History of Mathematics
http://www-history.mcs.st-andrews.ac.uk/index.html
Jamie Foster
AD 23-79: Prehistoric Mathematics
• A tally (or tally stick) was an
ancient memory aid device to
record and document
numbers, quantities, or even
messages. Tally sticks first
appear as notches carved on
animal bones.
• A notable example is the
Ishango Bone. Historical
reference is made by Pliny the
Elder (AD 23–79).
• Reference:
http://en.wikipedia.org/wiki/Leb
ombo_bone#Paleolithic_tally_s
ticks
1800 BC: Babylonian Mathematics
• Plimpton 322 is a Babylonian
clay tablet, notable as
containing an example of
Babylonian mathematics. This
tablet, believed to have been
written about 1800 BC, has a
table of four columns and 15
rows of numbers in the
cuneiform script of the period.
• This table lists what are now
called Pythagorean triples.
triples,
• Iraq
Reference:
• http://en.wikipedia.org/wiki/Hist
Reference:
ory_of_mathematics
http://en.wikipedia.org/wiki/Hist
ory_of_mathematics
1850 BC: Egyptian Mathematics
• The Moscow Mathematical
Papyrus is an ancient
Egyptian mathematical
papyrus, also called the
Golenishchev Mathematical
Papyrus.
• The 10th problem of the
Moscow Mathematical
Papyrus asks for a calculation
of the surface area of a
hemisphere.
• Approximate pi. 3.16049
• Reference:
http://en.wikipedia.org/wiki/Mo
scow_Mathematical_Papyrus
about 569 BC - about 475 BC
Greek Mathematics
• The Pythagorean theorem is
named after the Greek
mathematician Pythagoras,
who by tradition is credited
with its discovery and proof.
• The theorem can be written as
an equation relating the
lengths of the sides a, b and c,
often called the Pythagorean
equation.
• Reference:
http://en.wikipedia.org/wiki/Pyt
hagorean_theorem
(598-670 in India)
Indian mathematics
• In the 7th century,
Brahmagupta
explained the use of
zero as both a
placeholder and
decimal digit, and
explained the HinduArabic numeral
system.
• Reference:
http://en.wikipedia.org
/wiki/Brahmagupta
about 825: Islamic mathematics
• Al-Khwārizmī's contributions to
mathematics, he established
the basis for innovation in
algebra and trigonometry. His
systematic approach to solving
linear and quadratic equations
led to algebra, a word derived
from the title of his 830 book
on the subject.
• For example, x2 = 40x − 4x2 is
reduced to 5x2 = 40x.
• Reference:
http://en.wikipedia.org/wiki/Mu
%E1%B8%A5ammad_ibn_M
%C5%ABs%C4%81_alKhw%C4%81rizm%C4%AB
(about 1010-about 1070 in China)
Chinese mathematics
• Jia Xian
– Written two mathematics
books: Huangdi Jiuzhang
Suanjing Xicao (The Yellow
Emperor's detailed solutions
to the Nine Chapters on the
Mathematical Art), and Suanfa
Xuegu Ji (A collection of
ancient mathematical rules).
Both are lost and we know
nothing of the second of the
two books other than its title.
– Reference: http://wwwhistory.mcs.standrews.ac.uk/Biographies/Jia
_Xian.html
1500’s: Renaissance Mathematics
• Bartholomaeus: German
trigonometrist
• Driven by the demands of
navigation and the growing
need for accurate maps of
large areas, trigonometry grew
to be a major branch of
mathematics. Bartholomaeus
Pitiscus was the first to use the
word, publishing his
Trigonometria in 1595.
Regiomontanus's table of
sines and cosines was
published in 1533.
• Reference:
http://en.wikipedia.org/wiki/Bart
holomaeus_Pitiscus
19th Century Mathematics
• For the first time in 1823, the
limits of mathematics were
explored. Niels Henrik Abel, a
Norwegian, and Évariste
Galois, a Frenchman, proved
that there is no general
algebraic method for solving
polynomial equations of
degree greater than four
(Abel–Ruffini theorem).
• While studying in Cristiania
completed most of his notable
work.
• Reference:
http://en.wikipedia.org/wiki/Abe
l%E2%80%93Ruffini_theorem
20th Century Mathematics
• In 1976, Wolfgang Haken with
colleague Kenneth Appel at
the University of Illinois at
Urbana-Champaign, solved
one of the most famous
problems in mathematics, the
four-color theorem using a
computer. They proved that
any two-dimensional map, with
certain limitations, can be filled
in with four colors without any
adjacent "countries" sharing
the same color.
• Reference:
http://en.wikipedia.org/wiki/Wol
fgang_Haken