Lessons from the History of Mathematics

Tom Osler

Rowan University

Is Mathematics a Humanity or a Science?

• Humanities• The branch of learning regarded as having

primarily a cultural character and use, including languages, literature, history and philosophy.

• Sciences• A 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,

The 5 minute history of math

• There were only two principle explosions of mathematical creativity

• Greek 600 BC to 200 AD• European 1500 to today

The 5 minute history of math

• Today math research is performed all over the world by both men and women

• This was not true only 40 years ago, when most researchers were men with names of European descent

• Note: Until 1800, mathematicians were known as “Geometers”, not mathematicians

The fragility of mathematics

• Few cultures nourished math

• Most people born with math gift never had a chance to develop it

Math is unlike any other academic study

Does not change

Euclid’s Elements

No errors for 2300 years

God is a Mathematician

The mother of mathematics is astronomy/astrology

Babylonian planet and star chartsGreek Astronomy

Eratosthenes 276-194 BC measures earth diameter (error 5%)

Hipparchus 190-120 BC distance to moon (error 5%) and to sun (error 2000 %)

Lesson 4 The mother of mathematics is astronomy/astrology

Motion of Sun, Moon, Planets and Stars–Develop Calendar of Seasons

• Month – Lunar cycle• Year – Solar cycle

–Predict future events – Astrology• Positions of Sun, Moon and Planets

on the Ecliptic Zodiac

Apollonius 256-190 BC invents epicyclic motion

Ptolemy – Almagest 150 ADEarliest trig tablesPredicts planet positions with an

accuracy one degree in 100 years

The mother of mathematics is astronomy/astrology

• Navigation– Need to find longitude after 1500

• Newton (1643-1727) – Invents calculus– Law of gravity

– Universal Laws of motion• Nearly every great name in math from Kepler

(1600) to Gauss (1850) worked on Celestial Mechanics

• Poincare and Chaos

2r

GMmF

The wheel in Mathematics is the decimal number system

• If the Greeks had known it, they would have understood irrationals

• Possibly they would have invented algebra and analysis

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”

0422 xx

Lesson 7: Euclidean Geometry retarded Math development for almost 2000 years

• Today it is dead• Even Newton wrote his principia in

geometric language, and not with the calculus he invented