CHRONOLOGY
ca. 50,000
B
.
C
.
E
.
Animal bones etched with tally marks provide evidence
that the Paleolithic people of central Europe were able
to count.
ca. 15,000
B
.
C
.
E
.
Notched animal bones discovered in the Middle East
provide further evidence of early counting.
ca. 3000
B
.
C
.
E
.
The ancient Egyptians improve upon the tally system
and devise a numeration system that permits the
expression of large numbers with only a few symbols.
ca. 2600
B
.
C
.
E
.
The Great Pyramid at Giza is built by the Egyptians.
ca. 1800
B
.
C
.
E
.
Babylonian scholars develop a base-60
PLACE
-
VALUE
SYSTEM
of numeration. With it, they perform complex
arithmetic work, solve
QUADRATIC
equations, and com-
pute P
YTHAGOREAN TRIPLES
.
ca. 1650
B
.
C
.
E
.
Egyptian scribe Ahmes makes copy of an early mathe-
matical handbook onto a papyrus scroll. British anti-
quarian Alexander Henry Rhind (1833–63) purchased
the scroll in an Egyptian marketplace in 1858, and the
scroll is today known as the R
HIND PAPYRUS
. The text
details the method for computing the area of a circle
and other basic geometric shapes, the method of “false
position” for solving basic linear equations, and a tech-
nique for finding the steepness of a pyramid. The value
256/81 ≈3.1605 is used for π.
ca. 600
B
.
C
.
E
.
Indian scholars write the Sulba sultras, a set of reli-
gious instructional texts providing detailed geometric
methods for the construction of altarpieces. The mathe-
matics described in the texts includes formulae for the
areas of basic geometric shapes as well as for the vol-
umes of prisms and cylinders.
ca. 585
B
.
C
.
E
.
Greek mathematician T
HALES OF
M
ILETUS
founds the
earliest known school of philosophy and mathematics.
Thales develops seven important geometric proposi-
tions, heralding the demand for rigor and proof in
Greek mathematical thought.
ca. 569
B
.
C
.
E
.
P
YTHAGORAS
of Samos is born. Around 510
B
.
C
.
E
.,
Pythagoras founds a secret philosophical and mathe-
matical society that includes both men and women.
The Pythagoreans are noted as the first to provide a
proof of what is today known as P
YTHAGORAS
’
S THEO
-
REM
and are credited with the discovery of
IRRATIONAL
NUMBER
s.
ca. 450
B
.
C
.
E
.
Z
ENO OF
E
LEA
proposes a series of paradoxes that
challenge the notions of space, time, and motion.
ca. 387
B
.
C
.
E
.
Greek philosopher P
LATO
(ca. 428–348
B
.
C
.
E
.) founds
the Academy in Athens. His insistence that mathematics
539
A
PPENDIX
I