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 compute PYTHAGOREAN TRIPLES.
ca. 1650 B.C.E.
Egyptian scribe Ahmes makes copy of an early mathematical handbook onto a papyrus scroll. British antiquarian Alexander Henry Rhind (1833–63) purchased
the scroll in an Egyptian marketplace in 1858, and the
scroll is today known as the RHIND 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 technique 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 religious instructional texts providing detailed geometric
methods for the construction of altarpieces. The mathematics described in the texts includes formulae for the
areas of basic geometric shapes as well as for the volumes of prisms and cylinders.
ca. 585 B.C.E.
Greek mathematician THALES OF MILETUS founds the
earliest known school of philosophy and mathematics.
Thales develops seven important geometric propositions, heralding the demand for rigor and proof in
Greek mathematical thought.
ca. 569 B.C.E.
PYTHAGORAS of Samos is born. Around 510 B.C.E.,
Pythagoras founds a secret philosophical and mathematical society that includes both men and women.
The Pythagoreans are noted as the first to provide a
proof of what is today known as PYTHAGORAS’S THEOREM and are credited with the discovery of IRRATIONAL
NUMBERs.
ca. 450 B.C.E.
ZENO OF ELEA proposes a series of paradoxes that
challenge the notions of space, time, and motion.
ca. 387 B.C.E.
Greek philosopher PLATO (ca. 428–348 B.C.E.) founds
the Academy in Athens. His insistence that mathematics
539
APPENDIX I
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 compute PYTHAGOREAN TRIPLES.
ca. 1650 B.C.E.
Egyptian scribe Ahmes makes copy of an early mathematical handbook onto a papyrus scroll. British antiquarian Alexander Henry Rhind (1833–63) purchased
the scroll in an Egyptian marketplace in 1858, and the
scroll is today known as the RHIND 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 technique 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 religious instructional texts providing detailed geometric
methods for the construction of altarpieces. The mathematics described in the texts includes formulae for the
areas of basic geometric shapes as well as for the volumes of prisms and cylinders.
ca. 585 B.C.E.
Greek mathematician THALES OF MILETUS founds the
earliest known school of philosophy and mathematics.
Thales develops seven important geometric propositions, heralding the demand for rigor and proof in
Greek mathematical thought.
ca. 569 B.C.E.
PYTHAGORAS of Samos is born. Around 510 B.C.E.,
Pythagoras founds a secret philosophical and mathematical society that includes both men and women.
The Pythagoreans are noted as the first to provide a
proof of what is today known as PYTHAGORAS’S THEOREM and are credited with the discovery of IRRATIONAL
NUMBERs.
ca. 450 B.C.E.
ZENO OF ELEA proposes a series of paradoxes that
challenge the notions of space, time, and motion.
ca. 387 B.C.E.
Greek philosopher PLATO (ca. 428–348 B.C.E.) founds
the Academy in Athens. His insistence that mathematics
539
APPENDIX I