Quick Answers text
The Rosetta
Stone (Rosetta
Stone details) -
one message in hieroglyphic, demotic (later form of hieratic)
and Greek. From 196
BCE, discovered 1799 CE.
The Reisner
Papyrus (~2000
BCE) sections
Here are some views of the Rhind
Papyrus (~1650 BCE) - to give
you a sense of what this relic actually is.
Some values
from and comments about the 2/n table.
The Moscow
Papyrus
Here is a little bit from the Moscow
Papyrus (the
bit called problem 1.1 in our text). (~1900 BCE)
Some problems from the Rhind and
Moscow - translated. More
detailed version.
§1.2.2 and 1.3
Quick Answers text
The Berlin Papyrus (~1800 BCE)Some about Babylonian
base 60.
A nice overview of Babylonian tablets.
Babylonian quadratic solution on copy of YBC 6967 Details of
original solution. (~1800
BCE)
Bablyonian square root of 2 on YBC
7289 (~ 1700
BCE)
Plimpton 322 and some commentary, and some other information also. (~1800 BCE)
§2.1
Quick Answers text
§2.2
Speculative ancient roman music
Quick Answers text
Archimedes (~250 BCE) circle
formula, volumes,
and pi,
Hipparchus (134 BCE) (and
the moon). Roman calendars.
(45 BCE)
Heron's (~50 CE) formula.
Nicomachus (~100 CE), Menelaus (~100 CE) (planar
version of theorem / sphere
version), Ptolemy,
(~125 CE) Diophantus (~250 CE), Pappus (~325 CE), Hypatia (~400 CE), Proclus,
Eutocius, Boethius
§3.1
Very old Chinese music
Annotated Bibliography
assignment
Quick answers text
Outline of Chinese History. Written Chinese numeration. Image of Zhoubi suanjing (~100 BCE)
An image of nine chapters. Text from nine chapters.
Contents of nine chapters (excuse the
Wikipedia link - I do have this in a print source but this way I
don't need to scan it here). (1000 BCE -
200 CE)
Sun Zi (~450 CE) Chinese Remainder Theorem
Chang Ch'iu-Chien [Zhang Qiujian] (475 CE) indeterminant
problem
Wang Hs'iao-T'ung [Wang Xiaotong] (625 CE) cubic problem
Li Zhi (1248 CE) quartic problem
Yang Hui and Qin Jiushao (1247 CE) - Approximating quartics
Yang Hui's triangle
(1261 CE based on Jia Xian ~1050 CE)
Vedic
square doubling (-750 BCE)
Some Jain stories and many other links for multicultural
mathematics. (< 500 BCE)
Son of Chajaka (~300 CE)
Bakshali Manuscript "controversy" NOVA
about zero, Anaysis video,
AMS
article.
indeterminate equations from Bakshali.
Trig
tables (499 [Aryabhata] & ~550 CE)
Varahamihira (~550 CE) Arithmetic triangle for combinatorics -
perfumes made by choosing substances from a larger set
Brahmagupta (650 CE) Pulveriser (but reported in Bhaskara)
Lilavati
contents (~1150 CE)
Details from
Bhaskara (~1150 CE)
§4.1-2
Quick answers text
An overview of "Arabic mathematics".
Some from al-jabr. (800) by al-KhwarizmiEarly
decimal point (952)
al-Haytham on geometry. (~1000)
Abu'l Wafa's finger reckoning (~975) was an influence on things like this.
al-Biruni's
qibla problem (~1000)
Quick answers text
Lecture
Great
mosque - detail.
Friday
mosque
An
article about al-Khayyami and the ring of four almonds.
al-Khayyami on the cubic (1100)
al Samawa'l (1175)
al-Mu'taman's (1082) work with circles
and chords (long article)
ibn Mun'im's (1212) arithmetic triangle
Quick answers text
Translators, Rabbits, Pisa, and moreIf you want to know more (e.g. why 24?) about the Book of Squares
problem, look here.
§5.2
Quick answers text
Dionysius Exiguus 525
More on
Bede. 725
Letters
Alcuin Problems to Sharpen the Young 800
Pope
Sylvester II 980
Sestina
Jordanus
1250
§5.3
Quick answers text
1321 Levi ben Gerson justifies theory. Induction.1340
Nicole Oresme, graphs and infinite
series Harmonic
diverges
Quick answers text
Room of Masks (first century BC? - Rome)Abraham
with Angels (early
christian 548 AD)
Annunciation - Simone Martini
(14th century) attractive but not perspective
Madonna
in Majesty -
Duccio (14th century), progress is being made Last
Supper
1468
Paolo Uccello - Pawning
of the Host more progress
1415 Filippo Brunelleschi - Peepshow
1435
Leon Battista Alberti
1460
Piero della Francesca - Flagellation
School
of Athens
1494
Luca Pacioli - actual
Summa excerpts from
his Summa diagams
by da Vinci Last
Supper
1525
Albrecht Dürer - St.
Jerome, Designer
of the sitting man, Designer
of the lute. Melancholia
Perspective
Example
1545 Tartaglia notes on the controversy
(some of this will get pushed to next time)
1545 Cardano - Ars Magna (both his work and
Ferrari's)
1572
Bombelli
§6.2
Quick answers text1545 Cardano - Ars Magna (both his work and
Ferrari's)
1572
Bombelli
1463 Regiomontanus - on triangles
1525 Rudolff's notation
1550 Riese Arithmetic
book
1553
Stifel's triangle
1514 Copernicus
1525 Albrecht Dürer Some
pictures to end the day.
§7.1
Quick answers text
1582 Christoper Clavius (German working in Rome) last step to current calendar1650 Fermat - Last &
Little, 1636
Coordinates, Areas
1650 Pascal - Triangle (parallelogram visual), Conics (applet to visualise for circles - works for any conic section)
Quick Answers text
1585 Simon Stevin - decimals different tunings§7.3
1557 Recorde - English arithmetic
§8.1
Quick Answers text1734 Berkeley - analyst
1715 Brook Taylor - series
1742 Maclaurin - calculus book
excerpts book
1757 Simpson - writing
Some §8.2 preview
1702 Johann Bernoulli - integrating rational functions
1696 l'Hospital Textbook
§8.2
Bernoulli
family tree
1713 Jakob Bernoulli - large numbers
1742 Goldbach conjecture
1748 Euler - trig &
FLT original
introductio
1749 Agnesi calculus
book precalculus
1770 Lambert - irrational
π
§8.3
Quick Answers text
1740 Emilie du Châtelet§9.1 - 9.2
Quick Answers textAnalysis
Algebra
§9.3-4
Two theme music pieces for today from the reading:
1848 Johann
Strauß, Sr.
1849 Johann
Strauß, Jr.
Quick Answers text
1824 Abel - quintic
1828 Green
1854 Riemann - Geometry
1888 Dedekind - cuts
1872 Weierstraß
1882 Klein
1871 Betti
1870 Camille Jordan
§10.1
Quick Answers text
1791 Banneker - Overview&c more 1918 journal article about - Jefferson on Mathematics1820 Bowditch
1808 Adrain - Least
Squares and more
1843 Hamilton - Quaternions - bridge1, 2, 3 - Ireland
1870 Benjamin Peirce
1903 Charles Saunders Peirce
1871 Tait - Scottish
1873 Maxwell - Scotland /
England
1844 Grassman - Germany / Poland
1884 Gibbs
1867 Dodgson - commentary on mathematics - determinant theorem - England
§10.2
Theme music.
Quick Answers text
1878 Hill - AMS
1888 Glaisher
1891 Steinmetz
1892 E. H. Moore - geneology
1896 Bolza
1895 Barnum
1898 Slaught - 1915 MAA
1905 Veblen - Topology
Book
Linear Algebra
§11.1-2
1829 Lobachevsky
1825 Bolyai
1868 Beltrami
1854 Chebyshev
1886 Markov
1882 Mittag-Leffler
1889 Poincare
1960 Lorenz
1883 Cantor
1867
Nobel
1924
Fields Medal
1900 Hilbert
§11.3
Quick
Answers text
"A continuum K is called a curve if to each point in K there exist arbitrary small neighbourhoods whose boundaries do not contain any continua. A continuum K embedded in a space is called a curve if to any point in K arbitrary small neighbourhoods exist whose boundaries do not have any continua in common with K. A continuum is described in the usual way as a non-empty closed set which is indecomposable (a set which, if written as a disjoint union of two closed sets, would imply that one was empty)." Menger, 1925.
1927 HahnCrisis in Foundations
§11.4
Quick Answers text
Bieberbach
Pasch
Neugebauer
Weyl
Lefschetz
G.D.
Birkhoff
RL Moore
Marston Morse
Alexander
Bell
Dehn
Enigma, again
Rejewski - Bomb
1940 Turing - Bombe Colossus
Turing
machine. Simulator. Church-Turing Thesis
and computability.
Alfred Tauber
Goldbach - Renyi
Garrett Birkhoff
Nash
Arrow
Scholes / Black
Hanna & B.H. Neumann
Claude Shannon - article
1951 Arrow's Impossibility Theorem
Game Theory
1927 von Neumann + 1944 MorgensternMathematician map
Latin America
1912 PrietoSubsaharan Africa
1953 ObiJapan
MathematiciansPythagoreans - cult of small number ratios
Plato - platonic ideal of some mystical reality in a superhuman place - numbers and perfect geometry, know by having some supernatural experience
St. Augustine - ties classical philosophy to Christianity. c 400 CE
Leibniz - searches for an ideal language
Kant - moral imperative of one true geometry
Hyperbolic geometry and space-filling curves shake geometric foundations, so other foundations are sought
Brouwer intuitionism - eliminate REM, and proof by contradiction. No existence proofs.
Hilbert's formalism - mathematics is a meaningless fiction
Related: Cantor's real numbers - the uncountable part is *indescribable*.
There's another option: mathematics is a human creation. Aristotle didn't accept Plato's mythical ideals. Hume and d'Alembert write of a mathematics that lacks absolute certainty, but merely human agreement. CS Peirce writes of truth in mathematics being determined communally and of the necessity of intuition.
Ludwig Wittgenstein 1940 Austrian. Proofs and mathematics is true because we accept it as true. Rules are enforced by agreement. But then takes it further to therefore we can do it any way.
Imre Lakatos 1964 Hungarian. Logic is something that is an object inside mathematics, but not mathematics as a whole. We cannot understand all of mathematics by simply knowing how logic works. Mathematics is human, but starts at the basics that humans agree upon, not arbitrary basics, but basics connected to human experience.
Claude Bragdon Primer of Higher Space (1939)
Introduction to Four Dimensional Vistas (1916)
There are two notable emancipations of the mind from the tyranny of mere appearances that have received scant attention safe from mathematicians and theoretical phyisicsts.
In 1823 Bolyai declared with regard to Euclid's so-called axiom of parallels, "I will draw two lines through a given point, both of which will be parallel to a given line." The drawing of these lines led to the concept of the curvature of space, and this to the idea of higher space.
The recently developed Theory of Relativity has compelled the revision of the time concept as used in classical physics. One result of this has been introduce the notion of curved time.
These two ideas, of curved time and higher space, by their very nature are bound to profoundly modify human thought. They loosen the bonds within which advancing knowledge has increasingly labored, reconcile the discoveries of Western workers with the inspirations of Eastern dreamers; but best of all, the open vistas, the offer "glimpses that make us less forlorn."
Return to my homepage .
