Chaos (*) & complexity
From the end of the XIXth century, the mathematical complexity reveals “a treasure of mathematical objects totally new and wonderful”.
What appeared so far to be an “incredible disorder” found many similarities with the apparent disorder of the real world.
The Universe is actually plentiful of chaotic structures. For example the turbulent air flows, the design of sea shores, the Internet traffic flows or the distribution of galaxies in the Universe..
Today, the mathematical study of the complex systems is spreading the fundamental research as well as technical domains and relies also on the power of the latest computers.
For instance: The study of the “Open mathematical problems” –refer to Hilbert’s list in 1900 or to the Clay Institute in 2000- , the Chaos theory, robotics and many other systems which have emerged -or not- from Artificial Intelligence : cellular automation, cryptographic analysis, digital images compression and so on..
However, computers are useless to solve all questions or mathematical problems. At least one thing is mandatory: an algorithm (*) which can translate the problem..
(*) Notes :
- The word “chaos” is not equivalent to the word “disorder” used in our daily language.
It is not either equivalent to the word “random” but proceeds from a deterministic approach, from an algorithm. In other words proceeds from a structure.
- Algorithm (Maths & Data processing systems) : Limited sequence of elementary operations leading to the calculus scheme or to the problem solving.
Ref : Extracts from :
- "La Recherche" magazine
- "Pour la Science" magazine
- "Histoire des mathématiques" by Richard Mankiewicz (Seuil).