History of Math - First Section Flashcards

356 BCE – 323 BCE
• Student of Aristotle
• Not a mathematician
• Conquered one of the largest
empires in history
• Exported Greek culture throughout
the region
• Founded over 20 cites, all named
Alexandria, throughout his empire
• Died young
• Alexandria, Egypt
became a great
intellectual center

probably 1st or 2nd century AD was a Greek mathematician and engineer who was active in Alexandria during the Roman era. He has been described as the greatest experimentalist of antiquity and a representative of the Hellenistic scientific tradition^.

• Most prominent member of Plato’s Academy, there 20 years
• Athens 384-322 BCE
• Born near Macedonia, father a physician
• Left Athens after the death of Plato
• Returned to Macedonia, Court of Philip, tutored Alexander
• Returned to Athens, Founded his own school Lyceum, where
a broader range of subjects were studied
• Politics, ethics, epistemology, physics, biology, mathematics
• Logic was his biggest contribution to mathematics
• Syllogisms, codified logic
• Things that are accepted as true in all disciplines: axioms
• Things that are accepted as true in a particular discipline: postulates
• Distinguished between number (discrete) and magnitude (continuous)
• For better or worse, Aristotelean ideas of knowledge and the world persisted in
Europe and the Middle East through at least the 17th Century.

• ~200 CE - ~284 CE 3rd Century
• Difficulty establishing dates
• Alexandria, Egypt
• Father of Algebra
• Number Theory
• Arithmetica

~570 BCE – 490 BCE Around 500 BCE
• Samos is in Ionia, island off Asia Minor, just north of Miletus
• Visited Thales and Anaximander in Miletus
• Visited Egypt
• Moved to Italy around 518 BCE
• Founded semi-secret quasi-religious society/cult of mathematician/musician/philosophers
• First in Samos and later main school in Croton (now Crotone) on the east heel of southern Italy
• Two levels: acoustici, mathematici
• Inner circle kept secret knowledge
• Number Theory - Mystical properties of number
• Thought everything can be represented by a rational number
• Founder of Music Theory- consonance ratios of small natural number frequencies – lengths of string
• Associated numbers with nature
• Discovery of irrational numbers
• Most famous for the Pythagorean Theorem, known to Babylonians at least 1000 years earlier. May have been first to
prove it.
• Primarily a philosopher.
• Pythagoreans taught Earth is spherical, some that Sun was center of universe.
• Mathematics was to glorify the human spirit through a mystical contemplation of the good and beautiful.
• Pythagorean society expanded rapidly after 500 BCE, but it was violently suppressed in 460 BCE.

• Alexandria, Egypt
• ~325 BCE - ~265 BCE About 300 BCE
• Most prominent and influential mathematician/teacher
of the ancient world
• Leader and teacher at the important school:
Library and Museum at Alexandria
• The Elements
• 13 Books
• First textbook of mathematics
• Collected all earlier knowledge

• Mathematician and Astronomer of early Greek Period
• 409 BCE – 355BCE
• Studied in Croton with Pythagoreans (music, number theory)
• Also studied in Sicily (medicine), Athens, and Egypt (geometry, astronomy)
• Established a successful school in Cyzicus (northwestern Asia Minor)
• Returned to Cnidus and built an observatory

probably 1st or 2nd century AD was a Greek mathematician and engineer who was active in Alexandria during the Roman era. He has been described as the greatest experimentalist of antiquity and a representative of the Hellenistic scientific tradition^.

• 370 CE – 415 CE Late 4th - Early 5th Century CE
• Alexandria, Egypt
• First woman whose contributions to mathematics were significant enough to be remembered
among the great Greek mathematicians
• Daughter of mathematician and philosopher Theon of Alexandria, with whom she worked
• Head of Platonist school ~ 400 CE
• Lectured on Neoplatonism philosophy and mathematics
• Charismatic teacher
• Taught Synesius of Cyrene who later became Bishop of Ptolemais, letters exist
• Several works on mathematics including important commentaries on the works of earlier Greek
mathematicians
• Decline in the political support for the scholarly work at Alexandria under Roman rule.
• Early 400’s Hypatia became targeted as heretical by Cyril, Bishop of Alexandria who was in
political conflict with Orestes, Roman Prefect.
• Hypatia was brutally killed by a Christian mob in March of 415.
• The death of Hypatia marked the end of over a millennia of remarkable Greek mathematics.

• 290 CE – 350 CE Early 4th Century CE
• Alexandria, Egypt
• One of the last of the significant Greek geometers
• Synagoge or Mathematical Collection written to expound on the
entire field of Greek geometry, to be read along side original works
• Description of analysis and synthesis approaches
• Basis for projective geometry
• Tried to revive classical Greek geometry

• Athens, 427 BCE – 347 BCE
• One of the most important mathematicians and philosophers
• means “the broad”, real name may have been Aristocles
• Friends with Socrates
• Traveled to Egypt, Sicily, and Italy
• Pythagorean ideas influenced his work.
• Worked in the form of dialogues
• Contributed to dance, music, poetry, architecture, drama, ethics, metaphysics,
philosophy, mathematical and political philosophy, rhetoric, logic, education
• Mathematics as pure objects, representations are imperfect approximations
• Not known for his own direct contributions to mathematics
• More important for his contributions to logic and placing mathematics at the
heart of a good education

• 85 CE – 165 CE
• Alexandria Egypt
• Astronomer, Geographer, Mathematician
• Controversy concerning his abilities, from unethical, weak to
outstanding
• Very influential, most influential astronomer and geographer of
his time
• Claudius is a Roman name and Ptolemy is a Greek name.
• Ptolemy was the name of Alexander’s successor who ruled the
portion of the former Alexandrian Empire containing Egypt. The
rulers in Egypt were named Ptolemy. However, Claudius Ptolemy
was NOT such a ruler, and we have no idea of his connection to
that family if any.

• ~570 BCE – 490 BCE Around 500 BCE
• Samos is in Ionia, island off Asia Minor, just north of Miletus
• Visited Thales and Anaximander in Miletus
• Visited Egypt
• Moved to Italy around 518 BCE
• Founded semi-secret quasi-religious society/cult of mathematician/musician/philosophers
• First in Samos and later main school in Croton (now Crotone) on the east heel of southern Italy
• Two levels: acoustici, mathematici
• Inner circle kept secret knowledge
• Number Theory - Mystical properties of number
• Thought everything can be represented by a rational number
• Founder of Music Theory- consonance ratios of small natural number frequencies – lengths of string
• Associated numbers with nature
• Discovery of irrational numbers
• Most famous for the Pythagorean Theorem, known to Babylonians at least 1000 years earlier. May have been first to
prove it.
• Primarily a philosopher.
• Pythagoreans taught Earth is spherical, some that Sun was center of universe.
• Mathematics was to glorify the human spirit through a mystical contemplation of the good and beautiful.
• Pythagorean society expanded rapidly after 500 BCE, but it was violently suppressed in 460 BCE.

• ~624 BCE - ~547 BCE. Around 600 BCE
• Miletus was a Greek city in Asia Minor (present day Turkey).
• It is an overstatement to call Thales the Father of Mathematics, but he
sometimes gets this name because he is the first specific person in
recorded history who is said to have insisted on deductive logic and
proof. However, we don’t really know how much he really knew.
• No existing works. Comments from later historians and mathematicians.
• He is the first Greek philosopher, scientist, and mathematician known by
name.
• Traveled to Egypt. Brought knowledge of Geometry to Greece.
• Astronomy (predicted an eclipse), Philosophy, Geometry
• Measured the heights of pyramids using shadows
• Tried to explain reasons for natural phenomena
• The earliest of the “Seven Sages”

Academy brought most prominent mathematicians together including Eudoxus and -----------. His principal contributions were on irrational lengths, which was included in Book X of Euclid's Elements and proving that there are precisely five regular convex polyhedra.

• ~490 BCE - ~425 BCE, Elea, Lucania (present day southern Italy)
• Paradoxes (40) – dealt with questions about the understanding of the
infinitely big and infinitesimally small and how this related to motion
• “There is no motion because that which is moved must arrive at the middle of
its course before it arrives at the end.” In attempting to move from Point A to
Point B, one must first pass the midpoint of AB; but to do this, one must first
pass the ¼ point of AB; but first one must pass the 1/8 point of AB, ad infinitum.
Therefore, Zeno concludes, motion can never begin.
• Achilles and the Tortoise
• Paradoxes resolved with the concept of a limit.

Early: No place-value, letters for symbols, grouped in 10s

Late: more complicated symbols, grouped in 10s

Additive, no place-value, complicated symbols, grouped in 10s

Additive, no place-value, letters for symbols.

Developed hindu-arabic numerals.

• Athens, 427 BCE – 347 BCE
• One of the most important mathematicians and philosophers
• means “the broad”, real name may have been Aristocles
• Friends with Socrates
• Traveled to Egypt, Sicily, and Italy
• Pythagorean ideas influenced his work.
• Worked in the form of dialogues
• Contributed to dance, music, poetry, architecture, drama, ethics, metaphysics,
philosophy, mathematical and political philosophy, rhetoric, logic, education
• Mathematics as pure objects, representations are imperfect approximations
• Not known for his own direct contributions to mathematics
• More important for his contributions to logic and placing mathematics at the
heart of a good education

Babylon was one of the cultures in mesopotamian between tigris and euphrates

Additive, subtractive property added in middle ages

3rd centuey BCE

Alexandria

born in perga

known at the time for astronomy

”the great geometer”

conic sections