Who was the 18th century Swiss mathematician and physicist, who published more papers than any other mathematician in history and pioneered the theory of trigometric and logarithmic functions?
"full professor. Milne works on algebraic combinatorics, classical analysis, special functions, analytic number theory, and Lie algebras (generalizations of the Macdonald identities). From 1981 to 1983 he was a Sloan Fellow. In 2007 he was the joint recipient with Heiko Harborth of the Euler Medal. In 2012 Milne was elected a Fellow of the American Mathematical Society. Stephen Milne (mathematician) Stephen Carl Milne is an American mathematician who works in the fields of analysis, analytic number theory, and combinatorics. Milne received a bachelor's degree from San Diego State University in 1972 and a Ph.D. from the University of California, San"
"Contributions of Leonhard Euler to mathematics The 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field. His seminal work had a profound impact in numerous areas of mathematics and he is widely credited for introducing and popularizing modern notation and terminology. Euler introduced much of the mathematical notation in use today, such as the notation ""f""(""x"") to describe a function and the modern notation for the trigonometric functions. He was the first to use the letter ""e"" for the base of the natural logarithm, now also known as Euler's"
"Leonhard Euler Leonhard Euler ( ; ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory. Euler was one of the most eminent"
"forcefully against the prominent atheists of his time. Euler has an extensive bibliography. His best-known books include: A definitive collection of Euler's works, entitled ""Opera Omnia"", has been published since 1911 by the Euler Commission of the Swiss Academy of Sciences. A complete chronological list of Euler's works is available at the following page: ""The Eneström Index"" (PDF). Leonhard Euler Leonhard Euler ( ; ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making"
"and others. There are still many problems to be solved in this area of investigation opened up by Ludwig Schläfli. Ludwig Schläfli Ludwig Schläfli (15 January 1814 – 20 March 1895) was a Swiss mathematician, specialising in geometry and complex analysis (at the time called function theory) who was one of the key figures in developing the notion of higher-dimensional spaces. The concept of multidimensionality has come to play a pivotal role in physics, and is a common element in science fiction. Ludwig spent most of his life in Switzerland. He was born in Grasswil (now part of Seeberg), his"
"German geologist, who also published some well-known logarithm tables used up into the early 1980s. Carl Friedrich Gauss Johann Carl Friedrich Gauss (; ; ; (30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and sciences. Sometimes referred to as the ""Princeps mathematicorum"" () and ""the greatest mathematician since antiquity"", Gauss had an exceptional influence in many fields of mathematics and science, and is ranked among history's most influential mathematicians. Johann Carl Friedrich Gauss was born on 30 April 1777 in Brunswick (Braunschweig), in the Duchy of Brunswick-Wolfenbüttel (now"
"facilitated the use of differential equations, in particular introducing the Euler–Mascheroni constant: One of Euler's more unusual interests was the application of mathematical ideas in music. In 1739 he wrote the ""Tentamen novae theoriae musicae,"" hoping to eventually integrate music theory as part of mathematics. This part of his work, however did not receive wide attention and was once described as too mathematical for musicians and too musical for mathematicians. The works which Euler published separately are: Contributions of Leonhard Euler to mathematics The 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the"
"included Marcel Guénin. Ernst Stueckelberg Ernst Carl Gerlach Stueckelberg (full name after 1911: Baron Ernst Carl Gerlach Stueckelberg von Breidenbach zu Breidenstein und Melsbach; 1 February 1905 – 4 September 1984) was a Swiss mathematician and physicist, regarded as one of the most eminent physicists of the 20th century. Despite making key advances in theoretical physics, including the exchange particle model of fundamental forces, causal S-matrix theory, and the renormalization group, his idiosyncratic style and publication in minor journals led to his work being unrecognized until the mid-1990s. Born into a semi-aristocratic family in Basel in 1905, Stueckelberg's father was"
"Ludwig Schläfli Ludwig Schläfli (15 January 1814 – 20 March 1895) was a Swiss mathematician, specialising in geometry and complex analysis (at the time called function theory) who was one of the key figures in developing the notion of higher-dimensional spaces. The concept of multidimensionality has come to play a pivotal role in physics, and is a common element in science fiction. Ludwig spent most of his life in Switzerland. He was born in Grasswil (now part of Seeberg), his mother's hometown. The family then moved to the nearby Burgdorf, where his father worked as a tradesman. His father wanted"
"Gottfried Wilhelm Leibniz Gottfried Wilhelm (von) Leibniz (sometimes spelled Leibnitz) (; or ; ; – 14 November 1716) was a prominent German polymath and philosopher in the history of mathematics and the history of philosophy. His most notable accomplishment was conceiving the ideas of differential and integral calculus, independently of Isaac Newton's contemporaneous developments. Mathematical works have always favored Leibniz's notation as the conventional expression of calculus, while Newton's notation became unused. It was only in the 20th century that Leibniz's law of continuity and transcendental law of homogeneity found mathematical implementation (by means of non-standard analysis). He became one"
"star. Leonhard Euler is considered to be the preeminent mathematician of the 18th century and one of the greatest of all time. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: ""Read Euler, read Euler, he is the master of us all."" Euler made important discoveries in fields as diverse as calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. The Bernoulli family produced many notable scientists (Bernoulli number, Bernoulli's principle, Bernoulli's rule...). Albert Einstein (naturalized in 1901) was probably"
"laws in algebraic number fields. The Stickelberger relation also yields information about the structure of the class group of a cyclotomic field as a module over its abelian Galois group (cf Iwasawa theory). Ludwig Stickelberger Ludwig Stickelberger (May 18, 1850 – April 11, 1936) was a Swiss mathematician who made important contributions to linear algebra (theory of elementary divisors) and algebraic number theory (Stickelberger relation in the theory of cyclotomic fields). Stickelberger was born in Buch in the canton of Schaffhausen into a family of a pastor. He graduated from a gymnasium in 1867 and studied next in the University"
"Ernst Stueckelberg Ernst Carl Gerlach Stueckelberg (full name after 1911: Baron Ernst Carl Gerlach Stueckelberg von Breidenbach zu Breidenstein und Melsbach; 1 February 1905 – 4 September 1984) was a Swiss mathematician and physicist, regarded as one of the most eminent physicists of the 20th century. Despite making key advances in theoretical physics, including the exchange particle model of fundamental forces, causal S-matrix theory, and the renormalization group, his idiosyncratic style and publication in minor journals led to his work being unrecognized until the mid-1990s. Born into a semi-aristocratic family in Basel in 1905, Stueckelberg's father was a lawyer, and"
"Joseph-Louis Lagrange Joseph-Louis Lagrange ( or ; ; born Giuseppe Luigi Lagrangia or Giuseppe Ludovico De la Grange Tournier, 25 January 1736 – 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer. He made significant contributions to the fields of analysis, number theory, and both classical and celestial mechanics. In 1766, on the recommendation of Euler and d'Alembert, Lagrange succeeded Euler as the director of mathematics at the Prussian Academy of Sciences in Berlin, Prussia, where he stayed for over twenty years, producing volumes of work and winning several prizes"
"contributing numerous theorems and discoveries. Perhaps the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, analysis, differential geometry, matrix theory,number theory, and statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system that is consistent will contain unprovable propositions. Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today. According to Mikhail B. Sevryuk, in the"
"Bernhard Riemann Georg Friedrich Bernhard Riemann (; 17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis. His famous 1859 paper on the prime-counting function, containing the original statement of the Riemann hypothesis, is regarded as one of"
"Carl Friedrich Gauss Johann Carl Friedrich Gauss (; ; ; (30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and sciences. Sometimes referred to as the ""Princeps mathematicorum"" () and ""the greatest mathematician since antiquity"", Gauss had an exceptional influence in many fields of mathematics and science, and is ranked among history's most influential mathematicians. Johann Carl Friedrich Gauss was born on 30 April 1777 in Brunswick (Braunschweig), in the Duchy of Brunswick-Wolfenbüttel (now part of Lower Saxony, Germany), to poor, working-class parents. His mother was illiterate and never"
"Ludwig Boltzmann Ludwig Eduard Boltzmann (; February 20, 1844 – September 5, 1906) was an Austrian physicist and philosopher whose greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms (such as mass, charge, and structure) determine the physical properties of matter (such as viscosity, thermal conductivity, and diffusion). Boltzmann coined the word ""ergodic"" while he was working on a problem in statistical mechanics. Boltzmann was born in Vienna, the capital of the Austrian Empire. His father, Ludwig Georg Boltzmann, was a revenue official. His grandfather, who had moved to Vienna from"
"his admiration for Johann Heinrich Lambert. Johann Heinrich Lambert Johann Heinrich Lambert (, ""Jean-Henri Lambert"" in French; 26 August 1728 – 25 September 1777) was a Swiss polymath who made important contributions to the subjects of mathematics, physics (particularly optics), philosophy, astronomy and map projections. Edward Tufte calls him and William Playfair ""The two great inventors of modern graphical designs"" (""Visual Display of Quantitative Information"", p. 32). Lambert was born in 1728 into a Huguenot family in the city of Mulhouse (now in Alsace, France), at that time an exclave of Switzerland. Leaving school at 12, he continued to study"
"Graz. He was elected a member of the Royal Swedish Academy of Sciences in 1888 and a Foreign Member of the Royal Society (ForMemRS) in 1899. The following are named in his honour: Ludwig Boltzmann Ludwig Eduard Boltzmann (; February 20, 1844 – September 5, 1906) was an Austrian physicist and philosopher whose greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms (such as mass, charge, and structure) determine the physical properties of matter (such as viscosity, thermal conductivity, and diffusion). Boltzmann coined the word ""ergodic"" while he was working on"
"of Girard in the history of the study of equations using symmetric functions. In his work on the theory of equations, Lagrange cited Girard. Still later, in the nineteenth century, this work eventuated in the creation of group theory by Cauchy, Galois and others. Girard also showed how the area of a spherical triangle depends on its interior angles. The result is called Girard's theorem. He also was a lutenist and mentioned having written a treatise on music, though this was never published. Albert Girard Albert Girard () (1595 in Saint-Mihiel, France − 8 December 1632 in Leiden) was a"
"Johann Heinrich Lambert Johann Heinrich Lambert (, ""Jean-Henri Lambert"" in French; 26 August 1728 – 25 September 1777) was a Swiss polymath who made important contributions to the subjects of mathematics, physics (particularly optics), philosophy, astronomy and map projections. Edward Tufte calls him and William Playfair ""The two great inventors of modern graphical designs"" (""Visual Display of Quantitative Information"", p. 32). Lambert was born in 1728 into a Huguenot family in the city of Mulhouse (now in Alsace, France), at that time an exclave of Switzerland. Leaving school at 12, he continued to study in his free time whilst undertaking"
"and Blaise Pascal. Pascal and Fermat set the groundwork for the investigations of probability theory and the corresponding rules of combinatorics in their discussions over a game of gambling. Pascal, with his wager, attempted to use the newly developing probability theory to argue for a life devoted to religion, on the grounds that even if the probability of success was small, the rewards were infinite. In some sense, this foreshadowed the development of utility theory in the 18th–19th century. The most influential mathematician of the 18th century was arguably Leonhard Euler. His contributions range from founding the study of graph"
"Ferdinand Georg Frobenius Ferdinand Georg Frobenius (26 October 1849 – 3 August 1917) was a German mathematician, best known for his contributions to the theory of elliptic functions, differential equations, number theory, and to group theory. He is known for the famous determinantal identities, known as Frobenius–Stickelberger formulae, governing elliptic functions, and for developing the theory of biquadratic forms. He was also the first to introduce the notion of rational approximations of functions (nowadays known as Padé approximants), and gave the first full proof for the Cayley–Hamilton theorem. He also lent his name to certain differential-geometric objects in modern mathematical"
"David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory, calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and foundations of mathematics (particularly proof theory). Hilbert adopted and warmly defended Georg Cantor's set theory and transfinite numbers. A famous example of his"
"Oscar Schlömilch Oscar (Oskar) Xavier Schlömilch (13 April 1823 – 7 February 1901) was a German mathematician, born in Weimar, working in mathematical analysis. He took a doctorate at the University of Jena in 1842, and became a professor at Dresden Polytechnic in 1849. He is now known as the eponym of the Schlömilch function, a kind of Bessel function. He was also an important textbook writer, and editor of the journal "" Zeitschrift für Mathematik und Physik"", of which he was a founder in 1856. He published in 1868 for the first time the dissection paradox, earlier invented by"
"Ludwig Stickelberger Ludwig Stickelberger (May 18, 1850 – April 11, 1936) was a Swiss mathematician who made important contributions to linear algebra (theory of elementary divisors) and algebraic number theory (Stickelberger relation in the theory of cyclotomic fields). Stickelberger was born in Buch in the canton of Schaffhausen into a family of a pastor. He graduated from a gymnasium in 1867 and studied next in the University of Heidelberg. In 1874 he received a doctorate in Berlin under the direction of Karl Weierstrass for his work on transformation of quadratic forms to a diagonal form. In the same year he"
"mathematical journals of the world, dealt chiefly with Abelian and elliptic functions and the theory of numbers. During 1858 he solved the equation of the fifth degree by elliptic functions; and during 1873 he proved ""e"", the base of the natural system of logarithms, to be transcendental. This last was used by Ferdinand von Lindemann to prove during 1882 the same for π. The following is a list of his works.: ""This article incorporates text from the public-domain Catholic Encyclopedia of 1913."" Charles Hermite Prof Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a"
"Charles Hermite Prof Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra. Hermite polynomials, Hermite interpolation, Hermite normal form, Hermitian operators, and cubic Hermite splines are named in his honor. One of his students was Henri Poincaré. He was the first to prove that ""e"", the base of natural logarithms, is a transcendental number. His methods were used later by Ferdinand von Lindemann to prove that π is transcendental. In a letter to Thomas Joannes Stieltjes"
"Peter Gustav Lejeune Dirichlet Johann Peter Gustav Lejeune Dirichlet (; 13 February 1805 – 5 May 1859) was a German mathematician who made deep contributions to number theory (including creating the field of analytic number theory), and to the theory of Fourier series and other topics in mathematical analysis; he is credited with being one of the first mathematicians to give the modern formal definition of a function. Although his official surname is Lejeune Dirichlet, he is commonly referred to as just Dirichlet, particularly for the eponym. Gustav Lejeune Dirichlet was born on 13 February 1805 in Düren, a town"
"to English Wikipedia article if available. Gottfried Wilhelm Leibniz bibliography Gottfried Wilhelm Leibniz was a major contributor to mathematics, physics, philosophy, theology, logic, and early computer science; independent inventor of calculus in mathematics; inventor of energy and the action principle in physics; jurist, genealogist, diplomat, librarian; worked towards reunification of Catholic and Protestant faiths. This in-progress article will list all his published and unpublished works primarily based on the Leibniz Library in Hannover , and its online catalog. Notes: 1. Dates in the table refer to the estimated date of completion of manuscripts if first publication occurred after Leibniz's death"
"Salomon Eduard Gubler Salomon Eduard Gubler (1845–1921) was a Swiss mathematician. With Johann Heinrich Graf he published ""Einleitung in Die Theorie Der Bessel'schen Funktionen (A Treatise on the Theory of Bessel Functions)"" in two volumes (1898–1900). He was the author of very appreciated textbooks on mathematics and numerous reports about the methodology and organization on mathematics teaching, and he was a member of the Swiss commission for the teaching of mathematics and founder of the Swiss association of teachers of mathematics. His main research interest was the Bessel functions. Gubler graduated in the university of Bern in 1870 as Ludwig"
"visited Dirichlet in 1852. Bernhard Riemann Georg Friedrich Bernhard Riemann (; 17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis. His famous 1859 paper on the prime-counting function, containing the original statement of the Riemann hypothesis, is"