The power of algebra lies in abstraction, and abstraction is basically forgetting. By retracing the History of algebra from its roots to more recent advancements, this article unveils the numerous breakthrough in our understanding of the world, by abusing of the power of forgetting.
All along the 20th century, pure algebraists have dug deep into the fundamental structures of mathematics. In this extremely abstract effort, they were greatly help by the possibility of representing these structures by space deformations, which could then be understood much better. This has led to breakthroughs, including the proof of Fermat's las theorem. This article introduces the ideas of group representations.
Beauty is extremely hard to define. Yet, physicists and artists seem to agree on an important feature of beauty, created by mathematicians: Symmetries. This article aims at introducing the beauty and the concepts on symmetries, from the basic geometrical symmetries to the more abstract fundamental automorphisms.