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# Mathematician

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• English (default) Mathematicians are people with an extensive knowledge of mathematics who use this knowledge in their work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, collection, quantity, structure, space, and change.

## List of mathematicians of lasting influence

For a complete list of profiles in this project, please see: Mathematicians Project Profiles.

# Internal links ~ Mathematicians in the Geni-platform

## Areas

1. algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts" is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols, see ELEMENTS, Diophantus of Alexandria ( wiki ) - Arithmetica - adaequalitas in Latin, and became the technique of adequality developed by Pierre de Fermat mathématicien
2. algebraic geometry a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. a branch of mathematics, classically studying zeros of multivariate polynomials. Algebraic geometry now finds applications in statistics, control theory, robotics,] error-correcting codes, phylogenetics and geometric modelling.There are also connections to string theory, game theory, graph matchings, solitons and integer programming.
3. analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development. As a formal concept, the method has variously been ascribed to Alhazen, René Descartes, seigneur du Perron (Discourse on the Method), and Galileo Galilei. It has also been ascribed to Sir Isaac Newton, PRS, in the form of a practical method of physical discovery (which he did not name).
4. calculus has two major branches, differential calculus (concerning rates of change and slopes of curves),] and integral calculus (concerning accumulation of quantities and the areas under and between curves). Generally, modern calculus is considered to have been developed in the 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Today, calculus has widespread uses in science, engineering, and economics.
5. combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics, from evolutionary biology to computer science, etc.
6. group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. The popular puzzle Rubik's cube invented in 1974 by Ernő Rubik has been used as an illustration of permutation groups.
7. Lie groups and Lie algebras The foundation of Lie theory is the exponential map relating Lie algebras to Lie groups which is called the Lie group–Lie algebra correspondence.
8. Lie theory involves integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory. For instance, the latter subject is Lie sphere geometry.
9. Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic. Bertrand Russell and Alfred North Whitehead championed this theory, created by mathematicians Richard Dedekind and Gottlob Frege. Historically, logic has been studied in philosophy (since ancient times) and mathematics (since the mid-19th century), and recently logic has been studied in computer science, linguistics, psychology, and other fields. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. An early definition of mathematics in terms of logic was Benjamin Peirce's "the science that draws necessary conclusions" (1870).[In the Principia Mathematica, Bertrand Russell and Alfred North Whitehead advanced the philosophical program known as logicism, and attempted to prove that all mathematical concepts, statements, and principles can be defined and proved entirely in terms of symbolic logic. A logicist definition of mathematics is Russell's "All Mathematics is Symbolic Logic" (1903).
10. number theory is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline.
11. mathematical physics is the application of mathematics in physics. Its methods are mathematical, but its subject is physical.
12. probability theory is the branch of mathematics concerned with probability which is the measure of the likelihood that an event will occur. Cardano was one of the key figures in the foundation of probability and the earliest introducer of the binomial coefficients and the binomial theorem in the western world.
13. representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and the algebraic operations in terms of matrix addition and matrix multiplication.
14. set theory
15. topology

(Régebben) a „mennyiség és a tér tudományaként” (vagyis a számok és geometriai alakzatok tanaként) határozták meg, a múlt század elejétől kezdve pedig a matematikáról azt tartották, hogy az „a halmazelmélet absztrakt struktúráinak formális logikai szemlélettel és a javarészt erre épülő matematikai jelölésrendszerrel való vizsgálata”.

• Matematika
• A matematika alapjai - Halmazelmélet : · Naiv halmazelmélet Axiomatikus halmazelmélet · Matematikai logika
• Algebra Elemi algebra · Lineáris algebra · Polinomok Absztrakt algebra · Csoportelmélet · Gyűrűelmélet · Testelmélet
• Mátrixok · Univerzális algebra
• Analízis Valós analízis · Komplex analízis · Vektoranalízis Differenciálegyenletek · Funkcionálanalízis
• Mértékelmélet
• Geometria Euklideszi geometria · Nemeuklideszi geometria Affin geometria · Projektív geometria Differenciálgeometria · Algebrai geometria
• Topológia
• Számelmélet Algebrai számelmélet · Analitikus számelmélet
• Diszkrét matematika Kombinatorika · Gráfelmélet · Játékelmélet Algoritmusok · Formális nyelvek
• Információelmélet
• Alkalmazott matematika Numerikus analízis · Valószínűségszámítás Statisztika · Káoszelmélet · Matematikai fizika Matematikai biológia · Gazdasági matematika

Kriptográfia

• *Általános Matematikusok · Matematikatörténet Matematikafilozófia · Portál

# Történet

Az elméleti matematika kibontakozása: a Pythagoras of Samos és a püthagoreusok számelméleti és Thales of Miletus geometriai felfedezései (Kr. e. VI. szd.),

Archimedes az alkalmazott matematika legfontosabb korai alakja.

`A – mai szóval – irracionális számok püthagoreusok általi felfedezése hatalmas lökést adott a geometriai felfedezéseknek, és e folyamat végül [Euclid Euclid] híres tankönyvéhez, az [https://hu.wikipedia.org/wiki/Elemek Elemek] hez vezetett; ugyanakkor a tiszta algebra fejlődését némileg visszavetette. A korszak (vagy annak vége) fontos és híres, megoldhatatlannak bizonyult problémái a kockakettőzés és a körnégyszögesítés, a korszak eredményei közt van még a kúpszeletek felfedezése.`

=see also the English language version= Mathematicians are people with an extensive knowledge of mathematics who use this knowledge in their work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, collection, quantity, structure, space, and change.
az Elemek

## List of mathematicians of lasting influence

For a complete list of profiles in this project, please see: Mathematicians Project Profiles.

# Internal links ~ Mathematicians in the Geni-platform

## Areas

1. algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts" is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols, see ELEMENTS, Diophantus of Alexandria ( wiki ) - Arithmetica - adaequalitas in Latin, and became the technique of adequality developed by Pierre de Fermat mathématicien
2. algebraic geometry a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. a branch of mathematics, classically studying zeros of multivariate polynomials. Algebraic geometry now finds applications in statistics, control theory, robotics,] error-correcting codes, phylogenetics and geometric modelling.There are also connections to string theory, game theory, graph matchings, solitons and integer programming.
3. analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development. As a formal concept, the method has variously been ascribed to Alhazen, René Descartes, seigneur du Perron (Discourse on the Method), and Galileo Galilei. It has also been ascribed to Sir Isaac Newton, PRS, in the form of a practical method of physical discovery (which he did not name).
4. calculus has two major branches, differential calculus (concerning rates of change and slopes of curves),] and integral calculus (concerning accumulation of quantities and the areas under and between curves). Generally, modern calculus is considered to have been developed in the 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Today, calculus has widespread uses in science, engineering, and economics.
5. combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics, from evolutionary biology to computer science, etc. obtained from σ by transposing adjacent elements to increase the number of inversions Weak product G1⊗ G2 - a graph product with vertices V(G1)× V(G2), and edges (u1,v1)<-> (u2,v2) iff u1<-> u2 and v1<-> v2 Weakly connected - a directed graph whose underlying graph is connected Weight - 1) a real number; 2) for a binary vector, the number of ones Weighted - having an assignment of weights (to edges and/or vertices) Wheel - a graph obtained by taking the join of a cycle and a single vertex Whitney numbers (of the second kind) - rank sizes of poset Whitney numbers of the first kind - coefficients of the characteristic polynomial Width w(P) - size of largest antichain
X X-join - lexicographic product XYZ inequality - the events x < y and x < z are positively correlated (in any poset) Y Young lattice - lattice of partitions of all integers, ordered componentwise Young tableau - placement of the integers [n] in the positions of a Ferrers diagram so that entries are increasing in every row and column Z Zeta function - incidence function defined by ζ(x,y)=1 for all x≤y
6. group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. The popular puzzle Rubik's cube invented in 1974 by Ernő Rubik has been used as an illustration of permutation groups.
7. Lie groups and Lie algebras The foundation of Lie theory is the exponential map relating Lie algebras to Lie groups which is called the Lie group–Lie algebra correspondence.
8. Lie theory involves integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory. For instance, the latter subject is Lie sphere geometry.
9. [https://en.wikipedia.org/wiki/Logicismlogic, Logicism] is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic. Bertrand Russell and Alfred North Whitehead championed this theory, created by mathematicians Richard Dedekind and Gottlob Frege. Historically, logic has been studied in philosophy (since ancient times) and mathematics (since the mid-19th century), and recently logic has been studied in computer science, linguistics, psychology, and other fields. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. An early definition of mathematics in terms of logic was Benjamin Peirce's "the science that draws necessary conclusions" (1870).[In the Principia Mathematica, Bertrand Russell and Alfred North Whitehead advanced the philosophical program known as logicism, and attempted to prove that all mathematical concepts, statements, and principles can be defined and proved entirely in terms of symbolic logic. A logicist definition of mathematics is Russell's "All Mathematics is Symbolic Logic" (1903).
10. number theory is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline.
11. mathematical physics is the application of mathematics in physics. Its methods are mathematical, but its subject is physical.
12. probability theory is the branch of mathematics concerned with probability which is the measure of the likelihood that an event will occur. Cardano was one of the key figures in the foundation of probability and the earliest introducer of the binomial coefficients and the binomial theorem in the western world.
13. representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and the algebraic operations in terms of matrix addition and matrix multiplication.
14. set theory
15. topology