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Greek mathematics refers to
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
texts and ideas stemming from the Archaic through the
Hellenistic In Classical antiquity, the Hellenistic period covers the time in Mediterranean history after Classical Greece, between the death of Alexander the Great in 323 BC and the emergence of the Roman Empire, as signified by the Battle of Actium in ...
and
Roman Roman or Romans most often refers to: * Rome, the capital city of Italy * Ancient Rome, Roman civilization from 8th century BC to 5th century AD *Roman people, the people of ancient Rome *''Epistle to the Romans'', shortened to ''Romans'', a lett ...
periods, mostly extant from the 7th century BC to the 4th century AD, around the shores of the
Eastern Mediterranean Eastern Mediterranean is a loose definition of the eastern approximate half, or third, of the Mediterranean Sea, often defined as the countries around the Levantine Sea. It typically embraces all of that sea's coastal zones, referring to commun ...
. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean from
Italy Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical ...
to
North Africa North Africa, or Northern Africa is a region encompassing the northern portion of the African continent. There is no singularly accepted scope for the region, and it is sometimes defined as stretching from the Atlantic shores of Mauritania in ...
but were united by
Greek culture The culture of Greece has evolved over thousands of years, beginning in Minoan and later in Mycenaean Greece, continuing most notably into Classical Greece, while influencing the Roman Empire and its successor the Byzantine Empire. Other cul ...
and the
Greek language Greek ( el, label= Modern Greek, Ελληνικά, Elliniká, ; grc, Ἑλληνική, Hellēnikḗ) is an independent branch of the Indo-European family of languages, native to Greece, Cyprus, southern Italy ( Calabria and Salento), souther ...
. The word "mathematics" itself derives from the grc, , máthēma , meaning "subject of instruction". The study of mathematics for its own sake and the use of generalized mathematical theories and proofs is an important difference between Greek mathematics and those of preceding civilizations.


Origins of Greek mathematics

The origin of Greek mathematics is not well documented. The earliest advanced civilizations in
Greece Greece,, or , romanized: ', officially the Hellenic Republic, is a country in Southeast Europe. It is situated on the southern tip of the Balkans, and is located at the crossroads of Europe, Asia, and Africa. Greece shares land borders wi ...
and in
Europe Europe is a large peninsula conventionally considered a continent in its own right because of its great physical size and the weight of its history and traditions. Europe is also considered a Continent#Subcontinents, subcontinent of Eurasia ...
were the Minoan and later Mycenaean civilizations, both of which flourished during the 2nd millennium BCE. While these civilizations possessed writing and were capable of advanced engineering, including four-story palaces with drainage and
beehive tomb A beehive tomb, also known as a tholos tomb (plural tholoi; from Greek θολωτός τάφος, θολωτοί τάφοι, "domed tombs"), is a burial structure characterized by its false dome created by corbelling, the superposition of s ...
s, they left behind no mathematical documents. Though no direct evidence is available, it is generally thought that the neighboring
Babylonia Babylonia (; Akkadian: , ''māt Akkadī'') was an ancient Akkadian-speaking state and cultural area based in the city of Babylon in central-southern Mesopotamia (present-day Iraq and parts of Syria). It emerged as an Amorite-ruled state c ...
n and Egyptian civilizations had an influence on the younger Greek tradition. Unlike the flourishing of Greek literature in the span of 800 to 600 BC, not much is known about Greek mathematics in this early period—nearly all of the information was passed down through later authors, beginning in the mid-4th century BC.Boyer & Merzbach (2011) pp. 40–89.


Archaic and Classical periods

Greek mathematics allegedly began with
Thales of Miletus Thales of Miletus ( ; grc-gre, Θαλῆς; ) was a Greek mathematician, astronomer, statesman, and pre-Socratic philosopher from Miletus in Ionia, Asia Minor. He was one of the Seven Sages of Greece. Many, most notably Aristotle, regarded ...
(c. 624–548 BC). Very little is known about his life and works, although it is generally agreed that he was one of the
Seven Wise Men of Greece The Seven Sages (of Greece) or Seven Wise Men ( Greek: ''hoi hepta sophoi'') was the title given by classical Greek tradition to seven philosophers, statesmen, and law-givers of the 7–6th century BC who were renowned for their wisdom. T ...
. According to
Proclus Proclus Lycius (; 8 February 412 – 17 April 485), called Proclus the Successor ( grc-gre, Πρόκλος ὁ Διάδοχος, ''Próklos ho Diádokhos''), was a Greek Neoplatonist philosopher, one of the last major classical philosophe ...
, he traveled to Babylon from where he learned mathematics and other subjects, and came up with the proof of what is now called Thales' Theorem. An equally enigmatic figure is Pythagoras of Samos (c. 580–500 BC), who supposedly visited Egypt and Babylon,Heath (2003) pp. 36–111 and ultimately settled in Croton,
Magna Graecia Magna Graecia (, ; , , grc, Μεγάλη Ἑλλάς, ', it, Magna Grecia) was the name given by the Romans to the coastal areas of Southern Italy in the present-day Italian regions of Calabria, Apulia, Basilicata, Campania and Sicily; the ...
, where he started a kind of cult. Pythagoreans believed that "all is number" and were keen in looking for mathematical relations between numbers and things. Pythagoras himself was given credit for many later discoveries, including the construction of the five regular solids. However, Aristotle refused to attribute anything specifically to Pythagoras and only discussed the work of the Pythagoreans as a group. It has been customary to credit almost half of the material in
Euclid Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of ...
's '' Elements'' to the Pythagoreans, as well as the discovery of irrationals, attributed to Hippassus (c. 530–450 BC), and the earliest attempt to
square the circle Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a circle by using only a finite number of steps with a compass and straightedge. The difficult ...
, in the work of
Hippocrates of Chios Hippocrates of Chios ( grc-gre, Ἱπποκράτης ὁ Χῖος; c. 470 – c. 410 BC) was an ancient Greek mathematician, geometer, and astronomer. He was born on the isle of Chios, where he was originally a merchant. After some misadve ...
(c. 470–410 BC). The greatest mathematician associated with the group, however, may have been
Archytas Archytas (; el, Ἀρχύτας; 435/410–360/350 BC) was an Ancient Greek philosopher, mathematician, music theorist, astronomer, statesman, and strategist. He was a scientist of the Pythagorean school and famous for being the reputed found ...
(c. 435-360 BC), who solved the problem of doubling the cube, identified the
harmonic mean In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for situations when the average rate is desired. The harmonic mean can be expressed as the recipro ...
, and possibly contributed to
optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultrav ...
and
mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objec ...
. Other mathematicians active in this period, without being associated with any school, include Theodorus (fl. 450 BC),
Theaetetus Theaetetus (Θεαίτητος) is a Greek name which could refer to: * Theaetetus (mathematician) (c. 417 BC – 369 BC), Greek geometer * ''Theaetetus'' (dialogue), a dialogue by Plato, named after the geometer * Theaetetus (crater) Theaetetus ...
(c. 417-369 BC), and Eudoxus (c. 408–355 BC). Greek mathematics also drew the attention of philosophers during the Classical period.
Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...
(c. 428–348 BC), the founder of the
Platonic Academy The Academy ( Ancient Greek: Ἀκαδημία) was founded by Plato in c. 387 BC in Athens. Aristotle studied there for twenty years (367–347 BC) before founding his own school, the Lyceum. The Academy persisted throughout the Hellenisti ...
, mentions mathematics in several of his dialogues. While not considered a mathematician, Plato seems to have been influenced by Pythagorean ideas about number and believed that the elements of matter could be broken down into geometric solids. He also believed that geometrical proportions bound the
cosmos The cosmos (, ) is another name for the Universe. Using the word ''cosmos'' implies viewing the universe as a complex and orderly system or entity. The cosmos, and understandings of the reasons for its existence and significance, are studied in ...
together rather than physical or mechanical forces.
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
(c. 384–322 BC), the founder of the Peripatetic school, often used mathematics to illustrate many of his theories, as when he used geometry in his theory of the rainbow and the theory of proportions in his analysis of motion. Much of the knowledge known about ancient Greek mathematics in this period is thanks to records referenced by Aristotle in his own works.


Hellenistic and Roman periods

The
Hellenistic era In Classical antiquity, the Hellenistic period covers the time in Mediterranean history after Classical Greece, between the death of Alexander the Great in 323 BC and the emergence of the Roman Empire, as signified by the Battle of Actium in 3 ...
began in the 4th century BC with
Alexander the Great Alexander III of Macedon ( grc, Ἀλέξανδρος, Alexandros; 20/21 July 356 BC – 10/11 June 323 BC), commonly known as Alexander the Great, was a king of the ancient Greek kingdom of Macedon. He succeeded his father Philip II to ...
's conquest of the eastern
Mediterranean The Mediterranean Sea is a sea connected to the Atlantic Ocean, surrounded by the Mediterranean Basin and almost completely enclosed by land: on the north by Western and Southern Europe and Anatolia, on the south by North Africa, and on ...
,
Egypt Egypt ( ar, مصر , ), officially the Arab Republic of Egypt, is a List of transcontinental countries, transcontinental country spanning the North Africa, northeast corner of Africa and Western Asia, southwest corner of Asia via a land bridg ...
,
Mesopotamia Mesopotamia ''Mesopotamíā''; ar, بِلَاد ٱلرَّافِدَيْن or ; syc, ܐܪܡ ܢܗܪ̈ܝܢ, or , ) is a historical region of Western Asia situated within the Tigris–Euphrates river system, in the northern part of the ...
, the Iranian plateau,
Central Asia Central Asia, also known as Middle Asia, is a region of Asia that stretches from the Caspian Sea in the west to western China and Mongolia in the east, and from Afghanistan and Iran in the south to Russia in the north. It includes the fo ...
, and parts of
India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area, the List of countries and dependencies by population, second-most populous ...
, leading to the spread of the Greek language and culture across these areas. Greek became the language of scholarship throughout the Hellenistic world, and the mathematics of the Classical period merged with Egyptian and Babylonian mathematics to give rise to a Hellenistic mathematics. Greek mathematics and astronomy reached its acme during the Hellenistic and early Roman periods, and much of the work represented by scholars such as
Euclid Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of ...
(fl. 300 BC),
Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientis ...
(c. 287–212 BC), Apollonius (c. 240–190 BC),
Hipparchus Hipparchus (; el, Ἵππαρχος, ''Hipparkhos'';  BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the e ...
(c. 190–120 BC), and
Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
(c. 100–170 AD) was of a very advanced level. There is also evidence of combining mathematical knowledge with technical or practical applications, as found for instance in the construction of analogue computers like the
Antikythera mechanism The Antikythera mechanism ( ) is an Ancient Greek hand-powered orrery, described as the oldest example of an analogue computer used to predict astronomical positions and eclipses decades in advance. It could also be used to track the four-y ...
, in the accurate measurement for the
circumference of the Earth Earth's circumference is the distance around Earth. Measured around the Equator, it is . Measured around the poles, the circumference is . Measurement of Earth's circumference has been important to navigation since ancient times. The first know ...
by
Eratosthenes Eratosthenes of Cyrene (; grc-gre, Ἐρατοσθένης ;  – ) was a Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandr ...
(276 – 194 BC), or in the mechanical works of
Hero A hero (feminine: heroine) is a real person or a main fictional character who, in the face of danger, combats adversity through feats of ingenuity, courage, or strength. Like other formerly gender-specific terms (like ''actor''), ''her ...
(c. 10–70 AD). Several Hellenistic centers of learning appeared during this period, of which the most important one was the Musaeum in
Alexandria Alexandria ( or ; ar, ٱلْإِسْكَنْدَرِيَّةُ ; grc-gre, Αλεξάνδρεια, Alexándria) is the second largest city in Egypt, and the largest city on the Mediterranean coast. Founded in by Alexander the Great, Alexandri ...
,
Egypt Egypt ( ar, مصر , ), officially the Arab Republic of Egypt, is a List of transcontinental countries, transcontinental country spanning the North Africa, northeast corner of Africa and Western Asia, southwest corner of Asia via a land bridg ...
, which attracted scholars from across the Hellenistic world (mostly Greek, but also Egyptian, Jewish, Persian,
Phoenicia Phoenicia () was an ancient thalassocratic civilization originating in the Levant region of the eastern Mediterranean, primarily located in modern Lebanon. The territory of the Phoenician city-states extended and shrank throughout their his ...
n, and even
Indian Indian or Indians may refer to: Peoples South Asia * Indian people, people of Indian nationality, or people who have an Indian ancestor ** Non-resident Indian, a citizen of India who has temporarily emigrated to another country * South Asia ...
scholars). Although few in number, Hellenistic mathematicians actively communicated with each other; publication consisted of passing and copying someone's work among colleagues. Later mathematicians include
Diophantus Diophantus of Alexandria ( grc, Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 200 and 214; died around the age of 84, probably sometime between AD 284 and 298) was an Alexandrian mathematician, who was the aut ...
(c. 214–298 AD), who wrote on polygonal numbers and a work in pre-modern algebra (''
Arithmetica ''Arithmetica'' ( grc-gre, Ἀριθμητικά) is an Ancient Greek text on mathematics written by the mathematician Diophantus () in the 3rd century AD. It is a collection of 130 algebraic problems giving numerical solutions of determinate ...
''),
Pappus of Alexandria Pappus of Alexandria (; grc-gre, Πάππος ὁ Ἀλεξανδρεύς; AD) was one of the last great Greek mathematicians of antiquity known for his ''Synagoge'' (Συναγωγή) or ''Collection'' (), and for Pappus's hexagon theorem i ...
(c. 290-350 AD), who compiled many important results in the ''Collection'', and
Theon of Alexandria Theon of Alexandria (; grc, Θέων ὁ Ἀλεξανδρεύς;  335 – c. 405) was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's '' Elements'' and wrote commentaries on w ...
(c. 335-405 AD) and his daughter Hypatia (c. 370–415 AD), who edited Ptolemy's ''
Almagest The ''Almagest'' is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy ( ). One of the most influential scientific texts in history, it can ...
'' and other works. Although none of these mathematicians, save Diophantus, had notable original works, they are distinguished for their commentaries and expositions. These commentaries have preserved valuable extracts from works which have perished, or historical allusions which, in the absence of original documents, are precious because of their rarity. Most of the mathematical texts written in Greek survived through the copying of manuscripts over the centuries, though some fragments dating from antiquity have been found in Greece,
Egypt Egypt ( ar, مصر , ), officially the Arab Republic of Egypt, is a List of transcontinental countries, transcontinental country spanning the North Africa, northeast corner of Africa and Western Asia, southwest corner of Asia via a land bridg ...
,
Asia Minor Anatolia, tr, Anadolu Yarımadası), and the Anatolian plateau, also known as Asia Minor, is a large peninsula in Western Asia and the westernmost protrusion of the Asian continent. It constitutes the major part of modern-day Turkey. The re ...
,
Mesopotamia Mesopotamia ''Mesopotamíā''; ar, بِلَاد ٱلرَّافِدَيْن or ; syc, ܐܪܡ ܢܗܪ̈ܝܢ, or , ) is a historical region of Western Asia situated within the Tigris–Euphrates river system, in the northern part of the ...
, and
Sicily (man) it, Siciliana (woman) , population_note = , population_blank1_title = , population_blank1 = , demographics_type1 = Ethnicity , demographics1_footnotes = , demographi ...
.


Achievements

Greek mathematics constitutes an important period in the history of
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
: fundamental in respect of
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
and for the idea of
formal proof In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the seq ...
. Greek mathematicians also contributed to
number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Ma ...
, mathematical astronomy,
combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...
,
mathematical physics Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developm ...
, and, at times, approached ideas close to the integral calculus.
Eudoxus of Cnidus Eudoxus of Cnidus (; grc, Εὔδοξος ὁ Κνίδιος, ''Eúdoxos ho Knídios''; ) was an ancient Greek astronomer, mathematician, scholar, and student of Archytas and Plato. All of his original works are lost, though some fragments are ...
developed a theory of proportion that bears resemblance to the modern theory of
real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every ...
s using the
Dedekind cut In mathematics, Dedekind cuts, named after German mathematician Richard Dedekind but previously considered by Joseph Bertrand, are а method of construction of the real numbers from the rational numbers. A Dedekind cut is a partition of the r ...
, developed by
Richard Dedekind Julius Wilhelm Richard Dedekind (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to number theory, abstract algebra (particularly ring theory), and the axiomatic foundations of arithmetic. His ...
, who acknowledged Eudoxus as inspiration.
Euclid Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of ...
collected many previous results and theorems in the '' Elements'', a canon of geometry and elementary number theory for many centuries.
Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientis ...
was able to use the concept of the infinitely small in a way that anticipated modern ideas of the
integral calculus In mathematics, an integral assigns numbers to Function (mathematics), functions in a way that describes Displacement (geometry), displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding ...
. Using a technique dependent on a form of
proof by contradiction In logic and mathematics, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction. Proof by contradiction is also known ...
, he could reach answers to problems with an arbitrary degree of accuracy, while specifying the limits within which the answers lay. This technique is known as the
method of exhaustion The method of exhaustion (; ) is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. If the sequence is correctly constructed, the difference in are ...
, and he employed in several of his works, such as to approximate the value of π (''
Measurement of the Circle ''Measurement of a Circle'' or ''Dimension of the Circle'' ( Greek: , ''Kuklou metrēsis'') is a treatise that consists of three propositions by Archimedes, ca. 250 BCE. The treatise is only a fraction of what was a longer work. Propositions Pro ...
''). In ''
Quadrature of the Parabola ''Quadrature of the Parabola'' ( el, Τετραγωνισμὸς παραβολῆς) is a treatise on geometry, written by Archimedes in the 3rd century BC and addressed to his Alexandrian acquaintance Dositheus. It contains 24 propositions rega ...
'', Archimedes proved that the area enclosed by a
parabola In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One descri ...
and a straight line is times the area of a
triangle A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non- colline ...
with equal base and height using an infinite
geometric series In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. For example, the series :\frac \,+\, \frac \,+\, \frac \,+\, \frac \,+\, \cdots is geometric, because each suc ...
, whose sum was . In ''
The Sand Reckoner ''The Sand Reckoner'' ( el, Ψαμμίτης, ''Psammites'') is a work by Archimedes, an Ancient Greek mathematician of the 3rd century BC, in which he set out to determine an upper bound for the number of grains of sand that fit into the unive ...
'', Archimedes challenged the notion that the number of grains of sand was too large to be counted by trying to name how many grains of sand the universe could contain, devising his own counting scheme based on the
myriad A myriad (from Ancient Greek grc, μυριάς, translit=myrias, label=none) is technically the number 10,000 (ten thousand); in that sense, the term is used in English almost exclusively for literal translations from Greek, Latin or Sinospher ...
, which denoted 10,000. The most characteristic product of Greek mathematics may be the theory of
conic section In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a ...
s, which was largely developed in the
Hellenistic period In Classical antiquity, the Hellenistic period covers the time in Mediterranean history after Classical Greece, between the death of Alexander the Great in 323 BC and the emergence of the Roman Empire, as signified by the Battle of Actium in ...
, primarily by Apollonius. The methods employed made no explicit use of
algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...
, nor
trigonometry Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. ...
, the latter appearing around the time of
Hipparchus Hipparchus (; el, Ἵππαρχος, ''Hipparkhos'';  BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the e ...
. Ancient Greek mathematics was not limited to theoretical works but was also used in other activities, such as business transactions and in land mensuration, as evidenced by extant texts where computational procedures and practical considerations took more of a central role.


Transmission and the manuscript tradition

Although the earliest
Greek language Greek ( el, label= Modern Greek, Ελληνικά, Elliniká, ; grc, Ἑλληνική, Hellēnikḗ) is an independent branch of the Indo-European family of languages, native to Greece, Cyprus, southern Italy ( Calabria and Salento), souther ...
texts on mathematics that have been found were written after the Hellenistic period, many of these are considered to be copies of works written during and before the Hellenistic period. The two major sources are * Byzantine codices, written some 500 to 1500 years after their originals, and *
Syriac Syriac may refer to: *Syriac language, an ancient dialect of Middle Aramaic *Sureth, one of the modern dialects of Syriac spoken in the Nineveh Plains region * Syriac alphabet ** Syriac (Unicode block) ** Syriac Supplement * Neo-Aramaic languages a ...
or Arabic translations of Greek works and Latin translations of the Arabic versions. Nevertheless, despite the lack of original manuscripts, the dates of Greek mathematics are more certain than the dates of surviving Babylonian or Egyptian sources because a large number of overlapping chronologies exist. Even so, many dates are uncertain; but the doubt is a matter of decades rather than centuries.
Reviel Netz Reviel Netz (born January 2, 1968) is an Israeli scholar of the history of pre-modern mathematics, who is currently a professor of classics and of philosophy at Stanford University. Life and work Netz was born January 2, 1968, in Tel Aviv, Isra ...
has counted 144 ancient exact scientific authors, of these only 29 are extant in Greek: Aristarchus,
Autolycus In Greek mythology, Autolycus (; Ancient Greek: Αὐτόλυκος ''Autolykos'' 'the wolf itself') was a successful robber who had even the power of metamorphosing both the stolen goods and himself. He had his residence on Mount Parnassus and ...
, Philo of Byzantium,
Biton Biton (Hebrew: ביטון) is a Maghrebi Jewish surname which is common in Israel. It may refer to: * Avraham Biton (1923-2005), Israeli politician * Charlie Biton (born 1947), former Israeli politician * Dan Biton (born 1961), general in the Is ...
, Apollonius,
Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientis ...
,
Euclid Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of ...
, Theodosius, Hypsicles,
Athenaeus Athenaeus of Naucratis (; grc, Ἀθήναιος ὁ Nαυκρατίτης or Nαυκράτιος, ''Athēnaios Naukratitēs'' or ''Naukratios''; la, Athenaeus Naucratita) was a Greek rhetorician and grammarian, flourishing about the end of ...
,
Geminus Geminus of Rhodes ( el, Γεμῖνος ὁ Ῥόδιος), was a Greek astronomer and mathematician, who flourished in the 1st century BC. An astronomy work of his, the ''Introduction to the Phenomena'', still survives; it was intended as an int ...
,
Hero A hero (feminine: heroine) is a real person or a main fictional character who, in the face of danger, combats adversity through feats of ingenuity, courage, or strength. Like other formerly gender-specific terms (like ''actor''), ''her ...
,
Apollodorus Apollodorus (Greek: Ἀπολλόδωρος ''Apollodoros'') was a popular name in ancient Greece. It is the masculine gender of a noun compounded from Apollo, the deity, and doron, "gift"; that is, "Gift of Apollo." It may refer to: :''Note: A f ...
,
Theon of Smyrna Theon of Smyrna ( el, Θέων ὁ Σμυρναῖος ''Theon ho Smyrnaios'', ''gen.'' Θέωνος ''Theonos''; fl. 100 CE) was a Greek philosopher and mathematician, whose works were strongly influenced by the Pythagorean school of thought. Hi ...
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Cleomedes Cleomedes ( el, Κλεομήδης) was a Greek astronomer who is known chiefly for his book ''On the Circular Motions of the Celestial Bodies'' (Κυκλικὴ θεωρία μετεώρων), also known as ''The Heavens'' ( la, Caelestia). Pl ...
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Nicomachus Nicomachus of Gerasa ( grc-gre, Νικόμαχος; c. 60 – c. 120 AD) was an important ancient mathematician and music theorist, best known for his works '' Introduction to Arithmetic'' and '' Manual of Harmonics'' in Greek. He was bo ...
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Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
, Gaudentius, Anatolius, Aristides Quintilian, Porphyry,
Diophantus Diophantus of Alexandria ( grc, Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 200 and 214; died around the age of 84, probably sometime between AD 284 and 298) was an Alexandrian mathematician, who was the aut ...
, Alypius, Damianus, Pappus, Serenus,
Theon of Alexandria Theon of Alexandria (; grc, Θέων ὁ Ἀλεξανδρεύς;  335 – c. 405) was a Greek scholar and mathematician who lived in Alexandria, Egypt. He edited and arranged Euclid's '' Elements'' and wrote commentaries on w ...
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Anthemius Procopius Anthemius (died 11 July 472) was western Roman emperor from 467 to 472. Perhaps the last capable Western Roman Emperor, Anthemius attempted to solve the two primary military challenges facing the remains of the Western Roman Empire: ...
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Eutocius Eutocius of Ascalon (; el, Εὐτόκιος ὁ Ἀσκαλωνίτης; 480s – 520s) was a Palestinian-Greek mathematician who wrote commentaries on several Archimedean treatises and on the Apollonian ''Conics''. Life and work Little is ...
. Some works are extant only in Arabic translations:Toomer, G.J. Lost greek mathematical works in arabic translation. The Mathematical Intelligencer 6, 32–38 (1984). https://doi.org/10.1007/BF03024153 *Apollonius, ''Conics'' books V to VII *Apollonius, ''De Rationis Sectione'' *Archimedes, ''
Book of Lemmas The ''Book of Lemmas'' or ''Book of Assumptions'' (Arabic ''Maʾkhūdhāt Mansūba ilā Arshimīdis'') is a book attributed to Archimedes by Thābit ibn Qurra, though the authorship of the book is questionable. It consists of fifteen propositio ...
'' *Archimedes, ''Construction of the Regular Heptagon'' * Diocles, ''On Burning Mirrors'' *Diophantus, ''
Arithmetica ''Arithmetica'' ( grc-gre, Ἀριθμητικά) is an Ancient Greek text on mathematics written by the mathematician Diophantus () in the 3rd century AD. It is a collection of 130 algebraic problems giving numerical solutions of determinate ...
'' books IV to VII *Euclid, ''On Divisions of Figures'' *Euclid, ''On Weights'' *Hero, ''Catoptrica'' *Hero, ''Mechanica'' *
Menelaus In Greek mythology, Menelaus (; grc-gre, Μενέλαος , 'wrath of the people', ) was a king of Mycenaean (pre- Dorian) Sparta. According to the ''Iliad'', Menelaus was a central figure in the Trojan War, leading the Spartan contingent of ...
, ''Sphaerica'' *Pappus, ''Commentary on Euclid's Elements book X'' *Ptolemy, ''
Optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultrav ...
'' *Ptolemy, '' Planisphaerium''


See also

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Notes


References

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External links


Vatican ExhibitFamous Greek Mathematicians
{{DEFAULTSORT:Greek Mathematics