This is a timeline of

mathematicians A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

ancient Greece Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of cu ...

Timeline

Historians traditionally place the beginning of

Greek mathematics Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean. Greek mathe ...

proper to the age of

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 ...

(ca. 624–548 BC), which is indicated by the at 600 BC. The at 300 BC indicates the approximate year in which

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'' was first published. The at 300 AD passes through

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 ...

(), who was one of the last great

Greek mathematician Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean. Greek mathe ...

s of

late antiquity Late antiquity is the time of transition from classical antiquity to the Middle Ages, generally spanning the 3rd–7th century in Europe and adjacent areas bordering the Mediterranean Basin. The popularization of this periodization in English h ...

. Note that the solid thick is at

year zero A year zero does not exist in the Anno Domini (AD) calendar year system commonly used to number years in the Gregorian calendar (nor in its predecessor, the Julian calendar); in this system, the year is followed directly by year . However, the ...

, which is a year that does ''not'' exist in the ''

Anno Domini The terms (AD) and before Christ (BC) are used to label or number years in the Julian and Gregorian calendars. The term is Medieval Latin and means 'in the year of the Lord', but is often presented using "our Lord" instead of "the Lord" ...

'' (AD)

calendar A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A date is the designation of a single and specific day within such a system. A calendar is also a phy ...

year system The mathematician

Heliodorus of Larissa Heliodorus of Larissa (fl. 3rd century?) was a Greek mathematician, and the author of a short treatise on optics which is still extant. Biography Nothing is known about the life of Heliodorus.John Aikin, William Enfield, et al., (1804), ''General ...

is not listed due to the uncertainty of when he lived, which was possibly during the 3rd century AD, after

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 ...

Overview of the most important mathematicians and discoveries

Of these mathematicians, those whose work stands out include: *

() is the first known individual to use

deductive reasoning Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if it is impossible for the premises to be true and the conclusion to be fal ...

applied to geometry, by deriving four corollaries to

Thales' theorem In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line is a diameter, the angle ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved ...

. He is the first known individual to whom a mathematical discovery has been attributed. *

Pythagoras Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the Samian, or simply ; in Ionian Greek; ) was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His poli ...

() was credited with many mathematical and scientific discoveries, including the

Pythagorean theorem In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposit ...

Pythagorean tuning Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2.Bruce Benward and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice'', seventh edition, 2 vols. (Boston: ...

, the five regular solids, the Theory of Proportions, the sphericity of the Earth, and the identity of the

morning Morning is the period from sunrise to noon. There are no exact times for when morning begins (also true of evening and night) because it can vary according to one's lifestyle and the hours of daylight at each time of year. However, morning s ...

and evening stars as the planet

Venus Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never f ...

. *

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 ...

() Proved that there are ''exactly'' five regular

convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytop ...

polyhedra In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on ...

(it is emphasized that it was, in particular, ''proved'' that there does ''not exist'' any regular convex polyhedra other than these five). This fact led these five solids, now called the

Platonic solid In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all e ...

s, to play a prominent role in the philosophy of

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 ...

(and consequently, also influenced later

Western Philosophy Western philosophy encompasses the philosophy, philosophical thought and work of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with the ancient Greek philosophy of the Pre-Socratic p ...

) who associated each of the four

classical element Classical elements typically refer to earth, water, air, fire, and (later) aether which were proposed to explain the nature and complexity of all matter in terms of simpler substances. Ancient cultures in Greece, Tibet, and India had simi ...

s with a regular solid:

earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...

with the

cube In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. The cube is the only ...

air The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing f ...

with the

octahedron In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at ea ...

water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...

with the

icosahedron In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons". There are infinitely many non- similar shapes of icosahedra, some of them being more symmetrica ...

, and

fire Fire is the rapid oxidation of a material (the fuel) in the exothermic chemical process of combustion, releasing heat, light, and various reaction products. At a certain point in the combustion reaction, called the ignition point, flames ...

with the

tetrahedron In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all ...

(of the fifth Platonic solid, the

dodecahedron In geometry, a dodecahedron (Greek , from ''dōdeka'' "twelve" + ''hédra'' "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagon ...

, Plato obscurely remarked, "...the god used tfor arranging the constellations on the whole heaven"). The last book (Book XIII) of the Euclid's ''Elements'', which is probably derived from the work of Theaetetus, is devoted to constructing the Platonic solids and describing their properties;

Andreas Speiser Andreas Speiser (June 10, 1885 – October 12, 1970) was a Swiss mathematician and philosopher of science. Life and work Speiser studied in Göttingen, starting in 1904, notably with David Hilbert, Felix Klein, Hermann Minkowski. In 1917 he becam ...

has advocated the view that the construction of the 5 regular solids is the chief goal of the deductive system canonized in the ''Elements''.

Astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either ...

Johannes Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws ...

proposed a model of the

Solar System The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...

in which the five solids were set inside one another and separated by a series of inscribed and circumscribed spheres. *

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 ...

() is considered by some to be the greatest of

classical Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic pe ...

mathematicians, and in all

antiquity Antiquity or Antiquities may refer to: Historical objects or periods Artifacts *Antiquities, objects or artifacts surviving from ancient cultures Eras Any period before the European Middle Ages (5th to 15th centuries) but still within the histo ...

second only to

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 ...

. Book V of Euclid's ''Elements'' is though to be largely due to Eudoxus. *

Aristarchus of Samos Aristarchus of Samos (; grc-gre, Ἀρίσταρχος ὁ Σάμιος, ''Aristarkhos ho Samios''; ) was an ancient Greek astronomer and mathematician who presented the first known heliocentric model that placed the Sun at the center of the ...

() presented the first known

heliocentric model Heliocentrism (also known as the Heliocentric model) is the astronomical model in which the Earth and planets revolve around the Sun at the center of the universe. Historically, heliocentrism was opposed to geocentrism, which placed the Earth a ...

that placed the

Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...

at the center of the known universe with the Earth revolving around it. Aristarchus identified the "central fire" with the Sun, and he put the other planets in their correct order of distance around the Sun. In '' On the Sizes and Distances'', he calculates the sizes of the

and

Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

, as well as their distances from the Earth in terms of Earth's radius. However,

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 ...

() was the first person to calculate the circumference of the Earth.

Posidonius Posidonius (; grc-gre, Ποσειδώνιος , "of Poseidon") "of Apameia" (ὁ Ἀπαμεύς) or "of Rhodes" (ὁ Ῥόδιος) (), was a Greek politician, astronomer, astrologer, geographer, historian, mathematician, and teacher nativ ...

() also measured the diameters and distances of the Sun and the Moon as well as the Earth's diameter; his measurement of the diameter of the Sun was more accurate than Aristarchus', differing from the modern value by about half. *

(

fl. ''Floruit'' (; abbreviated fl. or occasionally flor.; from Latin for "they flourished") denotes a date or period during which a person was known to have been alive or active. In English, the unabbreviated word may also be used as a noun indicatin ...

300 BC) is often referred to as the "founder 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 ...

" or the "father of geometry" because of his incredibly influential

treatise A treatise is a formal and systematic written discourse on some subject, generally longer and treating it in greater depth than an essay, and more concerned with investigating or exposing the principles of the subject and its conclusions." Tre ...

called the '' Elements'', which was the first, or at least one of the first, axiomatized deductive systems. *

() is considered to be the greatest mathematician of

ancient history Ancient history is a time period from the beginning of writing and recorded human history to as far as late antiquity. The span of recorded history is roughly 5,000 years, beginning with the Sumerian cuneiform script. Ancient history cove ...

, and one of the greatest of all time. Archimedes anticipated modern

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...

and

analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...

by applying concepts of

infinitesimal In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally re ...

s and 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 ...

to derive and rigorously prove a range of

geometrical 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 ...

theorem In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of t ...

s, including: the

area of a circle In geometry, the area enclosed by a circle of radius is . Here the Greek letter represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159. One method of deriving this formula, which ori ...

; the

surface area The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of ...

and

volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...

of a

sphere A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the c ...

; area of an

ellipse In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in ...

; the area under 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 ...

; the volume of a segment of a paraboloid of revolution; the volume of a segment of a

hyperboloid of revolution In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes. A hyperboloid is the surface obtained from a hyperboloid of revolution by def ...

; and the area of a

spiral In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point. Helices Two major definitions of "spiral" in the American Heritage Dictionary are:apply mathematics to

physical phenomena Physical may refer to: *Physical examination In a physical examination, medical examination, or clinical examination, a medical practitioner examines a patient for any possible medical signs or symptoms of a medical condition. It generally cons ...

, founding

hydrostatics Fluid statics or hydrostatics is the branch of fluid mechanics that studies the condition of the equilibrium of a floating body and submerged body "fluids at hydrostatic equilibrium and the pressure in a fluid, or exerted by a fluid, on an imme ...

and

statics Statics is the branch of classical mechanics that is concerned with the analysis of force and torque (also called moment) acting on physical systems that do not experience an acceleration (''a''=0), but rather, are in static equilibrium with ...

, including an explanation of the principle of the

lever A lever is a simple machine consisting of a beam or rigid rod pivoted at a fixed hinge, or '' fulcrum''. A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, load and effort, the lever is d ...

. In a lost work, he discovered and enumerated the 13

Archimedean solid In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the convex uniform polyhedra composed of regular polygons meeting in identical vertices, excluding the five Platonic solids (which are compose ...

s, which were later rediscovered by

around 1620 A.D. *

Apollonius of Perga Apollonius of Perga ( grc-gre, Ἀπολλώνιος ὁ Περγαῖος, Apollṓnios ho Pergaîos; la, Apollonius Pergaeus; ) was an Ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the contributio ...

() is known for his work on

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 and his study of geometry in 3-dimensional space. He is considered one of the greatest ancient Greek mathematicians. *

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 ...

() is considered the founder of

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. ...

and also solved several problems of

spherical trigonometry Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are grea ...

. He was the first whose quantitative and accurate models for the motion of the

and

survive. In his work '' On Sizes and Distances'', he measured the apparent diameters of the Sun and Moon and their distances from Earth. He is also reputed to have measured the Earth's precession. *

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 ...

() wrote ''

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 ...

'' which dealt with solving algebraic equations and also introduced syncopated algebra, which was a precursor to modern symbolic algebra. Because of this, Diophantus is sometimes known as "the father 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 ...

," which is a title he shares with

Muhammad ibn Musa al-Khwarizmi Muḥammad ibn Mūsā al-Khwārizmī ( ar, محمد بن موسى الخوارزمي, Muḥammad ibn Musā al-Khwārazmi; ), or al-Khwarizmi, was a Persians, Persian polymath from Khwarazm, who produced vastly influential works in Mathematics ...

. In contrast to Diophantus, al-Khwarizmi wasn't primarily interested in integers and he gave an exhaustive and systematic description of solving

quadratic equation In algebra, a quadratic equation () is any equation that can be rearranged in standard form as ax^2 + bx + c = 0\,, where represents an unknown value, and , , and represent known numbers, where . (If and then the equation is linear, not qu ...

s and some higher order algebraic equations. However, al-Khwarizmi did not use symbolic or syncopated algebra but rather " rhetorical algebra" or ancient Greek "geometric algebra" (the ancient Greeks had expressed and solved some particular instances of algebraic equations in terms of geometric properties such as length and area but they did not solve such problems in general; only particular instances). An example of "geometric algebra" is: given a triangle (or rectangle, etc.) with a certain area and also given the length of some of its sides (or some other properties), find the length of the remaining side (and justify/prove the answer with geometry). Solving such a problem is often equivalent to finding the roots of a polynomial.

Hellenic mathematicians

The conquests of

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 ...

around led to Greek culture being spread around much of the Mediterranean region, especially in

Alexandria, Egypt 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, Alexandria ...

. This is why the Hellenistic period of Greek mathematics is typically considered as beginning in the 4th century BC. During the Hellenistic period, many people living in those parts of the

Mediterranean region In biogeography, the Mediterranean Basin (; also known as the Mediterranean Region or sometimes Mediterranea) is the region of lands around the Mediterranean Sea that have mostly a Mediterranean climate, with mild to cool, rainy winters and wa ...

subject to Greek influence ended up adopting the Greek language and sometimes also Greek culture. Consequently, some of the Greek mathematicians from this period may not have been "ethnically Greek" with respect to the modern

Western Western may refer to: Places *Western, Nebraska, a village in the US *Western, New York, a town in the US *Western Creek, Tasmania, a locality in Australia *Western Junction, Tasmania, a locality in Australia *Western world, countries that id ...

notion of

ethnicity An ethnic group or an ethnicity is a grouping of people who identify with each other on the basis of shared attributes that distinguish them from other groups. Those attributes can include common sets of traditions, ancestry, language, history, ...

, which is much more rigid than most other notions of ethnicity that existed in the Mediterranean region at the time.

, for example, was said to originated from

Upper Egypt Upper Egypt ( ar, صعيد مصر ', shortened to , , locally: ; ) is the southern portion of Egypt and is composed of the lands on both sides of the Nile that extend upriver from Lower Egypt in the north to Nubia in the south. In ancient E ...

, which is far South of

. Regardless, their contemporaries considered them Greek.

Straightedge and compass constructions

Regular Hexagon Inscribed in a Circle 240px

For the most part,

straightedge and compass construction In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an ideali ...

s dominated ancient Greek mathematics and most

s and results were stated and proved in terms of geometry. The straightedge is an idealized

ruler A ruler, sometimes called a rule, line gauge, or scale, is a device used in geometry and technical drawing, as well as the engineering and construction industries, to measure distances or draw straight lines. Variants Rulers have long ...

that can draw arbitrarily long lines but (unlike modern rulers) it has no markings on it. A

compass A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with ...

can draw a circle starting from two given points: the center and a point on the circle. Thus a straightedge is used to construct lines while compasses are used to construct circles. Geometric constructions using lines, such as those formed by the straightedge of a taut rope, and circles, such as those formed by a compass or by a straightedge (such a taut rope) rotated around a point, were also used outside of the Mediterranean region. The

Shulba Sutras The ''Shulva Sutras'' or ''Śulbasūtras'' ( Sanskrit: शुल्बसूत्र; ': "string, cord, rope") are sutra texts belonging to the Śrauta ritual and containing geometry related to fire-altar construction. Purpose and origins T ...

from the

Vedic period The Vedic period, or the Vedic age (), is the period in the late Bronze Age and early Iron Age of the history of India when the Vedic literature, including the Vedas (ca. 1300–900 BCE), was composed in the northern Indian subcontinent, betwe ...

Indian mathematics Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta ...

, for instance, contains geometric instructions on how to physically construct a (quality) fire-altar by using a taut rope as a straightedge. These alters could have various shapes but for theological reasons, they were all required to have the same area. This consequently required a high precision construction along with (written) instructions on how to geometrically construct such alters with the tools that were most widely available throughout the

Indian subcontinent The Indian subcontinent is a physiographical region in Southern Asia. It is situated on the Indian Plate, projecting southwards into the Indian Ocean from the Himalayas. Geopolitically, it includes the countries of Bangladesh, Bhutan, In ...

(and elsewhere) at the time. Ancient Greek mathematicians went one step further by axiomatizing plane geometry in such a way that straightedge and compass constructions became

mathematical proof A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every pr ...

's '' Elements'' was the culmination of this effort and for over two thousand years, even as late as the 19th century, it remained the "standard text" on mathematics throughout the Mediterranean region (including Europe and the Middle East), and later also in North and South America after

European colonization The historical phenomenon of colonization is one that stretches around the globe and across time. Ancient and medieval colonialism was practiced by the Phoenicians, the Greeks, the Turks, and the Arabs. Colonialism in the modern sense be ...

Algebra

Ancient Greek mathematicians are known to have solved specific instances of

polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An exampl ...

equations with the use of straightedge and compass constructions, which simultaneously gave a geometric proof of the solution's correctness. Once a construction was completed, the answer could be found by measuring the length of a certain line segment (or possibly some other quantity). A quantity multiplied by itself, such as

5 \cdot 5

for example, would often be constructed as a literal square with sides of length

5,

which is why the second power "

x^2 = x \cdot x

" is referred to as "

x

squared" in ordinary spoken language. Thus problems that would today be considered "algebra problems" were also solved by ancient Greek mathematicians, although not in full generality. A guide to systematically solving low-order polynomials equations for an unknown quantity (instead of just specific instances of such problems) would not appear until ''

The Compendious Book on Calculation by Completion and Balancing ''The Compendious Book on Calculation by Completion and Balancing'' ( ar, كتاب المختصر في حساب الجبر والمقابلة, ; la, Liber Algebræ et Almucabola), also known as ''Al-Jabr'' (), is an Arabic mathematical treati ...

'' by

, who used Greek geometry to "prove the correctness" of the solutions that were given in the treatise. However, this treatise was entirely rhetorical (meaning that everything, including numbers, was written using words structured in ordinary sentences) and did not have any "algebraic symbols" that are today associated with algebra problems – not even the syncopated algebra that appeared in ''

References

* (1991 pbk ed. ) * {{Ancient Greek mathematics Ancient Greek mathematicians Greek mathematics History of geometry History of mathematics Mathematics timelines

Timeline

Overview of the most important mathematicians and discoveries

Hellenic mathematicians

Straightedge and compass constructions

Algebra

See also

References