1. Lessons from the History of Mathematics
Tom Osler
Rowan University

2. 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,

3. The 5 minute history of math
There were only two principle explosions of mathematical creativity
Greek 600 BC to 200 AD
European to today

4. 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

5. The fragility of mathematics
Few cultures nourished math
Most people born with math gift never had a chance to develop it

6. Math is unlike any other academic study
Does not change
Euclid’s Elements
No errors for 2300 years
God is a Mathematician

8. The mother of mathematics is astronomy/astrology
Babylonian planet and star charts
Greek Astronomy
Eratosthenes BC measures earth diameter (error 5%)
Hipparchus BC distance to moon (error 5%) and to sun (error 2000 %)

9. 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

10. Apollonius 256-190 BC invents epicyclic motion
Ptolemy – Almagest 150 AD
Earliest trig tables
Predicts planet positions with an accuracy one degree in 100 years

11. The mother of mathematics is astronomy/astrology
Navigation
Need to find longitude after 1500
Newton ( )
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

12. 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

13. 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”

14. 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