinions expressed are my personal view
4We discuss only Higher Mathematics Every civilization needed a simple number system and primitive geometryThis is NOT what we discussHigher MathematicsAlgebra, Trigonometry, Geometry with proofs, Calculus etc
5The 5 minute history of math There were only two principle explosions of mathematical creativityGreek 600 BC to 200 ADEuropean to today
6The 5 minute history of math Today math research is performed all over the world by both men and womenThis was not true only 40 years ago, when most researchers were men with names of European descentNote: Until 1800, mathematicians were known as “Geometers”, not mathematicians
7Lesson 1 The fragility of mathematics Few cultures nourished mathMost people born with math gift never had a chance to develop it
8Lesson 2 Motivation for doing math PlayChallenge problemsExploring the mind of GodPythagorians BCEverything is numberPtolemy ca ADKepler
9Quote from PtolemyI know that I am mortal and the creature of a day; but when I search out the massed wheeling circles of the stars, my feet no longer touch the earth, but, side by side with Zeus himself, I take my fill of ambrosia, the food of the gods.
10Quote from Kepler“Why waste words? Geometry existed before the Creation, is co-eternal with the mind of God, is God himself (what exists in God that is not God himself?); geometry provided God with a model for the Creation and was implanted into man, together with God’s own likeness-and not merely conveyed to his mind through the eyes”
11Lesson 3 Math is unlike any other academic study Does not change Euclid’s ElementsNo errors for yearsGod is a Mathematician
17The Tyger by William Blake Tyger! Tyger! burning bright, In the forests of the night, What immortal hand or eye Could frame thy fearful symmetry? In what distant deeps or skies Burnt the fire in thine eyes? On what wings dare he aspire? What the hand dare seize the fire?
18And what shoulder, and what art. Could twist the sinews of thy heart And what shoulder, and what art? Could twist the sinews of thy heart? And when thy heart began to beat, What dread hand, and what dread feet? What the hammer? What the chain? In what furnace was thy brain? What the anvil? What dread grasp Dare its deadly terrors clasp?
19When the stars threw down their spears, And watered heaven with their tears, Did he smile his work to see? Did he who made the Lamb, make thee? Tyger! Tyger! burning bright, In the forests of the night, What immortal hand or eye Dare frame thy fearful symmetry?
20Lesson 4 The mother of mathematics is astronomy/astrology Babylonian planet and star chartsGreek AstronomyEratosthenes BCmeasures earth diameter (error 5%)Hipparchus BCdistance to moon (error 5%)and to sun (error 2000 %)
21Lesson 4 The mother of mathematics is astronomy/astrology Motion of Sun, Moon, Planets and StarsDevelop Calendar of SeasonsMonth – Lunar cycleYear – Solar cyclePredict future events – AstrologyPositions of Sun, Moon and Planets on the Ecliptic Zodiac
27Lesson 4 The mother of mathematics is astronomy/astrology NavigationNeed to find longitude after 1500Newton ( )Invents calculusLaw of gravityUniversal Laws of motionNearly every great name in math from Kepler (1600) to Gauss (1850) worked on Celestial MechanicsPoincare and Chaos
29Lesson 5: The wheel in Mathematics is the decimal number system If the Greeks had known it, they would have understood irrationalsPossibly they would have invented algebra and analysis
30Lesson 6: A second wheel is shorthand math symbolism Before 1500, most problems in math were expressed by rhetorical language and not letters and symbols as we do in algebra.“The square of the unknown added to twice the unknown plus 4 vanishes”
31Lesson 7: Euclidean Geometry retarded Math development for almost 2000 years Today it is deadEven Newton wrote his principia in geometric language, and not with the calculus he invented