The area of study known as the history of mathematics is primarily an
investigation into the origin of discoveries in mathematics and, to a
lesser extent, an investigation into the mathematical methods and
notation of the past. Before the modern age and the worldwide spread
of knowledge, written examples of new mathematical developments have
come to light only in a few locales. From 3000 BC the Mesopotamian
states of Sumer, Akkad and Assyria, together with
Contents 1 Prehistoric
2 Babylonian
3 Egyptian
4 Greek
5 Roman
6 Chinese
7 Indian
8 Islamic
9 Maya
10 Medieval European
11 Renaissance
12
12.1 17th century 12.2 18th century 13 Modern 13.1 19th century 13.2 20th century 13.3 21st century 14 Future 15 See also 16 Notes 17 References 18 Further reading 18.1 General 18.2 Books on a specific period 18.3 Books on a specific topic 19 External links 19.1 Documentaries 19.2 Educational material 19.3 Bibliographies 19.4 Organizations 19.5 Journals 19.6 Directories Prehistoric[edit]
The origins of mathematical thought lie in the concepts of number,
magnitude, and form.[11] Modern studies of animal cognition have shown
that these concepts are not unique to humans. Such concepts would have
been part of everyday life in hunter-gatherer societies. The idea of
the "number" concept evolving gradually over time is supported by the
existence of languages which preserve the distinction between "one",
"two", and "many", but not of numbers larger than two.[11]
Prehistoric artifacts discovered in Africa, dated 20,000 years old or
more suggest early attempts to quantify time.[not in citation given]
The Ishango bone, found near the headwaters of the
The Babylonian mathematical tablet Plimpton 322, dated to 1800 BC.
Image of Problem 14 from the Moscow Mathematical Papyrus. The problem includes a diagram indicating the dimensions of the truncated pyramid.
The Pythagorean theorem. The
One of the oldest surviving fragments of Euclid's Elements, found at
Title page of the 1621 edition of Diophantus' Arithmetica, translated
into
Around the same time,
The
The first woman mathematician recorded by history was
Equipment used by an ancient Roman land surveyor (gromatici), found at the site of Aquincum, modern Budapest, Hungary Although ethnic Greek mathematicians continued to live under the rule
of the late
Counting rod numerals The Tsinghua Bamboo Slips, containing the world's earliest decimal
multiplication table, dated 305 BC during the
The Nine Chapters on the Mathematical Art, one of the earliest
surviving mathematical texts from
An analysis of early
The numerals used in the Bakhshali manuscript, dated between the 2nd century BCE and the 2nd century CE. Indian numerals in stone and copper inscriptions[119] Ancient Brahmi numerals in a part of India The earliest civilization on the Indian subcontinent is the Indus
Valley Civilization (mature phase: 2600 to 1900 BC) that flourished in
the
The oldest extant mathematical records from India are the Sulba Sutras
(dated variously between the 8th century BC and the 2nd century
AD),[121] appendices to religious texts which give simple rules for
constructing altars of various shapes, such as squares, rectangles,
parallelograms, and others.[122] As with Egypt, the preoccupation with
temple functions points to an origin of mathematics in religious
ritual.[121] The
Explanation of the sine rule in Yuktibhāṣā In the 7th century,
Page from The Compendious Book on Calculation by Completion and
Balancing by
The Islamic Empire established across Persia, the Middle East, Central
Asia, North Africa, Iberia, and in parts of India in the 8th century
made significant contributions towards mathematics. Although most
Islamic texts on mathematics were written in Arabic, most of them were
not written by Arabs, since much like the status of Greek in the
Hellenistic world,
The
In the Pre-Columbian Americas, the
Medieval European interest in mathematics was driven by concerns quite
different from those of modern mathematicians. One driving element was
the belief that mathematics provided the key to understanding the
created order of nature, frequently justified by Plato's Timaeus and
the biblical passage (in the Book of Wisdom) that God had ordered all
things in measure, and number, and weight.[156]
Portrait of Luca Pacioli, a painting traditionally attributed to Jacopo de' Barbari, 1495, (Museo di Capodimonte). Further information:
Gottfried Wilhelm Leibniz. The 17th century saw an unprecedented increase of mathematical and
scientific ideas across Europe.
The most influential mathematician of the 18th century was arguably
Leonhard Euler. His contributions range from founding the study of
graph theory with the
π displaystyle pi to stand for the ratio of a circle's circumference to its diameter.
He made numerous contributions to the study of topology, graph theory,
calculus, combinatorics, and complex analysis, as evidenced by the
multitude of theorems and notations named for him.
Other important European mathematicians of the 18th century included
Joseph Louis Lagrange, who did pioneering work in number theory,
algebra, differential calculus, and the calculus of variations, and
Carl Friedrich Gauss. Throughout the 19th century mathematics became increasingly abstract.
Behavior of lines with a common perpendicular in each of the three types of geometry This century saw the development of the two forms of non-Euclidean
geometry, where the parallel postulate of
A map illustrating the Four Color Theorem The 20th century saw mathematics become a major profession. Every
year, thousands of new Ph.D.s in mathematics were awarded, and jobs
were available in both teaching and industry. An effort to catalogue
the areas and applications of mathematics was undertaken in Klein's
encyclopedia.
In a 1900 speech to the International Congress of Mathematicians,
Newtonian (red) vs. Einsteinian orbit (blue) of a lone planet orbiting a star, with relativistic precession of apsides
The absolute value of the
One of the more colorful figures in 20th-century mathematics was
History of algebra History of calculus History of combinatorics History of the function concept History of geometry History of logic History of mathematical notation History of numbers History of number theory History of statistics History of trigonometry History of writing numbers Kenneth O. May Prize List of important publications in mathematics Lists of mathematicians List of mathematics history topics Timeline of mathematics Notes[edit] ^ a b (Boyer 1991, "
References[edit] Berggren, Lennart; Borwein, Jonathan M.; Borwein, Peter B. (2004), Pi:
A Source Book, New York: Springer, ISBN 0-387-20571-3
Boyer, C.B. (1991) [1989], A History of
Further reading[edit] General[edit] Aaboe, Asger (1964). Episodes from the Early History of Mathematics. New York: Random House. Bell, E. T. (1937). Men of Mathematics. Simon and Schuster. Burton, David M. The History of Mathematics: An Introduction. McGraw Hill: 1997. Grattan-Guinness, Ivor (2003). Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. The Johns Hopkins University Press. ISBN 0-8018-7397-5. Kline, Morris. Mathematical Thought from Ancient to Modern Times. Osen, Lynn M. (1975). Women in Mathematics. The MIT Press. ISBN 978-0262650090. Struik, D. J. (1987). A Concise History of Mathematics, fourth revised edition. Dover Publications, New York. Books on a specific period[edit] Gillings, Richard J. (1972).
Heath, Sir Thomas (1981). A History of Greek Mathematics. Dover.
ISBN 0-486-24073-8.
van der Waerden, B. L.,
Books on a specific topic[edit] Hoffman, Paul, The Man Who Loved Only Numbers: The Story of Paul
Erdős and the Search for Mathematical Truth. New York: Hyperion, 1998
ISBN 0-7868-6362-5.
Menninger, Karl W. (1969).
Stigler, Stephen M. (1990). The History of Statistics: The Measurement of Uncertainty before 1900. Belknap Press. ISBN 0-674-40341-X. External links[edit] Wikiquote has quotations related to: History of mathematics Documentaries[edit]
Educational material[edit] MacTutor History of
Bibliographies[edit] A Bibliography of Collected Works and Correspondence of Mathematicians archive dated 2007/3/17 (Steven W. Rockey; Cornell University Library). Organizations[edit] International Commission for the History of Mathematics Journals[edit] Historia Mathematica Convergence, the Mathematical Association of America's online Math History Magazine Directories[edit] Links to Web Sites on the History of
v t e Areas of mathematics outline topic lists Branches Arithmetic History of mathematics
Philosophy of mathematics
Algebra
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Mathematical statistics
Statistics
Divisions Pure Applied Discrete Computational Category Portal Commons WikiProject v t e Indian mathematics Mathematicians Ancient Apastamba Baudhayana Katyayana Manava Pāṇini Pingala Yajnavalkya Classical Āryabhaṭa I Āryabhaṭa II Bhāskara I Bhāskara II Melpathur Narayana Bhattathiri Brahmadeva Brahmagupta Brihaddeshi Govindasvāmi Halayudha Jyeṣṭhadeva Kamalakara Mādhava of Saṅgamagrāma Mahāvīra Mahendra Sūri Munishvara Narayana Pandit Parameshvara Achyuta Pisharati Jagannatha Samrat Nilakantha Somayaji Śrīpati Sridhara Gangesha Upadhyaya Varāhamihira Sankara Variar Virasena Modern Shanti Swarup Bhatnagar Prize recipients in Mathematical Science Treatises Āryabhaṭīya Bakhshali manuscript Bijaganita Brāhmasphuṭasiddhānta Ganita Kaumudi Karanapaddhati Līlāvatī Lokavibhaga Paulisa Siddhanta Paitamaha Siddhanta Romaka Siddhanta Sadratnamala Siddhānta Shiromani Śulba Sūtras Surya Siddhanta Tantrasamgraha Vasishtha Siddhanta Veṇvāroha Yuktibhāṣā Yavanajataka Centres Kerala school of astronomy and mathematics
Ujjain
Historians of mathematics Bibhutibhushan Datta T. A. Sarasvati Amma A. A. Krishnaswami Ayyangar Sudhakara Dvivedi Radha Charan Gupta Kim Plofker K. V. Sarma Bapudeva Sastri Prabodh Chandra Sengupta Translators Walter Eugene Clark David Pingree Other regions Babylonian mathematics Chinese mathematics Greek mathematics Islamic mathematics European mathematics Modern institutions Indian Statistical Institute Chennai Mathematical Institute Institute of Mathematical Sciences, Chennai Indian Institute of Science Harish-Chandra Research Institute Bhaskaracharya Pratishthana Ramanujan Institute for Advanced Study in Mathematics Tata Institute of Fundamental Research Homi Bhabha Centre for Science Education v t e
Mathematicians 9th century 'Abd al-Hamīd ibn Turk Sind ibn Ali al-Jawharī Al-Ḥajjāj ibn Yūsuf Al-Kindi Al-Mahani al-Dinawari Banū Mūsā Hunayn ibn Ishaq al-Khwārizmī Yusuf Al-Khuri ibn Qurra Na'im ibn Musa Sahl ibn Bishr al-Marwazi Abu Said Gorgani 10th century al-Sufi Abu al-Wafa al-Khāzin Abū Kāmil Al-Qabisi al-Khojandi Ahmad ibn Yusuf Aṣ-Ṣaidanānī al-Uqlidisi Al-Nayrizi Al-Saghani Brethren of Purity Ibn Sahl Ibn Yunus Ibrahim ibn Sinan Al-Battani Sinan ibn Thabit Al-Isfahani Nazif ibn Yumn al-Qūhī Abu al-Jud al-Majriti al-Jabali 11th century al-Zarqālī Abu Nasr Mansur Said al-Andalusi Ibn al-Samh Al-Biruni Alhazen ibn Fatik Al-Sijzi al-Nasawī Al-Karaji Avicenna Muhammad al-Baghdadi ibn Hud al-Jayyānī Kushyar Gilani Al-Muradi Al-Isfizari Abu Mansur al-Baghdadi 12th century Al-Samawal al-Maghribi Avempace Al-Khazini Omar Khayyam Jabir ibn Aflah al-Hassar Al-Kharaqī Sharaf al-Dīn al-Ṭūsī Ibn al-Yasamin 13th century al-Hanafi al-Abdari Muhyi al-Dīn al-Maghribī Ibn 'Adlan Nasir al-Din al-Tusi Shams al-Dīn al-Samarqandī Ibn al‐Ha'im al‐Ishbili Ibn Abi al-Shukr al-Hasan al-Marrakushi 14th century al-Umawī Ibn al-Banna' Ibn Shuayb Ibn al-Shatir Kamāl al-Dīn al-Fārisī Al-Khalili Qutb al-Din al-Shirazi Ahmad al-Qalqashandi Ibn al-Durayhim 15th century al-Qalaṣādī Ali Qushji al-Wafa'i al-Kāshī al-Rūmī Ulugh Beg Ibn al-Majdi Sibt al-Maridini al-Kubunani 16th century Al-Birjandi Muhammad Baqir Yazdi Taqi ad-Din Ibn Hamza al-Maghribi Ibn Ghazi al-Miknasi Ahmad Ibn al-Qadi Mathematical works The Compendious Book on Calculation by Completion and Balancing De Gradibus Principles of Hindu Reckoning Book of Optics The Book of Healing Almanac Encyclopedia of the Brethren of Purity Toledan Tables Tabula Rogeriana Zij Concepts Alhazen's problem Islamic geometric patterns Centers Al-Azhar University Al-Mustansiriya University House of Knowledge House of Wisdom Constantinople observatory of Taqi al-Din Madrasa Maktab Maragheh observatory University of Al Quaraouiyine Influences Babylonian mathematics Greek mathematics Indian mathematics Influenced Byzantine mathematics European mathematics Indian mathematics v t e History of science Background Theories and sociology Historiography Pseudoscience By era Early cultures Classical Antiquity The Golden Age of Islam Renaissance Scientific Revolution Romanticism By culture African Byzantine Medieval European Chinese Indian Medieval Islamic Natural sciences Astronomy Biology Botany Chemistry Ecology Evolution Geology Geophysics Paleontology Physics Mathematics Algebra Calculus Combinatorics Geometry Logic Probability Statistics Trigonometry Social sciences Anthropology Economics Geography Linguistics Political science Psychology Sociology Sustainability Technology Agricultural science
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