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This is a list of important publications in mathematics, organized by field. Some reasons why a particular publication might be regarded as important:
[edit] Algebra[edit] Theory of equations[edit] Hisab al-Jabr w’al-muqabala, Kitab al-Jabr wa-l-MuqabalaDescription: The first book on the systematic algebraic solutions of linear and quadratic equations. The book is considered to be the foundation of modern algebra and Islamic mathematics. The word "algebra" itself is derived from the al-Jabr in the title of the book. [edit] Ars Magna
Description: Provided the first published methods for solving cubic and quartic equations (due to Scipione del Ferro, Niccolò Fontana Tartaglia, and Lodovico Ferrari), and exhibited the first published calculations involving non-real complex numbers. [1] [edit] Vollständige Anleitung zur Algebra
Description: Also known as Elements of Algebra, Euler's textbook on elementary algebra is one of the first to set out algebra in the modern form we would recognize today. The first volume deals with determinate equations, while the second part deals with Diophantine equations. The last section contains a proof of Fermat's Last Theorem for the case n = 3, making some valid assumptions regarding Q(√−3) that Euler did not prove.[2] [edit] Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse
Description: Gauss' doctoral dissertation[3], which contained a widely accepted (at the time) but incomplete proof[4] of the fundamental theorem of algebra. [edit] Abstract algebra[edit] Group theory[edit] Réflexions sur la résolution algébrique des equations
Description: Made the prescient observation that the roots of the Lagrange resolvent of a polynomial equation are tied to permutations of the roots of the original equation, laying a more general foundation for what had previously been an ad hoc analysis and helping motivate the later development of the theory of permutation groups. [edit] Articles Publiés par Galois dans les Annales de Mathematiques
Description: Posthumous publication of the mathematical manuscripts of Évariste Galois by Joseph Liouville. Included are Galois' papers Mémoire sur les conditions de résolubilité des équations par radicaux and Des équations primitives qui sont solubles par radicaux. [edit] Traité des substitutions et des équations algebraique
Description: The first book on group theory, giving a then-comprehensive study of permutation groups and Galois theory. In this book, Jordan introduced the notion of a simple group and epimorphism (which he called l'isomorphisme mériédrique)[5], proved part of the Jordan-Hölder theorem, and discussed matrix groups over finite fields as well as the Jordan normal form. [6] [edit] Theorie der Transformationsgruppen
Publication data: 3 volumes, B.G. Teubner, Verlagsgesellschaft, mbH, Leipzig, 1888-1893. Description: The first comprehensive work on transformation groups, serving as the foundation for the modern theory of Lie groups. [edit] Solvability of groups of odd order
Description: Gave a complete proof of the solvability of finite groups of odd order, establishing the long-standing Burnside conjecture that all finite non-abelian simple groups are of even order. Many of the original techniques used in this paper were used in the eventual classification of finite simple groups. [edit] Homological algebra[edit] Homological Algebra
Description: Provided the first fully-worked out treatment of abstract homological algebra, unifying previously disparate presentations of homology and cohomology for associative algebras, Lie algebras, and groups into a single theory. [edit] Sur Quelques Points d'Algèbre Homologique
Description: Revolutionized homological algebra by introducing abelian categories and providing a general framework for Cartan and Eilenberg’s notion of derived functors. [edit] Algebraic geometry[edit] Theorie der Abelschen Functionen
Publication data: Journal für die Reine und Angewandte Mathematik Description: Developed the concept of Riemann surfaces and their topological properties beyond Riemann's 1851 thesis work, proved an index theorem for the genus (the original formulation of the Riemann-Hurwitz formula), proved the Riemann inequality for the dimension of the space of meromorphic functions with prescribed poles (the original formulation of the Riemann-Roch theorem), discussed birational transformations of a given curve and the dimension of the corresponding moduli space of inequivalent curves of a given genus, and solved more general inversion problems than those investigated by Abel and Jacobi. André Weil once wrote that this paper "is one of the greatest pieces of mathematics that has ever been written; there is not a single word in it that is not of consequence." [7] [edit] Faisceaux Algébriques CohérentsPublication data: Annals of Mathematics, 1955 Description: FAC, as it is usually called, first introduced the use of sheaves into algebraic geometry. Serre introduced Čech cohomology of sheaves in this paper, and, despite its technical deficiencies, revolutionized algebraic geometry. For example, the long exact sequence in sheaf cohomology allows one to show that some surjective maps of sheaves induce surjective maps on sections; specifically, these are the maps whose kernel (as a sheaf) has a vanishing first cohomology group. Before FAC, this was next to impossible. While Grothendieck's derived functor cohomology has replaced Čech cohomology for technical reasons, actual calculations, such as of the cohomology of projective space, are usually carried out by Čech techniques, and for this reason Serre's paper remains important even today. [edit] Géométrie Algébrique et Géométrie Analytique
Description: In mathematics, algebraic geometry and analytic geometry are closely related subjects, where analytic geometry is the theory of complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex variables. A (mathematical) theory of the relationship between the two was put in place during the early part of the 1950s, as part of the business of laying the foundations of algebraic geometry to include, for example, techniques from Hodge theory. (NB While analytic geometry as use of Cartesian coordinates is also in a sense included in the scope of algebraic geometry, that is not the topic being discussed in this article.) The major paper consolidating the theory was Géometrie Algébrique et Géométrie Analytique by Serre, now usually referred to as GAGA. A GAGA-style result would now mean any theorem of comparison, allowing passage between a category of objects from algebraic geometry, and their morphisms, and a well-defined subcategory of analytic geometry objects and holomorphic mappings. [edit] Le théorème de Riemann-Roch, d'après A. Grothendieck
Description: Borel and Serre's exposition of Grothendieck's version of the Riemann Roch theorem, published after Grothendieck made it clear that he was not interested in writing up his own result. Grothendieck reinterpreted both sides of the formula that Hirzebruch proved in 1953 in the framework of morphisms between varieties, resulting in a sweeping generalization.[8] In his proof, Grothendieck broke new ground with his concept of Grothendieck groups, which led to the development of K-theory.[9] [edit] Éléments de géométrie algébrique
Description: Written with the assistance of Jean Dieudonné, this is Grothendieck's exposition of his reworking of the foundations of algebraic geometry. It has become the most important foundational work in modern algebraic geometry. The approach expounded in EGA, as these books are known, transformed the field and led to monumental advances. [edit] Séminaire de géométrie algébrique
Description: These seminar notes on Grothendieck's reworking of the foundations of algebraic geometry report on work done at IHÉS starting in the 1960s. SGA 1 dates from the seminars of 1960-1961, and the last in the series, SGA 7, dates from 1967–1969. In contrast to EGA, which is intended to set foundations, SGA describes ongoing research as it unfolded in Grothendieck’s seminar; as a result, it is quite difficult to read, since many of the more elementary and foundational results were relegated to EGA. One of the major results building on the results in SGA is Pierre Deligne's proof of the Weil conjectures in the 1970s. Other authors who worked on one or several volumes of SGA include Michel Raynaud, Michael Artin, Jean-Pierre Serre, Jean-Louis Verdier, Pierre Deligne, and Nicholas Katz. [edit] Number theory[edit] De fractionibus continuis dissertatio
Description: First presented in 1737, this paper [10] provided the first then-comprehensive account of the properties of continued fractions. It also contains the first proof that the number e is irrational.[11] [edit] Recherches d'Arithmétique
Description: Developed a general theory of binary quadratic forms to handle the general problem of when an integer is representable by the form ax2 + by2 + cxy. This included a reduction theory for binary quadratic forms, where he proved that every form is equivalent to a certain canonically chosen reduced form.[12][13] [edit] Disquisitiones Arithmeticae
Description: The Disquisitiones Arithmeticae is a profound and masterful book on 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 many important new results of his own. Among his contributions was the first complete proof known of the Fundamental theorem of arithmetic, the first two published proofs of the law of quadratic reciprocity, a deep investigation of binary quadratic forms going beyond Lagrange's work in Recherches d'Arithmétique, a first appearance of Gauss sums, cyclotomy, and the theory of constructible polygons with a particular application to the constructibility of the regular 17-gon. Of note, in section V, article 303 of Disquisitiones, Gauss summarized his calculations of class numbers of imaginary quadratic number fields, and in fact found all imaginary quadratic number fields of class numbers 1, 2, and 3 (confirmed in 1986) as he had conjectured.[14] In section V, article 358, Gauss proved what can be interpreted as the first non-trivial case of the Riemann Hypothesis for curves over finite fields (the Hasse-Weil theorem).[15] [edit] Beweis des Satzes, daß jede unbegrenzte arithmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Factor sind, unendlich viele Primzahlen enthältDescription: Pioneering paper in analytic number theory, which introduced Dirichlet characters and their L-functions to establish Dirichlet's theorem on arithmetic progressions.[16] In subsequent publications, Dirichlet used these tools to determine, among other things, the class number for quadratic forms. [edit] Über die Anzahl der Primzahlen unter einer gegebenen Grösse
Description: Über die Anzahl der Primzahlen unter einer gegebenen Grösse (or On the Number of Primes Less Than a Given Magnitude) 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. [edit] Vorlesungen über ZahlentheorieDescription: 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 [edit] Zahlbericht
Description: Unified and made accessible many of the developments in algebraic number theory made during the nineteenth century. Although criticized by André Weil (who stated "more than half of his famous Zahlbericht is little more than an account of Kummer’s number-theoretical work, with inessential improvements")[17] and Emmy Noether[18], it was highly influential for many years following its publication. [edit] Fourier Analysis in Number Fields and Hecke's Zeta-Functions
Description: Generally referred to simply as Tate's Thesis, Tate's Princeton Ph.D. thesis, under Emil Artin, is a reworking of Erich Hecke's theory of zeta- and L-functions in terms of Fourier analysis on the adeles. The introduction of these methods into number theory made it possible to formulate extensions of Hecke's results to more general L-functions such as those arising from automorphic forms. [edit] Automorphic Forms on GL(2)
Description: This publication offers evidence towards Langlands' conjectures by reworking and expanding the classical theory of modular forms and their L-functions through the introduction of representation theory. [edit] La conjecture de Weil. I.
Description: Proved the Riemann hypothesis for varieties over finite fields, settling the last of the open Weil conjectures. [edit] Modular Elliptic Curves and Fermat's Last Theorem
Description: This article proceeds to prove a special case of the Shimura-Taniyama conjecture through the study of the deformation theory of Galois representations. This in turn implies the famed Fermat's Last Theorem. The proof's method of identification of a deformation ring with a Hecke algebra (now referred to as an R=T theorem) to prove modularity lifting theorems has been an influential development in algebraic number theory. [edit] Analysis[edit] Introductio in analysin infinitorum
Description: The eminent historian of mathematics Carl Boyer once called Euler's Introductio in analysin infinitorum the greatest modern textbook in mathematics.[19] Published in two volumes[20][21], this book more than any other work succeeded in establishing analysis as a major branch of mathematics, with a focus and approach distinct from that used in geometry and algebra.[22] Notably, Euler identified functions rather than curves to be the central focus in his book.[23] Logarithmic, exponential, trigonometric, and transcendental functions were covered, as were expansions into partial fractions, evaluations of ζ(2k) for k a positive integer between 1 and 13, infinite series-infinite product formulas[19], continued fractions, and partitions of integers.[24] In this work, Euler proved that every rational number can be written as a finite continued fraction, that the continued fraction of an irrational number is infinite, and derived continued fraction expansions for e and √e.[20] This work also contains a statement of Euler's formula and a statement of the pentagonal number theorem, which he had discovered earlier and would publish a proof for in 1751. [edit] Calculus[edit] 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. [edit] Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas nec irrationales quantitates moratur, et singulare pro ili calculi genus
Description: Leibniz's first publication on differential calculus, containing the now familiar notation for differentials as well as rules for computing the derivatives of powers, products and quotients. [edit] Philosophiae Naturalis Principia MathematicaDescription: 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, and derives Kepler's laws for the motion of the planets (which were first obtained empirically). 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 formulating his physical theories, Newton freely used his unpublished work on calculus. When he submitted Principia for publication, however, Newton chose to recast the majority of his proofs as geometric arguments.[25] [edit] Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum
Description: Published in two books[26], Euler's textbook on differential calculus presented the subject in terms of the function concept, which he had introduced in his 1748 Introductio in analysin infinitorum. This work opens with a study of the calculus of finite differences and makes a thorough investigation of how differentiation behaves under substitutions. [1] Also included is a systematic study of Bernoulli polynomials and the Bernoulli numbers (naming them as such), a demonstration of how the Bernoulli numbers are related to the coefficients in the Euler–Maclaurin formula and the values of ζ(2n) [27], a further study of Euler's constant (including its connection to the gamma function), and an application of partial fractions to differentiation. [28] [edit] Über die Darstellbarkeit einer Function durch eine trigonometrische Reihe
Description: Written in 1853, Riemann's work on trigonometric series was published posthumously. In it, he extended Cauchy’s definition of the integral to that of the Riemann integral, allowing some functions with dense subsets of discontinuities on an interval to be integrated (which he demonstrated by an example)[29]. He also stated the Riemann series theorem[29], proved the Riemann-Lebesgue lemma for the case of bounded Riemann integrable functions[30], and developed the Riemann localization principle[31]. [edit] Intégrale, longueur, aire
Description: Lebesgue's doctoral dissertation, summarizing and extending his research to date regarding his development of measure theory and the Lebesgue integral. [edit] Complex analysis[edit] Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse
Description: Riemann's doctoral dissertation introduced the notion of a Riemann surface, conformal mapping, simple connectivity, the Riemann sphere, the Laurent series expansion for functions having poles and branch points, and the Riemann mapping theorem. [edit] Functional analysis[edit] Théorie des opérations linéaires
Description: The first mathematical monograph on the subject of linear metric spaces, bringing the abstract study of functional analysis to the wider mathematical community. The book introduced the ideas of a normed space and the notion of a so-called B-space, a complete normed space. The B-spaces are now called Banach spaces and are one of the basic objects of study in all areas of modern mathematical analysis. Banach also gave proofs of versions of the open mapping theorem, closed graph theorem, and Hahn-Banach theorem. [edit] Harmonic analysis[edit] Sur la convergence des séries trigonométriques qui servent à représenter une fonction arbitraire entre des limites données
Description: In his habilitation thesis on Fourier series, Riemann characterized this work of Dirichlet as the "the first profound paper about the subject"[32]. This paper gave the first rigorous proof of the convergence of Fourier series under fairly general conditions (piecewise continuity and monotonicity) by considering partial sums, which Dirichlet transformed into a particular Dirichlet integral involving what is now called the Dirichlet kernel. This paper introduced the nowhere continuous Dirichlet function and an early version of the Riemann-Lebesgue lemma.[33] [edit] On convergence and growth of partial sums of Fourier series
Description: Settled Lusin's conjecture that the Fourier expansion of any L2 function converges almost everywhere. [edit] Geometry[edit] Baudhayana Sulba SutraDescription: 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, 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 geometrical 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 up to four unknowns. [edit] Euclid's ElementsPublication data: c. 300 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. 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. [edit] The Nine Chapters on the Mathematical Art
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. [edit] La GéométrieDescription: 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. [edit] Grundlagen der GeometriePublication data: Hilbert, David (1899). Grundlagen der Geometrie. Teubner-Verlag Leipzig. Description: Axiomatization of Geometry [edit] Regular PolytopesDescription: Regular Polytopes is a comprehensive survey of the geometry of regular polytopes, the generalisation of regular polygons and regular polyhedra to higher dimensions. Originating with an essay entitled Dimensional Analogy written in 1923, the first edition of the book took Coxeter 24 years to complete. Originally written in 1947, the book was updated and republished in 1963 and 1973. [edit] Differential geometry[edit] Recherches sur la courbure des surfaces
Description: Established the theory of surfaces, and introduced the idea of principal curvatures, laying the foundation for subsequent developments in the differential geometry of surfaces. Publication data: Memoires de l'academie des sciences de Berlin 16 (1760) pp. 119-143; published 1767. (Full text and an English translation available from the Dartmouth Euler archive.) [edit] Disquisitiones generales circa superficies curvas
Description: Groundbreaking work in differential geometry, introducing the notion of Gaussian curvature and Gauss' celebrated Theorema Egregium. Publication data: "Disquisitiones generales circa superficies curvas", Commentationes Societatis Regiae Scientiarum Gottingesis Recentiores Vol. VI (1827), pp. 99-146; "General Investigations of Curved Surfaces" (published 1965) Raven Press, New York, translated by A.M.Hiltebeitel and J.C.Morehead. [edit] Über die Hypothesen, welche der Geometrie zu Grunde Liegen
Description: Riemann's famous Habiltationsvortrag, in which he introduced the notions of a manifold, Riemannian metric, and curvature tensor. [edit] Leçons sur la théorie génerale des surfacesPublication data: Darboux, Gaston (1887,1889,1896). Leçons sur la théorie génerale des surfaces: Volume I, Volume II, Volume III, Volume IV. Gauthier-Villars. Description: A treatise covering virtually every aspect of the 19th century differential geometry of surfaces. [edit] Topology[edit] Analysis situs
Description: Poincaré's Analysis situs and his Compléments à l'Analysis Situs laid the general foundations for algebraic topology. In these papers, Poincaré introduced the notions of homology and the fundamental group, provided an early formulation of Poincaré duality, gave the Euler-Poincaré characteristic for chain complexes, and mentioned several important conjectures including the Poincaré conjecture. [edit] L’anneau d’homologie d’une représentation, Structure de l’anneau d’homologie d’une représentation
Description: These two Comptes Rendus notes of Leray from 1946 introduced the novel concepts of sheafs, sheaf cohomology, and spectral sequences, which he had developed during his years of captivity as a prisoner of war. Leray's announcements and applications (published in other Comptes Rendus notes from 1946) drew immediate attention from other mathematicians. Subsequent clarification, development, and generalization by Henri Cartan, Jean-Louis Koszul, Armand Borel, Jean-Pierre Serre, and Leray himself allowed these concepts to be understood and applied to many other areas of mathematics.[34] Dieudonné would later write that these notions created by Leray "undoubtedly rank at the same level in the history of mathematics as the methods invented by Poincaré and Brouwer". [35] [edit] Quelques propriétés globales des variétés differentiables
Description: In this paper, Thom proved the Thom transversality theorem, introduced the notions of oriented and unoriented cobordism, and demonstrated that cobordism groups could be computed as the homotopy groups of certain Thom spaces. Thom completely characterized the unoriented cobordism ring and achieved strong results for several problems, including Steenrod's problem on the realization of cycles.[36][37] [edit] Category theory[edit] General theory of natural equivalences
Description: The first paper on category theory. Mac Lane later wrote in Categories for the Working Mathematician that he and Eilenberg introduced categories so that they could introduce functors, and they introduced functors so that they could introduce natural equivalences. Prior to this paper, "natural" was used in an informal and imprecise way to designate constructions that could be made without making any choices. Afterwards, "natural" had a precise meaning which occurred in a wide variety of contexts and had powerful and important consequences. [edit] Categories for the Working Mathematician
Description: Saunders Mac Lane, one of the founders of category theory, wrote this exposition to bring categories to the masses. Mac Lane does not get lost in pointless abstraction, but instead brings to the fore the important concepts that make category theory useful, such as adjoint functors and universal properties. His text is more comprehensive than most mathematicians will ever need, and consequently is also an excellent reference. [edit] Set theory[edit] Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen
Description: Contains the first proof that the set of all real numbers is uncountable; also contains a proof that the set of algebraic numbers is denumerable. [edit] Grundzüge der MengenlehreDescription: First published in 1914, this was the first comprehensive introduction to set theory. Besides the systematic treatment of known results in set theory, the book also contains chapters on measure theory and topology, which were then still considered parts of set theory. Here Hausdorff presents and develops highly original material which was later to become the basis for those areas. [edit] The consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory
Description: Gödel proves the results of the title. Also, in the process, introduces the class L of constructible sets, a major influence in the development of axiomatic set theory. [edit] The Independence of the Continuum Hypothesis
Description: Cohen's breakthrough work proved the independence of the continuum hypothesis and axiom of choice with respect to Zermelo-Fraenkel set theory. In proving this Cohen introduced the concept of forcing which led to many other major results in axiomatic set theory. [edit] Logic[edit] Begriffsschrift
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. It was arguably the most significant publication in logic since Aristotle. [edit] Formulario mathematico
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. [edit] Principia Mathematica
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 surprising way, by |
