Groups theory: origins and destiny

Document Type : Mathematical history Paper

Author

Chamran University of Ahvaz

Abstract

The concept of groups emerged in the 19th century as a result of humanity's millennia-long quest to solve polynomial equations. Almost immediately, it was observed that groups appeared in other branches of mathematics, including number theory, geometry, differential equations, and physics. Discovering the applications of groups in various sciences emphasized the importance of studying them, and the classification of finite simple groups became one of the major goals of mathematicians. By the early 21st century, the classification of finite simple groups was completed. However, this achievement cast a shadow over the theory of groups, with some considering the classification the end of the road for this theory. This article briefly touches upon the formation of group theory, the theorem of classifying finite simple groups, and the challenges faced by group theorists after completing the classification.

Keywords

References

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History

  • Receive Date: 24 May 2017
  • Revise Date: 25 October 2017
  • Accept Date: 27 October 2017
  • Publish Date: 22 May 2018

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