About
"Simplicity is the final achievement. After one has played a vast quantity of notes and more notes, it is simplicity that emerges as the crowning reward of art."
Frederic Chopin
The motivation for this blog's title came from the admiration of math in its more abstract form. Having a background in Materials Science made the first encounters with more abstract concepts a daunting challenge.
Since high school it seems that the more abstract a subject is, the more complex and difficult its understanding becomes. For me, the idea of considering matrices as mathematical objects at that time seemed unreal.
Pursuing a better understanding of the Finite Elements Method (FEM) gave me the opportunity to discover the existence of even more rich and abstract (at first time this definition was pejorative) fields of mathematics.
The closing point of this brief reflection and the explanation for the title of this page comes from the feeling that abstraction is a price that one could pay in order to have more powerful tools. And even if this price means spending more time to grasp and visualize such concepts, in the end it is possible to see and admire the simplicity of an abstract (now used in a positive manner) definition.
Finally, patience will be a trademark of this blog, so one should expect a non-regular pattern of publications.
The figure on the sidebar shows the Lie group E8, projected into the plane. Lie groups were invented by the Norwegian mathematician Sophus Lie (1842–1899) to express symmetries in differential equations and today they play a central role in various parts of mathematics 1. Personally it is currently a completely mysterious and beautiful subject. One day, however, I shall understand.
"What you have to handle when you start doing mathematics as an older child or as an adult is accepting the state of being stuck. (...) It’s part of the process. It’s not something to be frightened of."
Sir Andrew Wiles, Fields Medal winner by solving a nearly 400-year-old problem, Fermat's Last Theorem 2References
This information and whole idea comes from the front page of the thesis from the Department of Mathematics, University of Oslo. Sophus Lie was a notorious Norwegian mathematician. ↩