Who is the founder of algebraic geometry?
The French mathematician Alexandre Grothendieck revolutionized algebraic geometry in the 1950s by generalizing varieties to schemes and extending the Riemann-Roch theorem. Arithmetic geometry combines algebraic geometry and number theory to study integer solutions of polynomial equations.
When was algebraic geometry invented?
Some of the roots of algebraic geometry date back to the work of the Hellenistic Greeks from the 5th century BC.
Who is the father of analytic geometry?
René Descartes
René Descartes (1596-1650) is generally regarded as the father of Analytical Geometry . His name in Latin is Renatius Cartesius — so you can see that our terminology “Cartesian plane” and “Cartesian coordinate system” are derived from his name!
Is algebraic geometry algebra?
In a sentence, algebraic geometry is the study of solutions to algebraic equations. People learning it for the first time, would see a lot of algebra, but not much geometry.
Is algebraic geometry active?
Algebraic geometry is one of the oldest and vastest branches of mathematics. Besides being an active field of research for many centuries, it plays a central role in number theory, differential geometry, group theory, mathematical physics and other branches of science.
Why is algebraic geometry so abstract?
The rapid development of abstract algebraic geometry was due to the recognition of the fact that it is possible, in the framework of the theory of schemes, to apply to the “abstract case” practically all of the known concepts of the classical complex case and, in particular, the homology theory of complex-analytic …
What is the work of Rene Descartes that was named after him?
René Descartes is most commonly known for his philosophical statement, “I think, therefore I am” (originally in French, but best known by its Latin translation: “Cogito, ergo sum”).
What is modern algebraic geometry based on?
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. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems…
What is the first chapter about In geometry?
The first chapter is an introduction to the algebraic approach to solving a classic geometric problem. It develops concepts that are useful and interesting on their own, like the Sylvester matrix and resultants of polynomials.
What are the fundamental objects of study in algebraic geometry?
The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations.
What are the best books on algebraic geometry?
Algebraic Geometry A Problem Solving Approach. American Mathematical Society. ISBN 978-0-821-89396-8. Griffiths, Phillip; Harris, Joe (1994). Principles of Algebraic Geometry. Wiley-Interscience. ISBN 978-0-471-05059-9. Zbl 0836.14001. Harris, Joe (1995). Algebraic Geometry A First Course. Springer-Verlag. ISBN 978-0-387-97716-4. Zbl 0779.14001.