Before 1000 BC

• ca. 70,000 BC – South Africa, ochre rocks adorned with scratched geometric patterns (see Blombos Cave).^[1]
• ca. 35,000 BC to 20,000 BC – Africa and France, earliest known prehistoric attempts to quantify time (see Lebombo bone).^[2][3][4]
• c. 20,000 BC – Nile Valley, Ishango bone: possibly the earliest reference to prime numbers and Egyptian multiplication.
• c. 3400 BC – Mesopotamia, the Sumerians invent the first numeral system, and a system of weights and measures.
• c. 3100 BC – Egypt, earliest known decimal system allows indefinite counting by way of introducing new symbols.^[5]
• c. 2800 BC – Indus Valley Civilisation on the Indian subcontinent, earliest use of decimal ratios in a uniform system of ancient weights and measures, the smallest unit of measurement used is 1.704 millimetres and the smallest unit of mass used is 28 grams.
• 2700 BC – Egypt, precision surveying.
• 2400 BC – Egypt, precise astronomical calendar, used even in the Middle Ages for its mathematical regularity.
• c. 2000 BC – Mesopotamia, the Babylonians use a base-60 positional numeral system, and compute the first known approximate value of π at 3.125.
• c. 2000 BC – Scotland, carved stone balls exhibit a variety of symmetries including all of the symmetries of Platonic solids, though it is not known if this was deliberate.
• 1800 BC – Egypt, Moscow Mathematical Papyrus, finding the volume of a frustum.
• c. 1800 BC – Berlin Papyrus 6619 (Egypt, 19th dynasty) contains a quadratic equation and its solution.^[5]
• 1650 BC – Rhind Mathematical Papyrus, copy of a lost scroll from around 1850 BC, the scribe Ahmes presents one of the first known approximate values of π at 3.16, the first attempt at squaring the circle, earliest known use of a sort of cotangent, and knowledge of solving first order linear equations.
• The earliest recorded use of combinatorial techniques comes from problem 79 of the Rhind papyrus which dates to the 16th century BCE.^[6]

1st millennium BC

• c. 1000 BC – Simple fractions used by the Egyptians. However, only unit fractions are used (i.e., those with 1 as the numerator) and interpolation tables are used to approximate the values of the other fractions.^[7]
• first half of 1st millennium BC – Vedic India – Yajnavalkya, in his Shatapatha Brahmana, describes the motions of the Sun and the Moon, and advances a 95-year cycle to synchronize the motions of the Sun and the Moon.
• 800 BC – Baudhayana, author of the Baudhayana Shulba Sutra, a Vedic Sanskrit geometric text, contains quadratic equations, and calculates the square root of two correctly to five decimal places.
• c. 8th century BC – the Yajurveda, one of the four Hindu Vedas, contains the earliest concept of infinity, and states "if you remove a part from infinity or add a part to infinity, still what remains is infinity."
• 1046 BC to 256 BC – China, Zhoubi Suanjing, arithmetic, geometric algorithms, and proofs.
• 624 BC – 546 BC – Greece, Thales of Miletus has various theorems attributed to him.
• c. 600 BC – Greece, the other Vedic "Sulba Sutras" ("rule of chords" in Sanskrit) use Pythagorean triples, contain of a number of geometrical proofs, and approximate π at 3.16.
• second half of 1st millennium BC – The Luoshu Square, the unique normal magic square of order three, was discovered in China.
• 530 BC – Greece, Pythagoras studies propositional geometry and vibrating lyre strings; his group also discovers the irrationality of the square root of two.
• c. 510 BC – Greece, Anaxagoras
• c. 500 BC – Indian grammarian Pānini writes the Astadhyayi, which contains the use of metarules, transformations and recursions, originally for the purpose of systematizing the grammar of Sanskrit.
• c. 500 BC – Greece, Oenopides of Chios
• 470 BC – 410 BC – Greece, Hippocrates of Chios utilizes lunes in an attempt to square the circle.
• 490 BC – 430 BC – Greece, Zeno of Elea Zeno's paradoxes
• 5th century BC – India, Apastamba, author of the Apastamba Sulba Sutra, another Vedic Sanskrit geometric text, makes an attempt at squaring the circle and also calculates the square root of 2 correct to five decimal places.
• 5th c. BC – Greece, Theodorus of Cyrene
• 5th century – Greece, Antiphon the Sophist
• 460 BC – 370 BC – Greece, Democritus
• 460 BC – 399 BC – Greece, Hippias
• 5th century (late) – Greece, Bryson of Heraclea
• 428 BC – 347 BC – Greece, Archytas
• 423 BC – 347 BC – Greece, Plato
• 417 BC – 317 BC – Greece, Theaetetus
• c. 400 BC – India, write the Surya Prajinapti, a mathematical text classifying all numbers into three sets: enumerable, innumerable and infinite. It also recognises five different types of infinity: infinite in one and two directions, infinite in area, infinite everywhere, and infinite perpetually.
• 408 BC – 355 BC – Greece, Eudoxus of Cnidus
• 400 BC – 350 BC – Greece, Thymaridas
• 395 BC – 313 BC – Greece, Xenocrates
• 390 BC – 320 BC – Greece, Dinostratus
• 380–290 – Greece, Autolycus of Pitane
• 370 BC – Greece, Eudoxus states the method of exhaustion for area determination.
• 370 BC – 300 BC – Greece, Aristaeus the Elder
• 370 BC – 300 BC – Greece, Callippus
• 350 BC – Greece, Aristotle discusses logical reasoning in Organon.
• 4th century BC – Indian texts use the Sanskrit word "Shunya" to refer to the concept of "void" (zero).
• 4th century BC – China, Counting rods
• 330 BC – China, the earliest known work on Chinese geometry, the Mo Jing, is compiled.
• 310 BC – 230 BC – Greece, Aristarchus of Samos
• 390 BC – 310 BC – Greece, Heraclides Ponticus
• 380 BC – 320 BC – Greece, Menaechmus
• 300 BC – India, Bhagabati Sutra, which contains the earliest information on combinations.
• 300 BC  – Greece, Euclid in his Elements studies geometry as an axiomatic system, proves the infinitude of prime numbers and presents the Euclidean algorithm; he states the law of reflection in Catoptrics, and he proves the fundamental theorem of arithmetic.
• c. 300 BC – India, Brahmi numerals (ancestor of the common modern base 10 numeral system)
• 370 BC – 300 BC – Greece, Eudemus of Rhodes works on histories of arithmetic, geometry and astronomy now lost.^[8]
• 300 BC – Mesopotamia, the Babylonians invent the earliest calculator, the abacus.
• c. 300 BC – Indian mathematician Pingala writes the Chhandah-shastra, which contains the first Indian use of zero as a digit (indicated by a dot) and also presents a description of a binary numeral system, along with the first use of Fibonacci numbers and Pascal's triangle.
• 280 BC – 210 BC – Greece, Nicomedes (mathematician)
• 280 BC – 220BC – Greece, Philo of Byzantium
• 280 BC – 220 BC – Greece, Conon of Samos
• 279 BC – 206 BC – Greece, Chrysippus
• c. 3rd century BC – India, Kātyāyana
• 250 BC – 190 BC – Greece, Dionysodorus
• 262 -198 BC – Greece, Apollonius of Perga
• 260 BC – Greece, Archimedes proved that the value of π lies between 3 + 1/7 (approx. 3.1429) and 3 + 10/71 (approx. 3.1408), that the area of a circle was equal to π multiplied by the square of the radius of the circle and that the area enclosed by a parabola and a straight line is 4/3 multiplied by the area of a triangle with equal base and height. He also gave a very accurate estimate of the value of the square root of 3.
• c. 250 BC – late Olmecs had already begun to use a true zero (a shell glyph) several centuries before Ptolemy in the New World. See 0 (number).
• 240 BC – Greece, Eratosthenes uses his sieve algorithm to quickly isolate prime numbers.
• 240 BC 190 BC– Greece, Diocles (mathematician)
• 225 BC – Greece, Apollonius of Perga writes On Conic Sections and names the ellipse, parabola, and hyperbola.
• 202 BC to 186 BC –China, Book on Numbers and Computation, a mathematical treatise, is written in Han dynasty.
• 200 BC – 140 BC – Greece, Zenodorus (mathematician)
• 150 BC – India, Jain mathematicians in India write the Sthananga Sutra, which contains work on the theory of numbers, arithmetical operations, geometry, operations with fractions, simple equations, cubic equations, quartic equations, and permutations and combinations.
• c. 150 BC – Greece, Perseus (geometer)
• 150 BC – China, A method of Gaussian elimination appears in the Chinese text The Nine Chapters on the Mathematical Art.
• 150 BC – China, Horner's method appears in the Chinese text The Nine Chapters on the Mathematical Art.
• 150 BC – China, Negative numbers appear in the Chinese text The Nine Chapters on the Mathematical Art.
• 150 BC – 75 BC – Phoenician, Zeno of Sidon
• 190 BC – 120 BC – Greece, Hipparchus develops the bases of trigonometry.
• 190 BC – 120 BC – Greece, Hypsicles
• 160 BC – 100 BC – Greece, Theodosius of Bithynia
• 135 BC – 51 BC – Greece, Posidonius
• 78 BC – 37 BC – China, Jing Fang
• 50 BC – Indian numerals, a descendant of the Brahmi numerals (the first positional notation base-10 numeral system), begins development in India.
• mid 1st century Cleomedes (as late as 400 AD)
• final centuries BC – Indian astronomer Lagadha writes the Vedanga Jyotisha, a Vedic text on astronomy that describes rules for tracking the motions of the Sun and the Moon, and uses geometry and trigonometry for astronomy.
• 1st C. BC – Greece, Geminus
• 50 BC – 23 AD – China, Liu Xin

1st millennium AD

• 1st century – Greece, Heron of Alexandria, Hero, the earliest, fleeting reference to square roots of negative numbers.
• c 100 – Greece, Theon of Smyrna
• 60 – 120 – Greece, Nicomachus
• 70 – 140 – Greece, Menelaus of Alexandria Spherical trigonometry
• 78 – 139 – China, Zhang Heng
• c. 2nd century – Greece, Ptolemy of Alexandria wrote the Almagest.
• 132 – 192 – China, Cai Yong
• 240 – 300 – Greece, Sporus of Nicaea
• 250 – Greece, Diophantus uses symbols for unknown numbers in terms of syncopated algebra, and writes Arithmetica, one of the earliest treatises on algebra.
• 263 – China, Liu Hui computes π using Liu Hui's π algorithm.
• 300 – the earliest known use of zero as a decimal digit is introduced by Indian mathematicians.
• 234 – 305 – Greece, Porphyry (philosopher)
• 300 – 360 – Greece, Serenus of Antinoöpolis
• 335 – 405– Greece, Theon of Alexandria
• c. 340 – Greece, Pappus of Alexandria states his hexagon theorem and his centroid theorem.
• 350 – 415 – Byzantine Empire, Hypatia
• c. 400 – India, the Bakhshali manuscript , which describes a theory of the infinite containing different levels of infinity, shows an understanding of indices, as well as logarithms to base 2, and computes square roots of numbers as large as a million correct to at least 11 decimal places.
• 300 to 500 – the Chinese remainder theorem is developed by Sun Tzu.
• 300 to 500 – China, a description of rod calculus is written by Sun Tzu.
• 412 – 485 – Greece, Proclus
• 420 – 480 – Greece, Domninus of Larissa
• b 440 – Greece, Marinus of Neapolis "I wish everything was mathematics."
• 450 – China, Zu Chongzhi computes π to seven decimal places. This calculation remains the most accurate calculation for π for close to a thousand years.
• c. 474 – 558 – Greece, Anthemius of Tralles
• 500 – India, Aryabhata writes the Aryabhata-Siddhanta, which first introduces the trigonometric functions and methods of calculating their approximate numerical values. It defines the concepts of sine and cosine, and also contains the earliest tables of sine and cosine values (in 3.75-degree intervals from 0 to 90 degrees).
• 480 – 540 – Greece, Eutocius of Ascalon
• 490 – 560 – Greece, Simplicius of Cilicia
• 6th century – Aryabhata gives accurate calculations for astronomical constants, such as the solar eclipse and lunar eclipse, computes π to four decimal places, and obtains whole number solutions to linear equations by a method equivalent to the modern method.
• 505 – 587 – India, Varāhamihira
• 6th century – India, Yativṛṣabha
• 535 – 566 – China, Zhen Luan
• 550 – Hindu mathematicians give zero a numeral representation in the positional notation Indian numeral system.
• 600 – China, Liu Zhuo uses quadratic interpolation.
• 602 – 670 – China, Li Chunfeng
• 625 China, Wang Xiaotong writes the Jigu Suanjing, where cubic and quartic equations are solved.
• 7th century – India, Bhāskara I gives a rational approximation of the sine function.
• 7th century – India, Brahmagupta invents the method of solving indeterminate equations of the second degree and is the first to use algebra to solve astronomical problems. He also develops methods for calculations of the motions and places of various planets, their rising and setting, conjunctions, and the calculation of eclipses of the sun and the moon.
• 628 – Brahmagupta writes the Brahma-sphuta-siddhanta, where zero is clearly explained, and where the modern place-value Indian numeral system is fully developed. It also gives rules for manipulating both negative and positive numbers, methods for computing square roots, methods of solving linear and quadratic equations, and rules for summing series, Brahmagupta's identity, and the Brahmagupta theorem.
• 721 – China, Zhang Sui (Yi Xing) computes the first tangent table.
• 8th century – India, Virasena gives explicit rules for the Fibonacci sequence, gives the derivation of the volume of a frustum using an infinite procedure, and also deals with the logarithm to base 2 and knows its laws.
• 8th century – India, Sridhara gives the rule for finding the volume of a sphere and also the formula for solving quadratic equations.
• 773 – Iraq, Kanka brings Brahmagupta's Brahma-sphuta-siddhanta to Baghdad to explain the Indian system of arithmetic astronomy and the Indian numeral system.
• 773 – Muḥammad ibn Ibrāhīm al-Fazārī translates the Brahma-sphuta-siddhanta into Arabic upon the request of King Khalif Abbasid Al Mansoor.
• 9th century – India, Govindasvāmi discovers the Newton-Gauss interpolation formula, and gives the fractional parts of Aryabhata's tabular sines.
• 810 – The House of Wisdom is built in Baghdad for the translation of Greek and Sanskrit mathematical works into Arabic.
• 820 – Al-Khwarizmi – Persian mathematician, father of algebra, writes the Al-Jabr, later transliterated as Algebra, which introduces systematic algebraic techniques for solving linear and quadratic equations. Translations of his book on arithmetic will introduce the Hindu–Arabic decimal number system to the Western world in the 12th century. The term algorithm is also named after him.
• 820 – Iran, Al-Mahani conceived the idea of reducing geometrical problems such as doubling the cube to problems in algebra.
• c. 850 – Iraq, al-Kindi pioneers cryptanalysis and frequency analysis in his book on cryptography.
• c. 850 – India, Mahāvīra writes the Gaṇitasārasan̄graha otherwise known as the Ganita Sara Samgraha which gives systematic rules for expressing a fraction as the sum of unit fractions.
• 895 – Syria, Thābit ibn Qurra: the only surviving fragment of his original work contains a chapter on the solution and properties of cubic equations. He also generalized the Pythagorean theorem, and discovered the theorem by which pairs of amicable numbers can be found, (i.e., two numbers such that each is the sum of the proper divisors of the other).
• c. 900 – Egypt, Abu Kamil had begun to understand what we would write in symbols as ${\displaystyle x^{n}\cdot x^{m}=x^{m+n}}$
• 940 – Iran, Abu al-Wafa' al-Buzjani extracts roots using the Indian numeral system.
• 953 – The arithmetic of the Hindu–Arabic numeral system at first required the use of a dust board (a sort of handheld blackboard) because "the methods required moving the numbers around in the calculation and rubbing some out as the calculation proceeded." Al-Uqlidisi modified these methods for pen and paper use. Eventually the advances enabled by the decimal system led to its standard use throughout the region and the world.
• 953 – Persia, Al-Karaji is the "first person to completely free algebra from geometrical operations and to replace them with the arithmetical type of operations which are at the core of algebra today. He was first to define the monomials ${\displaystyle x}$, ${\displaystyle x^{2}}$, ${\displaystyle x^{3}}$, ... and ${\displaystyle 1/x}$, ${\displaystyle 1/x^{2}}$, ${\displaystyle 1/x^{3}}$, ... and to give rules for products of any two of these. He started a school of algebra which flourished for several hundreds of years". He also discovered the binomial theorem for integer exponents, which "was a major factor in the development of numerical analysis based on the decimal system".
• 975 – Mesopotamia, al-Battani extended the Indian concepts of sine and cosine to other trigonometrical ratios, like tangent, secant and their inverse functions. Derived the formulae: ${\displaystyle \sin \alpha =\tan \alpha /{\sqrt {1+\tan ^{2}\alpha }}}$ and ${\displaystyle \cos \alpha =1/{\sqrt {1+\tan ^{2}\alpha }}}$.

1000–1500

• c. 1000 – Abu Sahl al-Quhi (Kuhi) solves equations higher than the second degree.
• c. 1000 – Abu-Mahmud Khujandi first states a special case of Fermat's Last Theorem.
• c. 1000 – Law of sines is discovered by Muslim mathematicians, but it is uncertain who discovers it first between Abu-Mahmud al-Khujandi, Abu Nasr Mansur, and Abu al-Wafa' al-Buzjani.
• c. 1000 – Pope Sylvester II introduces the abacus using the Hindu–Arabic numeral system to Europe.
• 1000 – Al-Karaji writes a book containing the first known proofs by mathematical induction. He used it to prove the binomial theorem, Pascal's triangle, and the sum of integral cubes.^[9] He was "the first who introduced the theory of algebraic calculus".^[10]
• c. 1000 – Abu Mansur al-Baghdadi studied a slight variant of Thābit ibn Qurra's theorem on amicable numbers, and he also made improvements on the decimal system.
• 1020 – Abu al-Wafa' al-Buzjani gave the formula: sin (α + β) = sin α cos β + sin β cos α. Also discussed the quadrature of the parabola and the volume of the paraboloid.
• 1021 – Ibn al-Haytham formulated and solved Alhazen's problem geometrically.
• 1030 – Alī ibn Ahmad al-Nasawī writes a treatise on the decimal and sexagesimal number systems. His arithmetic explains the division of fractions and the extraction of square and cubic roots (square root of 57,342; cubic root of 3, 652, 296) in an almost modern manner.^[11]
• 1070 – Omar Khayyam begins to write Treatise on Demonstration of Problems of Algebra and classifies cubic equations.
• c. 1100 – Omar Khayyám "gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections". He became the first to find general geometric solutions of cubic equations and laid the foundations for the development of analytic geometry and non-Euclidean geometry. He also extracted roots using the decimal system (Hindu–Arabic numeral system).
• 12th century – Indian numerals have been modified by Arab mathematicians to form the modern Arabic numeral system .
• 12th century – the Arabic numeral system reaches Europe through the Arabs.
• 12th century – Bhaskara Acharya writes the Lilavati, which covers the topics of definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry, solid geometry, the shadow of the gnomon, methods to solve indeterminate equations, and combinations.
• 12th century – Bhāskara II (Bhaskara Acharya) writes the Bijaganita (Algebra), which is the first text to recognize that a positive number has two square roots. Furthermore, it also gives the Chakravala method which was the first generalized solution of so called Pell's equation
• 12th century – Bhaskara Acharya develops preliminary concepts of differentiation , and also develops Rolle's theorem, Pell's equation, a proof for the Pythagorean theorem, proves that division by zero is infinity, computes π to 5 decimal places, and calculates the time taken for the Earth to orbit the Sun to 9 decimal places.
• 1130 – Al-Samawal al-Maghribi gave a definition of algebra: "[it is concerned] with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known."^[12]
• 1135 – Sharaf al-Din al-Tusi followed al-Khayyam's application of algebra to geometry, and wrote a treatise on cubic equations that "represents an essential contribution to another algebra which aimed to study curves by means of equations, thus inaugurating the beginning of algebraic geometry".^[12]
• 1202 – Leonardo Fibonacci demonstrates the utility of Hindu–Arabic numerals in his Liber Abaci (Book of the Abacus).
• 1247 – Qin Jiushao publishes Shùshū Jiǔzhāng (Mathematical Treatise in Nine Sections).
• 1248 – Li Ye writes Ceyuan haijing, a 12 volume mathematical treatise containing 170 formulas and 696 problems mostly solved by polynomial equations using the method tian yuan shu.
• 1260 – Al-Farisi gave a new proof of Thabit ibn Qurra's theorem, introducing important new ideas concerning factorization and combinatorial methods. He also gave the pair of amicable numbers 17296 and 18416 that have also been jointly attributed to Fermat as well as Thabit ibn Qurra.^[13]
• c. 1250 – Nasir al-Din al-Tusi attempts to develop a form of non-Euclidean geometry.
• 1280 – Guo Shoujing and Wang Xun use cubic interpolation for generating sine.
• 1303 – Zhu Shijie publishes Precious Mirror of the Four Elements, which contains an ancient method of arranging binomial coefficients in a triangle.
• 1356- Narayana Pandita completes his treatise Ganita Kaumudi, which for the first time contains Fermat's factorization method, generalized fibonacci sequence, and the first ever algorithm to systematically generate all permutations as well as many new magic figure techniques.
• 14th century – Madhava discovers the power series expansion for ${\displaystyle \sin x}$, ${\displaystyle \cos x}$, ${\displaystyle \arctan x}$ and ${\displaystyle \pi /4}$ ^[14][15] This theory is now well known in the Western world as the Taylor series or infinite series.^[16]
• 14th century – Parameshvara Nambudiri, a Kerala school mathematician, presents a series form of the sine function that is equivalent to its Taylor series expansion, states the mean value theorem of differential calculus, and is also the first mathematician to give the radius of circle with inscribed cyclic quadrilateral.

Modern

Contemporary