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This is a list of important publications in mathematics, organized by field. Euclid, detail from The School of Athens by Raphael. ...
Some reasons why a particular publication might be regarded as important:
- Topic creator – A publication that created a new topic
- Breakthrough – A publication that changed scientific knowledge significantly
- Introduction – A publication that is a good introduction or survey of a topic
- Influence – A publication which has significantly influenced the world
- Latest and greatest – The current most advanced result in a topic
Early manuscripts These are publications that are not necessarily relevant to a mathematician nowadays, but are nonetheless important publications in the history of mathematics. The word mathematics comes from the Greek μάθημα (máthema) which means science, knowledge, or learning; μαθηματικός (mathematikós) means fond of learning. Today, the term refers to a specific body of knowledge - the rigorous, deductive study of quantity, structure, space, and change. ...
Description: It is one of the oldest mathematical texts, dating to the Second Intermediate Period of ancient Egypt. It was copied by the scribe Ahmes (properly Ahmose) from an older Middle Kingdom papyrus. It laid the foundations of Egyptian mathematics and in turn, later influenced Greek and Hellenistic mathematics. Besides describing how to obtain an approximation of π only missing the mark by under one per cent, it is describes one of the earliest attempts at squaring the circle and in the process provides persuasive evidence against the theory that the Egyptians deliberately built their pyramids to enshrine the value of π in the proportions. Even though it would be a strong overstatement to suggest that the papyrus represents even rudimentary attempts at analytical geometry, Ahmes did make use of a kind of an analogue of the cotangent. The Moscow and Rhind Mathematical Papyri are two of the oldest mathematical texts discovered. ...
Ahmes (more accurately Ahmose) was an Egyptian scribe who lived during the Second Intermediate Period. ...
Illustration of a 15th century scribe This is about scribe, the profession. ...
The Second Intermediate Period marks a period when Ancient Egypt once again fell into disarray between the end of the Middle Kingdom, and the start of the New Kingdom. ...
Ancient Egypt was an African civilization located along the upper Nile, reaching from the Nile Delta in the north to as far south as Jebel Barkal at the Fourth Cataract of the Nile at the time of its greatest extension (15th century BC). ...
Ahmes (more accurately Ahmose) was an Egyptian scribe who lived during the Second Intermediate Period. ...
This name may refer to (amongst others): Ahmose I, a pharaoh of ancient Egypt and founder of the Eighteenth dynasty. ...
The Middle Kingdom is: a old name for China a period in the History of Ancient Egypt, the Middle Kingdom of Egypt This is a disambiguation page — a navigational aid which lists pages that might otherwise share the same title. ...
Papyrus plant Cyperus papyrus at Kew Gardens, London Papyrus is an early form of paper made from the pith of the papyrus plant, Cyperus papyrus, a wetland sedge that grows to 5 meters (15 ft) in height and was once abundant in the Nile Delta of Egypt. ...
Egyptian mathematics refers to the style and methods of mathematics performed by scribes in Ancient Egypt, deriving in large part from the rare discoveries of ancient papyri: in particular, the Rhind Mathematical Papyrus, dating from the Second Intermediate Period (though it is a copy of a now lost Middle Kingdom...
Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 6th century BCE to the 5th century CE around the Eastern shores of the Mediterranean. ...
This square and circle have the same area. ...
Geometric shape created by connecting a polygonal base to an apex For other versions including architectural Pyramids, see Pyramid (disambiguation). ...
Trigonometry In trigonometry, the cotangent is a function (see trigonometric function) defined as: or An interpretation of the cotangent of an angle x is as follows. ...
Importance: Topic creator, Breakthrough, Influence
Description: Although the only mathematical tools at its author's disposal were what we might now consider secondary-school geometry, he used those methods with rare brilliance, explicitly using infinitesimals to solve problems that would now be treated by integral calculus. Among those problems were that of the center of gravity of a solid hemisphere, that of the center of gravity of a frustum of a circular paraboloid, and that of the area of a region bounded by a parabola and one of its secant lines. Contrary to historically ignorant statements found in some 20th-century calculus textbooks, he did not use anything like Riemann sums, either in the work embodied in this palimpsest or in any of his other works. For explicit details of the method used, see how Archimedes used infinitesimals. The Archimedes Palimpsest is a palimpsest on parchment in the form of a codex which originally was a copy of an otherwise unknown work of the ancient mathematician, physicist, and engineer Archimedes of Syracuse. ...
Archimedes of Syracuse. ...
Table of Geometry, from the 1728 Cyclopaedia. ...
In mathematics, an infinitesimal, or infinitely small number, is a number that is smaller in absolute value than any positive real number. ...
This article or section may contain original research or unverified claims. ...
A parabola The parabola (from the Greek: παÏαβολή) is a conic section generated by the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface. ...
In mathematics, a Riemann sum is a method for approximating the values of integrals. ...
The ancient Greek mathematician, physicist, and engineer Archimedes of Syracuse was the first mathematician to make explicit use of infinitesimals. ...
Online version: Online version The Sand Reckoner is probably the most accessible work of Archimedes, in some sense, it is the first research-expository paper. ...
Archimedes of Syracuse. ...
Description: The first known (European) system of number-naming that can be expanded beyond the needs of everyday life. A numeral is a symbol or group of symbols that represents a number. ...
Table of Geometry, from the 1728 Cyclopaedia. ...
Description: Written around the 8th century BC, this is one of the oldest geometrical texts. It laid the foundations of Indian mathematics and was influential in South Asia and its surrounding regions, and perhaps even Greece. Among the important geometrical discoveries included in this text are: the earliest list of Pythagorean triples discovered algebraically, the earliest statement of the Pythagorean theorem, the earliest geometrical proof of the Pythagorean theorem, geometric solutions of linear equations, several approximations of π, the first use of irrational numbers, and an accurate computation of the square root of 2, correct to a remarkable five decimal places. Though this was primarily a goemetrical text, it also contained some important algebraic developments, including the earliest use of quadratic equations of the forms ax2 = c and ax2 + bx = c, and integral solutions of simultaneous Diophantine equations with upto four unknowns. Baudhayana, (circa 800 BC), was a Vedic Indian mathematician/scribe. ...
The Sulba Sutras or Sulva Sutras are a text of Vedic mathematics. ...
Baudhayana, (circa 800 BC), was a Vedic Indian mathematician/scribe. ...
(2nd millennium BCE - 1st millennium BCE - 1st millennium) // Overview Events Assyria conquers Damascus and Samaria Nineveh destroyed (789 BCE) First recorded Olympic Games held in Greece (776 BCE) Zhou Dynasty moved its capital to Luoyang (771 BC); The Spring and Autumn Period (771-481 BCE) began. ...
The chronology of Indian mathematics spans from the Indus Valley civilization (3300-1500 BC) and Vedic civilization (1500-500 BC) to modern India (21st century CE). ...
South Asia or Southern Asia is a southern geopolitical region of the Asian continent comprising territories on and in proximity to the Indian subcontinent. ...
The chronology of Indian mathematics spans from the Indus Valley civilization (3300-1500 BC) and Vedic civilization (1500-500 BC) to modern India (21st century CE). ...
Lower-case pi The mathematical constant Ï€ is a real number which may be defined as the ratio of a circles circumference (Greek πεÏιφÎÏεια, periphery) to its diameter in Euclidean geometry, and which is in common use in mathematics, physics, and engineering. ...
In mathematics, a Diophantine equation is a polynomial equation that only allows the variables to be integers. ...
Importance: Topic creator, Breakthrough, Influence
Publication data: c. 300 BC The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise, consisting of 13 books, written by the Hellenistic mathematician Euclid in Egypt during the early 3rd century BC. It comprises a collection of definitions, postulates...
Euclid Euclid of Alexandria (Greek: ) (ca. ...
Centuries: 4th century BC - 3rd century BC - 2nd century BC Decades: 350s BC 340s BC 330s BC 320s BC 310s BC - 300s BC - 290s BC 280s BC 270s BC 260s BC 250s BC Years: 305 BC 304 BC 303 BC 302 BC 301 BC - 300 BC - 299 BC 298 BC...
Online version: Interactive Java version
Description: This is often regarded as not only the most important work in geometry but one of the most important works in mathematics. It contains many important results in geometry, number theory and the first algorithm as well. The Elements is still a valuable resource and a good introduction to algorithm. More than any specific result in the publication, it seems that the major achievement of this publication is the popularization of logic and mathematical proof as a method of solving problems. Table of Geometry, from the 1728 Cyclopaedia. ...
Table of Geometry, from the 1728 Cyclopaedia. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ...
Importance: Topic creator, Breakthrough, Influence, Introduction, Latest and greatest (though it is one of the first, some of the results are still the latest)
Description: This was a Chinese mathematics book, mostly geometric, composed during the Han Dynasty, perhaps as early as 200 BC. It remained the most important textbook in China and East Asia for over a thousand years, similar to the position of Euclid's Elements in Europe. Among its contents: Linear problems solved using the principle known later in the West as the rule of false position. Problems with several unknowns, solved by a principle similar to Gaussian elimination. Problems involving the principle known in the West as the Pythagorean theorem. The earliest solution of a matrix using a method equivalent to the modern method. The Nine Chapters on the Mathematical Art (ä¹ç« ç®—è¡“) is a Chinese mathematics book, probably composed in the 1st century AD, but perhaps as early as 200 BC. This book is the earliest surviving mathematical text from China that has come down to us by being copied by scribes and (centuries later...
Euclid, detail from The School of Athens by Raphael. ...
The Han Dynasty (Traditional Chinese: æ¼¢æœ; Simplified Chinese: 汉æœ; Hanyu Pinyin: ; Wade-Giles: Han Chau; 206 BC–AD 220) followed the Qin Dynasty and preceded the Three Kingdoms in China. ...
Centuries: 3rd century BC - 2nd century BC - 1st century BC Decades: 250s BC 240s BC 230s BC 220s BC 210s BC - 200s BC - 190s BC 180s BC 170s BC 160s BC 150s BC Years: 205 BC 204 BC 203 BC 202 BC 201 BC - 200 BC - 199 BC 198 BC...
Geographic scope of East Asia East Asia is a subregion of Asia that can be defined in either geographical or cultural terms. ...
In numerical analysis, the false position method or regula falsi method is a root-finding algorithm that combines features from the bisection method and the secant method. ...
In mathematics, Gaussian elimination or Gauss–Jordan elimination, named after Carl Friedrich Gauss and Wilhelm Jordan (for many, Gaussian elimination is regarded as the front half of the complete Gauss–Jordan elimination), is an algorithm in linear algebra for determining the solutions of a system of linear equations, for determining...
The Pythagorean theorem: The sum of the areas of the two squares on the legs (blue and red) equals the area of the square on the hypotenuse (purple). ...
In mathematics, a matrix (plural matrices) is a rectangular table of numbers or, more generally, of elements of a ring-like algebraic structure. ...
Importance: Topic creator, Breakthrough, Influence
Description: La Géométrie was published in 1637 and written by René Descartes. The book was influential in developing the Cartesian coordinate system and specifically discussed the representation of points of a plane, via real numbers; and the representation of curves, via equations. La Géométrie was published in 1637 and written by René Descartes. ...
For other things named Descartes, see Descartes (disambiguation). ...
This article is concerned with the production of books, magazines, and other literary material (whether in printed or electronic formats). ...
Events February 3 - Tulipmania collapses in Netherlands by government order February 15 - Ferdinand III becomes Holy Roman Emperor December 17 - Shimabara Rebellion erupts in Japan Pierre de Fermat makes a marginal claim to have proof of what would become known as Fermats last theorem. ...
see also Creative Writing Writing may refer to two activities: the inscribing of characters on a medium, with the intention of forming words and other constructs that represent language or record information, and the creation of material to be conveyed through written language. ...
For other things named Descartes, see Descartes (disambiguation). ...
Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ...
Point can refer to: Look up Point in Wiktionary, the free dictionary // Mathematics In mathematics: Point (geometry), an entity that has a location in space but no extent Fixed point (mathematics), a point that is mapped to itself by a mathematical function Point at infinity Point group Point charge, an...
Two intersecting planes in R3 In mathematics, a plane is a fundamental two-dimensional object. ...
In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. ...
In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ...
In mathematics, one often (not quite always) distinguishes between an identity, which is an assertion that two expressions are equal regardless of the values of any variables that occur within them, and an equation, which may be true for only some (or none) of the values of any such variables. ...
Importance: Topic creator, Breakthrough, Influence
Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ...
Description: Published in 1879, the title Begriffsschrift is usually translated as concept writing or concept notation; the full title of the book identifies it as "a formula language, modelled on that of arithmetic, of pure thought". Frege's motivation for developing his formal logical system was similar to Leibniz's desire for a calculus ratiocinator. Frege defines a logical calculus to support his research in the foundations of mathematics. Begriffsschrift is both the name of the book and the calculus defined therein. Begriffsschrift is the title of a short book on logic by Gottlob Frege, published in 1879, and is also the name of the formal system set out in that book. ...
Friedrich Ludwig Gottlob Frege (8 November 1848, Wismar – 26 July 1925, Bad Kleinen) was a German mathematician who evolved into a logician and philosopher. ...
1879 (MDCCCLXXIX) was a common year starting on Wednesday (see link for calendar). ...
In mathematics and in the sciences, a formula is a concise way of expressing information symbolically (as in a mathematical or chemical formula), or a general relationship between quantities. ...
Arithmetic or arithmetics (from the Greek word αÏιθμός = number) in common usage is a branch of (or the forerunner of) mathematics which records elementary properties of certain operations on numerals, though professional mathematicians often treat arithmetic as a synonym for number theory. ...
Thought or thinking is a mental process which allows beings to model the world, and so to deal with it effectively according to their goals, plans, ends and desires. ...
Gottfried Leibniz Gottfried Wilhelm von Leibniz (July 1, 1646 in Leipzig - November 14, 1716 in Hannover) was a German philosopher, scientist, mathematician, diplomat, librarian, and lawyer of Sorb descent. ...
The Calculus Ratiocinator is a concept appearing in the writings of Gottfried Leibniz, usually paired with his characteristica universalis, which he mentioned much more frequently. ...
Foundations of mathematics is a term sometimes used for certain fields of mathematics itself, namely for mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. ...
Importance: Arguably the most significant publication in logic since Aristotle. Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ...
Aristotle (Ancient Greek: Aristotelēs 384–March 7 322 BCE) was an ancient Greek philosopher, who studied with Plato and taught Alexander the Great. ...
Description: First published in 1895, the Formulario mathematico was the first mathematical book written entirely in a formalized language. It contained a description of mathematical logic and many important theorems in other branches of mathematics. Many of the notations introduced in the book are now in common use. Formulario Mathematico (interlingua: Formulation of mathematics) is a book by Giuseppe Peano which expresses fundamental theorems of mathematics in a symbolic language developed by Peano. ...
Giuseppe Peano Giuseppe Peano (August 27, 1858 – April 20, 1932) was an Italian mathematician and philosopher best known for his contributions to set theory. ...
1895 (MDCCCXCV) was a common year starting on Tuesday (see link for calendar) of the Gregorian calendar (or a common year starting on Thursday of the 12-day-slower Julian calendar). ...
In mathematics, logic and computer science, a formal language is a set of finite-length words (i. ...
Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ...
Importance:Influence
Description: The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Bertrand Russell and Alfred North Whitehead and published in 1910-1913. It is an attempt to derive all mathematical truths from a well-defined set of axioms and inference rules in symbolic logic. The questions remained whether a contradiction could be derived from the Principia's axioms, and whether there exists a mathematical statement which could neither be proven nor disproven in the system. These questions were settled, in a rather disappointing way, by Gödel's incompleteness theorem in 1931. The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910-1913. ...
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970), was a famous and influential British philosopher, logician, and mathematician, working mostly in the 20th century. ...
Alfred North Whitehead, OM (February 15, 1861 – December 30, 1947) was a British mathematician who became a philosopher. ...
Euclid, detail from The School of Athens by Raphael. ...
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970), was a famous and influential British philosopher, logician, and mathematician, working mostly in the 20th century. ...
Alfred North Whitehead, OM (February 15, 1861 – December 30, 1947) was a British mathematician who became a philosopher. ...
-1...
1913 (MCMXIII) was a common year starting on Wednesday. ...
Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ...
In mathematical logic, Gödels incompleteness theorems are two celebrated theorems proven by Kurt Gödel in 1931. ...
1931 (MCMXXXI) was a common year starting on Thursday (link is to a full 1931 calendar). ...
Importance: Influence
(Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik, vol. 38 (1931).) In mathematical logic, Gödels incompleteness theorems are two celebrated theorems proven by Kurt Gödel in 1931. ...
Online version: Online version Kurt Gödel (IPA: ) (April 28, 1906 Brno, then Austria-Hungary, now Czech Republic – January 14, 1978 Princeton, New Jersey) was a logician, mathematician, and philosopher of mathematics. ...
Description: In mathematical logic, Gödel's incompleteness theorems are two celebrated theorems proved by Kurt Gödel in 1930. The first incompleteness theorem states: Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ...
Kurt Gödel (IPA: ) (April 28, 1906 Brno, then Austria-Hungary, now Czech Republic – January 14, 1978 Princeton, New Jersey) was a logician, mathematician, and philosopher of mathematics. ...
1930 (MCMXXX) is a common year starting on Wednesday. ...
For any formal system such that (1) it is ω-consistent (omega-consistent), (2) it has a recursively definable set of axioms and rules of derivation, and (3) every recursive relation of natural numbers is definable in it, there exists a formula of the system such that, according to the intended interpretation of the system, it expresses a truth about natural numbers and yet it is not a theorem of the system. In mathematical logic, an omega-consistent (or ω-consistent) theory is a theory (collection of sentences) that is not only consistent (that is, does not prove a contradiction), but also avoids proving certain infinite combinations of sentences that are intuitively contradictory. ...
In computability theory a countable set is called recursive, computable or decidable if we can construct an algorithm which terminates after a finite amount of time and decides whether a given element belongs to the set or not. ...
For the algebra software named Axiom, see Axiom computer algebra system. ...
In logic, especially in mathematical logic, a rule of inference is a scheme for constructing valid inferences. ...
See: Recursion Recursively enumerable language Recursively enumerable set Recursive filter Recursive function Recursive set Primitive recursive function This is a disambiguation page — a list of pages that otherwise might share the same title. ...
In mathematics, a mathematical object X of some type T is definable, if there exists some predicate P(x) which is expressible using a finite string of mathematical symbols drawn from a finite language, such that P(X) is true and P(Y) is false for all Y of type...
A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. ...
Importance: Breakthrough, Influence
See the list of publications in information theory. To meet Wikipedias quality standards, this article or section may require cleanup. ...
This is a list of important publications in computer science, organized by field. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
Description: The Disquisitiones Arithmeticae is a textbook of number theory written by German mathematician Carl Friedrich Gauss and first published in 1801 when Gauss was 24. In this book Gauss brings together results in number theory obtained by mathematicians such as Fermat, Euler, Lagrange and Legendre and adds important new results of his own. The Disquisitiones Arithmeticae is a textbook of number theory written by German mathematician Carl Friedrich Gauss and first published in 1801 when Gauss was 24. ...
(help· info) (30 April 1777 – 23 February 1855) was a German mathematician and scientist of profound genius who contributed significantly to many fields, including number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. ...
The Disquisitiones Arithmeticae is a textbook of number theory written by German mathematician Carl Friedrich Gauss and first published in 1801 when Gauss was 24. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
A mathematician is a person whose primary area of study and research is mathematics. ...
(help· info) (30 April 1777 – 23 February 1855) was a German mathematician and scientist of profound genius who contributed significantly to many fields, including number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. ...
The Union Jack, flag of the newly formed United Kingdom of Great Britain and Ireland. ...
Pierre de Fermat Pierre de Fermat (August 17, 1601 – January 12, 1665) was a French lawyer at the Parliament of Toulouse and a mathematician who is given credit for the development of modern calculus. ...
Leonhard Euler aged 49 (oil painting by Emanuel Handmann, 1756) Leonhard Euler (April 15, 1707 - September 18, 1783) (pronounced oiler) was a Swiss mathematician and physicist. ...
Joseph Louis Lagrange Joseph Louis Lagrange (January 25, 1736 – April 10, 1813; born Giuseppe Luigi Lagrangia in Turin, Lagrange moved to Paris (1787) and became a French citizen, adopting the French translation of his name, Joseph Louis Lagrange) was an Italian-French mathematician and astronomer who made important contributions to...
Adrien-Marie Legendre (September 18, 1752–January 10, 1833) was a French mathematician. ...
Importance: Breakthrough, Influence
Description: On the Number of Primes Less Than a Given Magnitude (or Über die Anzahl der Primzahlen unter einer gegebenen Grösse) is a seminal 8-page paper by Bernhard Riemann published in the November 1859 edition of the Monthly Reports of the Berlin Academy. Although it is the only paper he ever published on number theory, it contains ideas which influenced dozens of researchers during the late 19th century and up to the present day. The paper consists primarily of definitions, heuristic arguments, sketches of proofs, and the application of powerful analytic methods; all of these have become essential concepts and tools of modern analytic number theory. On the Number of Primes Less Than a Given Magnitude (or Über die Anzahl der Primzahlen unter einer gegebenen Grösse) is a seminal 8-page paper by Bernhard Riemann published in the November 1859 edition of the Monthly Reports of the Berlin Academy. ...
Bernhard Riemann. ...
Bernhard Riemann. ...
1859 is a common year starting on Saturday. ...
Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ...
Analytic number theory is the branch of number theory that uses methods from mathematical analysis. ...
Importance: Breakthrough, Influence
Description: Vorlesungen über Zahlentheorie (Lectures on Number Theory) is a textbook of number theory written by German mathematicians P.G.L. Dirichlet and Richard Dedekind, and published in 1863. The Vorlesungen can be seen as a watershed between the classical number theory of Fermat, Jacobi and Gauss, and the modern number theory of Dedekind, Riemann and Hilbert. Dirichlet does not explicitly recognise the concept of the group that is central to modern algebra, but many of his proofs show an implicit understanding of group theory Vorlesungen über Zahlentheorie (Lectures on Number Theory) is a textbook of number theory written by German mathematicians P.G.L. Dirichlet and Richard Dedekind, and published in 1863. ...
Peter Gustav Lejeune Dirichlet. ...
Richard Dedekind Julius Wilhelm Richard Dedekind (October 6, 1831 – February 12, 1916) was a German mathematician who did important work in abstract algebra and the foundations of the real numbers. ...
Vorlesungen über Zahlentheorie (Lectures on Number Theory) is a textbook of number theory written by German mathematicians P.G.L. Dirichlet and Richard Dedekind, and published in 1863. ...
To meet Wikipedias quality standards, this article or section may require cleanup. ...
Peter Gustav Lejeune Dirichlet. ...
Richard Dedekind Julius Wilhelm Richard Dedekind (October 6, 1831 – February 12, 1916) was a German mathematician who did important work in abstract algebra and the foundations of the real numbers. ...
Pierre de Fermat Pierre de Fermat (August 17, 1601 – January 12, 1665) was a French lawyer at the Parliament of Toulouse and a mathematician who is given credit for the development of modern calculus. ...
Karl Gustav Jacob Jacobi (Potsdam December 10, 1804 - Berlin February 18, 1851), was not only a great German mathematician but also considered by many as the most inspiring teacher of his time (Bell, p. ...
(help· info) (30 April 1777 – 23 February 1855) was a German mathematician and scientist of profound genius who contributed significantly to many fields, including number theory, analysis, differential geometry, geodesy, magnetism, astronomy and optics. ...
Bernhard Riemann. ...
David Hilbert David Hilbert (January 23, 1862 – February 14, 1943) was a German mathematician born in Wehlau, near Königsberg, Prussia (now Znamensk, near Kaliningrad, Russia) who is recognized as one of the most influential mathematicians of the 19th and early 20th centuries. ...
Group theory is that branch of mathematics concerned with the study of groups. ...
Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields. ...
Importance: Breakthrough, Influence
Number Theory, An approach through history from Hammurapi to Legendre Description:An historical study of number theory, written by one of the 20th century's greatest researchers in the field. The book covers some thirty six centuries of arithmetical work but the bulk of it is devoted to a detailed study and exposition of the work of Fermat, Euler, Lagrange, and Legendre. The author wishes to take the reader into the workshop of his subjects to share their successes and failures. A rare opportunity to see the historical development of a subject through the mind of one of its greatest practitioners. André Weil (May 6, 1906 - August 6, 1998) was one of the great mathematicians of the 20th century. ...
Importance:
Integral and differential calculus is a central branch of mathematics, developed from algebra and geometry. ...
Yuktibhasa Description: Written in India in 1501, this was the world's first calculus text. "This work laid the foundation for a complete system of fluxions" (Charles Whish, 1835) and served as a summary of the Kerala School's achievements in calculus, trigonometry and mathematical analysis, most of which were earlier discovered by the 14th century mathematician Madhava. It's possible that this text influenced the later development of calculus in Europe. Some of its important developments in calculus include: the fundamental ideas of differentiation and integration, the derivative, differential equations, term by term integration, numerical integration by means of infinite series, the relationship between the area of a curve and its integral, and the mean value theorem. Some of its important developments in analysis include: the infinite series expansion of a function, the power series, the Taylor series, the trigonometric series of sine, cosine, tangent and arctangent, the second and third order Taylor series approximations of sine and cosine, the power series of π, π/4, θ, the radius, diamater and circumference, and tests of convergence. Jyestadeva (1500-1610), was an astronomer of the Kerala school founded by Madhava of Sangamagrama and a student of Damodara. ...
1501 was a common year starting on Tuesday (see link for calendar) of the Gregorian calendar. ...
| Come and take it, slogan of the Texas Revolution 1835 was a common year starting on Thursday (see link for calendar). ...
The Kerala School was a school of mathematics and astronomy founded by Madhava in Kerala (in South India) which included as its prominent members Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. ...
Wikibooks has more about this subject: Trigonometry Table of Trigonometry, 1728 Cyclopaedia Trigonometry (from the Greek trigonon = three angles and metro = measure) is a branch of mathematics dealing with angles, triangles and trigonometric functions such as sine, cosine and tangent. ...
Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. ...
This 14th-century statue from south India depicts the gods Shiva (on the left) and Uma (on the right). ...
Madhava (माधव) of Sangamagrama (1350-1425) was a major mathematician from Kerala, in South India. ...
The Kerala School was a school of mathematics and astronomy founded by Madhava in Kerala (in South India) which included as its prominent members Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. ...
Differentiation can mean the following: In biology: cellular differentiation; evolutionary differentiation; In mathematics: see: derivative In cosmogony: planetary differentiation Differentiation (geology); Differentiation (logic); Differentiation (marketing). ...
Integration may be any of the following: In the most general sense, integration may be any bringing together of things: the integration of two or more economies, cultures, religions (usually called syncretism), etc. ...
In mathematics, the derivative is defined to be the instantaneous rate of change of a function. ...
Graph of a differential equation In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ...
For any function that is continuous on [a, b] and differentiable on (a, b) there exists some c in the interval (a, b) such that the secant joining the endpoints of the interval [a, b] is parallel to the tangent at c. ...
In mathematics, a series is a sum of a sequence of terms. ...
In mathematics, a power series (in one variable) is an infinite series of the form where the coefficients an, the center c, and the argument x are usually real or complex numbers. ...
As the degree of the Taylor series rises, it approaches the correct function. ...
In mathematics, a Fourier series of a periodic function, named in honor of Joseph Fourier (1768-1830), represents the function as a sum of periodic functions of the form where e is Eulers number and i the imaginary unit. ...
In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ...
In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ...
This article is about the mathematical concept of tangent. For other meanings, see tangent (disambiguation). ...
In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ...
In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ...
In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ...
Lower-case pi The mathematical constant Ï€ is a real number which may be defined as the ratio of a circles circumference (Greek πεÏιφÎÏεια, periphery) to its diameter in Euclidean geometry, and which is in common use in mathematics, physics, and engineering. ...
Note: A theta probe is a device for measuring soil moisture. ...
The integral test for convergence is a method used to test infinite series of nonnegative terms for convergence. ...
Importance: Topic creator, Breakthrough, Influence
Description: The Philosophiae Naturalis Principia Mathematica (Latin: "mathematical principles of natural philosophy", often Principia or Principia Mathematica for short) is a three-volume work by Isaac Newton published on July 5, 1687. Perhaps the most influential scientific book ever published, it contains the statement of Newton's laws of motion forming the foundation of classical mechanics as well as his law of universal gravitation. He derives Kepler's laws for the motion of the planets (which were first obtained empirically). In formulating his physical theories, Newton had developed a field of mathematics known as calculus. Newtons own copy of his Principia, with hand written corrections for the second edition. ...
Sir Isaac Newton, PRS, (4 January 1643 – 31 March 1727) [OS: 25 December 1642 – 20 March 1727] was an English physicist, mathematician, astronomer, alchemist, inventor, and natural philosopher who is generally regarded as one of the most influential scientists in history. ...
Latin is an ancient Indo-European language originally spoken in the region around Rome called Latium. ...
Sir Isaac Newton, PRS, (4 January 1643 – 31 March 1727) [OS: 25 December 1642 – 20 March 1727] was an English physicist, mathematician, astronomer, alchemist, inventor, and natural philosopher who is generally regarded as one of the most influential scientists in history. ...
July 5 is the 186th day of the year (187th in leap years) in the Gregorian Calendar, with 179 days remaining. ...
Events March 19 - The men under explorer Robert Cavelier de La Salle murder him while searching for the mouth of the Mississippi River. ...
Newtons First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. ...
Classical mechanics is a branch of physics which studies the deterministic motion of objects. ...
Gravity is a force of attraction that acts between bodies that have mass. ...
Johannes Keplers primary contributions to astronomy/astrophysics were the three laws of planetary motion. ...
A planet is generally considered to be a relatively large mass of accreted matter in orbit around a star that is not a star itself. ...
Integral and differential calculus is a central branch of mathematics, developed from algebra and geometry. ...
Up to the publication of this book, mathematics was only used to describe nature. This is the first instance when mathematics is used to explain nature. Here was born the practice, now so standard we identify it with science, of explaining nature by postulating mathematical axioms and demonstrating that their conclusion are observable phenomena. In other words, the greatness of the Principia is not only in developing a number of fundamental theories in physics and mathematics but first and foremost (amply demonstrated in the title!) in the very linking of science and mathematics. The influence of this book is so deep that nowadays we find this link obvious and cannot imagine doing science in any other way.
Importance: Topic creator, Breakthrough, Influence
Newton's Principia for the Common Reader Description: An exposition, using modern notation and language, of a large part of Newton's above-cited masterwork. Mathematical and physical language and notation have evolved considerably since Newton's time, making it difficult for a modern reader to read Newton's original work even in translation from the original Latin. Chandrasekhar's labor of love makes it possible for a modern reader, familiar with the modern treatment of algebra, geometry and calculus to appreciate Newton's genius through following his work as he originally conceived it. Subrahmanyan Chandrasekhar (October 19, 1910 – August 21, 1995) was an Indian-American physicist, astrophysicist and mathematician. ...
Importance: Interpretation for the modern reader of a great classic of mathematics and science
Description: Introductions to differential and integral calculus in a single and many variables respectively. Integral and differential calculus is a central branch of mathematics, developed from algebra and geometry. ...
Michael Spivaks Calculus on Manifolds is a text treating analysis in several variables in Euclidean spaces and on differentiable manifolds. ...
Michael David Spivak is a mathematician specializing in differential geometry, an expositor of mathematics, and the founder of Publish-or-Perish Press. ...
Importance: Introduction
Numerical analysis is the study of algorithms for the problems of continuous mathematics (as distinguished from discrete mathematics). ...
Description: Method of Fluxions was a book written by Isaac Newton. The book was completed in 1671, and published in 1736. Method of Fluxions was a book by Isaac Newton. ...
Sir Isaac Newton, PRS, (4 January 1643 – 31 March 1727) [OS: 25 December 1642 – 20 March 1727] was an English physicist, mathematician, astronomer, alchemist, inventor, and natural philosopher who is generally regarded as one of the most influential scientists in history. ...
Sir Isaac Newton, PRS, (4 January 1643 – 31 March 1727) [OS: 25 December 1642 – 20 March 1727] was an English physicist, mathematician, astronomer, alchemist, inventor, and natural philosopher who is generally regarded as one of the most influential scientists in history. ...
Events May 9 - Thomas Blood, disguised as a clergyman, attempts to steal the Crown Jewels from the Tower of London. ...
Events January 26 - Stanislaus I of Poland abdicates his throne. ...
Within this book, Newton describes a method (the Newton-Raphson method) for finding the real zeroes of a function. In numerical analysis, Newtons method (or the Newton-Raphson method) is an efficient algorithm for finding approximations to the zeros (or roots) of a real-valued function. ...
Partial plot of a function f. ...
Importance: Topic creator, Breakthrough, Influence
Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. ...
John Maynard Smith Book cover Evolution and the Theory of Games is a 1982 book by the British evolutionary biologist John Maynard Smith on evolutionary game theory. ...
John Maynard Smith Professor John Maynard Smith, F.R.S. (6 January 1920 – 19 April 2004) was a British evolutionary biologist and geneticist. ...
(Theory of Games and Economic Behavior, 3rd ed., Princeton University Press 1953) In 1944 Princeton University Press published Theory of Games and Economic Behavior, a book by the mathematician John von Neumann and economist Oskar Morgenstern. ...
Description: This book led to the investigation of modern game theory as a prominent branch of mathematics. This profound work contained the method -- alluded to above -- for finding optimal solutions for two-person zero-sum games. Oskar Morgenstern (January 24, 1902 - July 26, 1977) was an German- American economist who, working with John von Neumann, helped found the mathematical field of game theory. ...
John von Neumann in the 1940s. ...
Importance: Influence, Topic creator, Breakthrough
Description: The book is in two, {0,1|}, parts. The zeroth part is about numbers, the first part about games - both the values of games and also some real games that can be played such as Nim, Hackenbush, Col and Snort amongst the many described. On Numbers and Games is a mathematics book by John Conway, published by Academic Press Inc in 1976, ISBN 0121863506, and re-released by AK Peters in 2000 (ISBN 1568811276). ...
See John B. Conway for the functional analyst. ...
Nim is a two-player mathematical game of strategy in which players take turns removing objects from heaps, one or more objects at a time but only from a single heap. ...
Hackenbush is a two-player partisan mathematical game that consists of several colored line segments connected to the ground. ...
Col may refer to: the French word for mountain pass a common abbreviation for the military rank colonel This is a disambiguation page, a list of pages that otherwise might share the same title. ...
Snort is an open source network intrusion detection system, capable of performing real-time traffic analysis and packet logging on IP networks. ...
Importance:
Description: A compendium of information on mathematical games. It was first published in 1982 in two volumes, one focusing on Combinatorial game theory and surreal numbers, and the other concentrating on a number of specific games. Winning Ways for your Mathematical Plays (ISBN 1568811306) by Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy is a compendium of information on mathematical games. ...
Elwyn Ralph Berlekamp is professor of mathematics at University of California, Berkeley. ...
See John B. Conway for the functional analyst. ...
Richard K. Guy is a Professor Emeritus in the Department of Mathematics at the University of Calgary. ...
Mathematical games include many topics which are a part of recreational mathematics, but can also cover topics such as the mathematics of games, and playing games with mathematics. ...
1982 (MCMLXXXII) was a common year starting on Friday of the Gregorian calendar. ...
Combinatorial game theory (CGT) is a mathematical theory that studies a certain kind of game. ...
In mathematics, the surreal numbers are a field containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number, and therefore the surreals are algebraically similiar to superreal numbers and hyperreal numbers. ...
Importance:
The boundary of the Mandelbrot set is a famous example of a fractal. ...
Description: A discussion of self-similar curves that have fractional dimensions between 1 and 2. These curves are examples of fractals, although Mandelbrot does not use this term in the paper, as he did not coin it until 1975. Shows Mandelbrot's early thinking on fractals, and is an example of the linking of mathematical objects with natural forms that was a theme of much of his later work. How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension is a paper by mathematician Benoît Mandelbrot, first published in Science in 1967. ...
Benoît Mandelbrot Benoît B. Mandelbrot (born November 20, 1924) is a Polish-born French mathematician and leading proponent of fractal geometry. ...
Importance:
Textbooks
Online version: Online version A Course of Pure Mathematics is a classic textbook in introductory mathematical analysis, written by G. H. Hardy. ...
G. H. Hardy Professor Godfrey Harold Hardy FRS (February 7, 1877 – December 1, 1947) was a prominent British mathematician, known for his achievements in number theory and mathematical analysis. ...
Description: A classic textbook in introductory mathematical analysis, written by G. H. Hardy. It was first published in 1908, and went through many editions. It was intended to help reform mathematics teaching in the UK, and more specifically in the University of Cambridge, and in schools preparing pupils to study mathematics at Cambridge. As such, it was aimed directly at "scholarship level" students — the top 10% to 20% by ability. The book contains a large number of difficult problems. The content covers introductory calculus and the theory of infinite series. Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. ...
G. H. Hardy Professor Godfrey Harold Hardy FRS (February 7, 1877 – December 1, 1947) was a prominent British mathematician, known for his achievements in number theory and mathematical analysis. ...
1908 (MCMVIII) was a leap year starting on Wednesday (link will take you to calendar). ...
The University of Cambridge (often called Cambridge University), located in Cambridge, England, is the second-oldest university in the English-speaking world. ...
Integral and differential calculus is a central branch of mathematics, developed from algebra and geometry. ...
In mathematics, a series is a sum of a sequence of terms. ...
Importance:
- Richard Rusczyk and Sandor Lehoczky
Description: The Art of Problem Solving began as a set of two books coauthored by Richard Rusczyk and Sandor Lehoczky. The books, which are about 750 pages together, are for students who are interested in math and/or compete in math competitions. The Art of Problem Solving began as a set of two books coauthored by Richard Rusczyk and Sandor Lehoczky. ...
Importance:
Metalogic: an Introduction to the Metatheory of Standard First Order Logic Description: An excellent introduction to the mathematical theory of logical formal systems, covering completeness-proofs, consistency-proofs, and so on and even set-theory. In logic, mathematics, and computer science, a formal system is a formal grammar used for modelling purposes. ...
In mathematics and related technical fields, a mathematical object is complete if nothing needs to be added to it. ...
Consistency has three technical meanings: In mathematics and logic, as well as in theoretical physics, it refers to the proposition that a formal theory or a physical theory contains no contradictions. ...
Importance:
Popular writing
Description: Gödel, Escher, Bach: an Eternal Golden Braid is a Pulitzer Prize-winning book, first published in 1979 by Basic Books. It is a book about how the creative achievements of logician Kurt Gödel, artist M. C. Escher and composer Johann Sebastian Bach interweave. As the author states: "I realized that to me, Gödel and Escher and Bach were only shadows cast in different directions by some central solid essence. I tried to reconstruct the central object, and came up with this book." GEB cover Gödel, Escher, Bach: an Eternal Golden Braid (commonly GEB) is a Pulitzer Prize-winning book by Douglas Hofstadter, published in 1979 by Basic Books. ...
Douglas Richard Hofstadter (born February 15, 1945) is an American academic. ...
Importance:
The World of Mathematics Description: The World of Mathematics was specially designed to make mathematics more accessible to the inexperienced. It comprises nontechnical essays on every aspect of the vast subject, including articles by and about scores of eminent mathematicians, as well as literary figures, economists, biologists, and many other eminent thinkers. Includes the work of Archimedes, Galileo, Descartes, Newton, Gregor Mendel, Edmund Halley, Jonathan Swift, John Maynard Keynes, Henri Poincaré, Lewis Carroll, George Boole, Bertrand Russell, Alfred North Whitehead, John von Neumann, and many others. In addition, an informative commentary by distinguished scholar James R. Newman precedes each essay or group of essays, explaining thei |
