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algebraic geometry

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(mathematics) a branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry.

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branch of mathematics
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In 1945, he fruitfully discussed foundational matters for algebraic geometry with André Weil.
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Everyone learns Algebra, Geometry
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Claire Voisin (born 4 March 1962) is a French mathematician known for her work in algebraic geometry.
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Islamic mathematicians such as al-Khwarizmi, Avicenna and Jamshīd al-Kāshī developed methods in algebra, geometry and trigonometry.
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Quantity and space both play a role in analytic geometry, differential geometry, and algebraic geometry.
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Hartshorne is the author of the text Algebraic Geometry.
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Algebraic geometry, a branch of geometry, in its primitive form specifying curves and surfaces as solutions of polynomial equations.
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Karen Ellen Smith (born 1965, Red Bank, New Jersey) is an American mathematician, specializing in commutative algebra and algebraic geometry.
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Another Persian mathematician Omar Khayyam is credited with identifying the foundations of algebraic geometry and found the general geometric solution of the cubic equation.
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The Chinese independently developed number sets including very large and negative numbers, decimals, a place value decimal system, a binary system, algebra, geometry, and trigonometry.
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Alexander Grothendieck (/ˈɡroʊtəndiːk/; German: ; French: ; 28 March 1928 – 13 November 2014) was a French mathematician who became the leading figure in the creation of modern algebraic geometry.
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The book was published in 1935 and reissued 36 years later, with detailed notes by Zariski's students that illustrated how the field of algebraic geometry had changed.
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Towards the end of the century, the Italian school of algebraic geometry (Enriques, Segre, Severi) broke out of the traditional subject matter into an area demanding deeper techniques.
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She is noted for her work in algebraic geometry particularly as it pertains to variations of Hodge structures and mirror symmetry, and has written several books on Hodge theory.
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In 1883 or 1884, at the age of 13, Montessori entered a secondary, technical school, Regia Scuola Tecnica Michelangelo Buonarroti, where she studied Italian, arithmetic, algebra, geometry, accounting, history, geography, and sciences.
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He left Kiev in 1920 to study at the University of Rome where he became a disciple of the Italian school of algebraic geometry, studying with Guido Castelnuovo, Federigo Enriques and Francesco Severi.
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Some of his major results, Zariski's main theorem and the Zariski theorem on holomorphic functions, were amongst the results generalized and included in the programme of Alexander Grothendieck that ultimately unified algebraic geometry.
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Within algebraic geometry is the description of geometric objects as solution sets of polynomial equations, combining the concepts of quantity and space, and also the study of topological groups, which combine structure and space.
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Several major types of more abstract mathematics (including invariant theory, the Italian school of algebraic geometry, and Felix Klein's Erlangen programme resulting in the study of the classical groups) were based on projective geometry.
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They understood basic concepts of algebra and geometry, and could solve simple sets of simultaneous equations.
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'in which Al- Biruni describes how he combined algebra and geometry
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The topic of projective geometry is itself now divided into many research subtopics, two examples of which are projective algebraic geometry (the study of projective varieties) and projective differential geometry (the study of differential invariants of the projective transformations).
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While the visual nature of geometry makes it initially more accessible than other mathematical areas such as algebra or number theory, geometric language is also used in contexts far removed from its traditional, Euclidean provenance (for example, in fractal geometry and algebraic geometry).
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The Arithmetica touches on algebraic notation, arithmetic, the relationship between geometry and algebra, and the solution of equations.
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In mathematics, Hilbert's syzygy theorem is one of the three fundamental theorems about polynomial rings over fields, first proved by David Hilbert in 1890, which were introduced for solving important open questions in invariant theory, and are at the basis of modern algebraic geometry.
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