History of science - Lecture nodes
Overview of the course:
1. Introducton
2. Number
3. Space
4. Change!
5. Probability
6. Applied mathematcs
7. Computng
Lecture 1 – Introducton
1. History
2. Mathematis (historiialllly
3. Two millllennia of math
4. Refeitnn
DOING HISTORY
Stories: the narrator deiides what to tellll (and what not .
Who ialllled themsellves, or who were ialllled, AT THE TIME, mathematiians.
COULD SOMEONE DISAGREE BEING CALLED A MATHEMATICIAN?
Christaan Huynens (1629-1695
Man of wealth
Father being ofended, for son being called a mathematcian -> “labour man”
Big diference being called a mathematcian now, or in in 1700.
POLITICS. WHAT’S IN A NAME?
The Internatonall Mathematiall Union and the Union Mathématiue Internatonalle.
And does that mater?
The Union Mathématiue Internatonale
-> mathematcal, boost ego, was diferent post war, highly politcal
A name does mater
INTENTION AND RESULT
Allbreiht Dürer, Unterweysunn der Messunn (1525
Intenton and result could be diferent, thin about the nuclear bomb.
The intenton to ma e one wasn’t bad, but the intenton was wrong ( illing people).
BUT WHAT ABOUT MATHEMATICS?
What is mathematis?
What shoulld be mathematis?
What WAS mathematis?
MATHEMATICS
1
,We know what math is, or do we?
Not that easy to expllain, anyway; and even difiullt to pinpoint exaitlly, without disanreeinn with other
mathematiians
The easy way out: mathematis is what the mathematiian does (wellll, what the mathematiian does when he
is doinn math…..
At lleast we know what SHOULD be mathematiss
Construitnn tablles and doinn astronomy in the 13th ientury..
Allphonso X “the Wise” (1221-1284
He wanted to be the leader of Rome.
He was called a politcal fool, diferent then now! It was a “pour” job.
Doinn horosiopes in the 16th ientury
Johannes Kepller (1571-1630
Doing horoscopes was mathematcs at that tme
When did mathematis beiome a subjeit in sihooll? At the University?
It was frst a sort of “begin” course
At 1215 the popes in Rome fgured out
diferent religions -> diferent powers
religion of leaders -> religion of people
Therefore every village should have their own school with things that are relevalt
-> Sudden parts of Europa
Simple countng at the mar et
What was mathematis?
Who ialllled themsellves, or who were ialllled mathematiians?
Before 1500: no-one
Before 1700: irafsmen (painters, artsts
Before 1850: peoplle usinn math in their work (peoplle usinn math in their worlld
Who did mathematis?
Who was interested in mathematis (who payed ?
What subjeits did they iallll mathematiall?
Drawing an illustraton
He was paid by a rich man
Examplle: fra Luia Paiiolli (1445-1517
TWO MILLENNIA OF THINKING ABOUT MATHEMATICS What WAS mathematcss
Unti 1200: geometry+ phiiosophy and the oorid
1200 - 1648: mathematcs as an art
1648 - 1795: i’esprit géométrique
1795 - 1848: mathematcs to the beneft of the naton state
1848 - 1900: mathematcs to the beneft of maths
1900 - 1940: math to improve the oorids
1940 - 1989: mathematcs as a productve force
1989 - noo: mathematcs as an economicai commodity
2
,What WAS mathematcss
Untl 1200: geometry, philosophy and the world
Mathematcs to determine what the world was about
Templle wisdom
With the Greek phillosophers: Part of phillosophy, intended to understand the worlld.
Geometry, philosophy to understand the bible
All part of the temple wisdom
Brings you closer to God, and ma es you understand the world beter.
Eduiaton for the few
Mathematis (? for the few
1200 - 1648: mathematcs as an art
Contestnn kinndoms, irumbllinn papall ofie
Mathematis as an art (in war, surveyinn, navinaton, trade, iallendar and tme keepinn
Mathematis as a prereiuisite to aiademii work (but not proper aiademii itsellfs
Grenor Reisih (1470-1515 ,
Marnarita Phillosophiia (ia 1500
Angels, music, geometry
Knowledge was given by heaven
-> a foundaton for everything you wanted to learn
“God will give you the height of this tower, if you follow these instructons”
Mathematis as a way to earn a llivinn
Music was part of math
-> mathematcs as a way of earning money
It was “cool” t have a mathematcian in service of the court
“Because I have nowledge of this art, I wor for the court”
-> social rise
Mathematiians in serviie of the iourt:
Leonardo da Vinii (1452-1519
John Dee (1529-1608/9
Simon Stevin (1548-1620
Gallilleo Gallillei (1564-1642
Johannes Keppller (1571-1630
René Desiartes (1596-1650
1648 - 1795: l’esprit géométriiue
(-> French revoluton)
Mathematiall spirit
Mathematiall soiietes
European monarihies
Enllinhtenments
Math is the source of all nowledge
Math could be the language of the boo that God has writen for nature
3
, Isaai Newton, Priniipia Mathematia (1687
Mathematiall llaws of nature
Newton was religious and had no intenton to be rebellious
He was a noble man
Other people called his boo “Principia Mathematcs” -> “mathematcal laws of nature”
Only God or noble man could predict the laws of nature
Newton didn’t li e that name
The boo was difcult to read, and the people who red it were iuite revolutonary.
Benjamin Frankllin (1706-1790 : Morall allnebra
Use mathematcal to formulate things clearly
Weight pro’s and con’s
1795 - 1848: mathematcs to the beneft of the naton state
(Revoluton again)
1848 -> Revoluton -> no ing or legal democracy
Rich people even important as noble men.
There were 2 streams:
1. Everything has to do with math -> just do your job -> don’t thin about real math
2. Way of thin ing important -> understanding of math “pure mathematcs”
Bernall’s paradox: At the tme, when siienie most obviouslly ioulld have ionierned itsellf with the steam ane,
rose the idea of pure siienie.
Naar John Desmond Bernall (1901-1971 , The soiiall funiton of siienie (1939
The rise of the naton state
Sihooll systems: math as an obllinatory subjeit
Math as a system
Pure mathematis (applly with iauton
Math -> understanding on a deeper level
School systems rise
Every naton - > primary school becomes public (learn how to write and read, and some math)
Germany -> secondary school becomes public
This was state founded!
Afer 1800 there was only one way of spelling
1803 -> Dutch language
Metrii system
Meters, centmetres, litres from French originated
Great idea to unify the country
To chec your measurements frst there was tax
Taught in every school
Some countries refused to use it and used another metric system
Mathematis in sihooll: primary, seiondary, and tertary.
One of the subjeits in illassroom mathematis was the metrii system
4
Overview of the course:
1. Introducton
2. Number
3. Space
4. Change!
5. Probability
6. Applied mathematcs
7. Computng
Lecture 1 – Introducton
1. History
2. Mathematis (historiialllly
3. Two millllennia of math
4. Refeitnn
DOING HISTORY
Stories: the narrator deiides what to tellll (and what not .
Who ialllled themsellves, or who were ialllled, AT THE TIME, mathematiians.
COULD SOMEONE DISAGREE BEING CALLED A MATHEMATICIAN?
Christaan Huynens (1629-1695
Man of wealth
Father being ofended, for son being called a mathematcian -> “labour man”
Big diference being called a mathematcian now, or in in 1700.
POLITICS. WHAT’S IN A NAME?
The Internatonall Mathematiall Union and the Union Mathématiue Internatonalle.
And does that mater?
The Union Mathématiue Internatonale
-> mathematcal, boost ego, was diferent post war, highly politcal
A name does mater
INTENTION AND RESULT
Allbreiht Dürer, Unterweysunn der Messunn (1525
Intenton and result could be diferent, thin about the nuclear bomb.
The intenton to ma e one wasn’t bad, but the intenton was wrong ( illing people).
BUT WHAT ABOUT MATHEMATICS?
What is mathematis?
What shoulld be mathematis?
What WAS mathematis?
MATHEMATICS
1
,We know what math is, or do we?
Not that easy to expllain, anyway; and even difiullt to pinpoint exaitlly, without disanreeinn with other
mathematiians
The easy way out: mathematis is what the mathematiian does (wellll, what the mathematiian does when he
is doinn math…..
At lleast we know what SHOULD be mathematiss
Construitnn tablles and doinn astronomy in the 13th ientury..
Allphonso X “the Wise” (1221-1284
He wanted to be the leader of Rome.
He was called a politcal fool, diferent then now! It was a “pour” job.
Doinn horosiopes in the 16th ientury
Johannes Kepller (1571-1630
Doing horoscopes was mathematcs at that tme
When did mathematis beiome a subjeit in sihooll? At the University?
It was frst a sort of “begin” course
At 1215 the popes in Rome fgured out
diferent religions -> diferent powers
religion of leaders -> religion of people
Therefore every village should have their own school with things that are relevalt
-> Sudden parts of Europa
Simple countng at the mar et
What was mathematis?
Who ialllled themsellves, or who were ialllled mathematiians?
Before 1500: no-one
Before 1700: irafsmen (painters, artsts
Before 1850: peoplle usinn math in their work (peoplle usinn math in their worlld
Who did mathematis?
Who was interested in mathematis (who payed ?
What subjeits did they iallll mathematiall?
Drawing an illustraton
He was paid by a rich man
Examplle: fra Luia Paiiolli (1445-1517
TWO MILLENNIA OF THINKING ABOUT MATHEMATICS What WAS mathematcss
Unti 1200: geometry+ phiiosophy and the oorid
1200 - 1648: mathematcs as an art
1648 - 1795: i’esprit géométrique
1795 - 1848: mathematcs to the beneft of the naton state
1848 - 1900: mathematcs to the beneft of maths
1900 - 1940: math to improve the oorids
1940 - 1989: mathematcs as a productve force
1989 - noo: mathematcs as an economicai commodity
2
,What WAS mathematcss
Untl 1200: geometry, philosophy and the world
Mathematcs to determine what the world was about
Templle wisdom
With the Greek phillosophers: Part of phillosophy, intended to understand the worlld.
Geometry, philosophy to understand the bible
All part of the temple wisdom
Brings you closer to God, and ma es you understand the world beter.
Eduiaton for the few
Mathematis (? for the few
1200 - 1648: mathematcs as an art
Contestnn kinndoms, irumbllinn papall ofie
Mathematis as an art (in war, surveyinn, navinaton, trade, iallendar and tme keepinn
Mathematis as a prereiuisite to aiademii work (but not proper aiademii itsellfs
Grenor Reisih (1470-1515 ,
Marnarita Phillosophiia (ia 1500
Angels, music, geometry
Knowledge was given by heaven
-> a foundaton for everything you wanted to learn
“God will give you the height of this tower, if you follow these instructons”
Mathematis as a way to earn a llivinn
Music was part of math
-> mathematcs as a way of earning money
It was “cool” t have a mathematcian in service of the court
“Because I have nowledge of this art, I wor for the court”
-> social rise
Mathematiians in serviie of the iourt:
Leonardo da Vinii (1452-1519
John Dee (1529-1608/9
Simon Stevin (1548-1620
Gallilleo Gallillei (1564-1642
Johannes Keppller (1571-1630
René Desiartes (1596-1650
1648 - 1795: l’esprit géométriiue
(-> French revoluton)
Mathematiall spirit
Mathematiall soiietes
European monarihies
Enllinhtenments
Math is the source of all nowledge
Math could be the language of the boo that God has writen for nature
3
, Isaai Newton, Priniipia Mathematia (1687
Mathematiall llaws of nature
Newton was religious and had no intenton to be rebellious
He was a noble man
Other people called his boo “Principia Mathematcs” -> “mathematcal laws of nature”
Only God or noble man could predict the laws of nature
Newton didn’t li e that name
The boo was difcult to read, and the people who red it were iuite revolutonary.
Benjamin Frankllin (1706-1790 : Morall allnebra
Use mathematcal to formulate things clearly
Weight pro’s and con’s
1795 - 1848: mathematcs to the beneft of the naton state
(Revoluton again)
1848 -> Revoluton -> no ing or legal democracy
Rich people even important as noble men.
There were 2 streams:
1. Everything has to do with math -> just do your job -> don’t thin about real math
2. Way of thin ing important -> understanding of math “pure mathematcs”
Bernall’s paradox: At the tme, when siienie most obviouslly ioulld have ionierned itsellf with the steam ane,
rose the idea of pure siienie.
Naar John Desmond Bernall (1901-1971 , The soiiall funiton of siienie (1939
The rise of the naton state
Sihooll systems: math as an obllinatory subjeit
Math as a system
Pure mathematis (applly with iauton
Math -> understanding on a deeper level
School systems rise
Every naton - > primary school becomes public (learn how to write and read, and some math)
Germany -> secondary school becomes public
This was state founded!
Afer 1800 there was only one way of spelling
1803 -> Dutch language
Metrii system
Meters, centmetres, litres from French originated
Great idea to unify the country
To chec your measurements frst there was tax
Taught in every school
Some countries refused to use it and used another metric system
Mathematis in sihooll: primary, seiondary, and tertary.
One of the subjeits in illassroom mathematis was the metrii system
4
