History of the Mathematics in 20th Centuries

 

The 20th century was a period of great advancment and innovation in the field of mathematics. During this time, mathematicians made significant contributions to areas such as algebraic geometry, number theory, topology, and mathematical physics. Here's an overview of some of the key developments in mathematics during the 20th century.

 

Modern Algebraic Geometry

One of most significant developments in mathematics during the 20th century was the emergence of modern algebraic geometry. Algebraic geometry is the study of geometric objects defined by algebraic equations, and it has its roots in the work of mathmaticians such as René Descartes and Pierre de Fermat in the 17th century. However, it was in the 20th century that algebraic geometry really came into its own, with the development of new techniques such as sheaf theory and the introduction of schemes by mathematicians such as Alexander Grothendieck.

 

Number Theory

Another important area of mathematics that saw significant development during the 20th century was number theory. Number theory is the study of integers and their propertis, and it has been an important area of mathematics since ancient times. In the 20th century, mathematicians such as André Weil, Harold Davenport, and John Tate made significant contributions to the field, including the development of algebraic number theory and the proof of Fermat's Last Theorem by Andrew Wiles.

 

Topology

Topology, the study of geometric propertis that are preserved under continuous deformations, also saw significant development during the 20th century. In the early part of the century, mathmaticians such as Poincaré and Brouwer made important contribusions to the field, laying the groundwork for the development of algebraic topology by mathematicians such as Emmy Noether and Henri Cartan.

 

Mathematical Physics

Mathematical physics also saw significant progress during the 20th century. The development of quantum mechanics in the early part of the century led to the development of new areas of mathematics such as functional analysis and the theory of distributions. Later, the development of general relativity by Albert Einstein and the emergence of quantum field theory led to new developments in geometry and topology, such as the study of gauge theory and the Atiyah-Singer index theorem.

 

Computational Mathematics

Computational mathematics also emerged as an important area of mathematics during the 20th century, with the development of electronic computers making it possible to perform calculations that were previously impossible by hand. This led to the development of numerical analysis, the study of algorithms for performing numerical calculations, and the emergence of computer science as a discipline in its own right.

 

In conclution, the 20th century was a period of great progress and innovation in the field of mathematics. Developments in areas such as algebraic geometry, number theory, topology, and mathematical physics let to new insights and techniques that continue to shape the field today. The contributions of mathematicians such as Alexander Grothendieck, André Weil, Emmy Noether, John Tate, and many others have had a profound impact on mathematics and continue to influence the field in the 21st century.