| In the year 1900 at the International Congress of Mathematicians in Paris David Hilbert delivered what is now considered the most important talk ever given in the history of mathematics. In this talk Hilbert outlined his philosophy of mathematics and proposed 23 major problems worth working at in future. Some of these problems were in fact more like programs for research than problems to be solved. 100 years later the impact of this talk is still strong: some problems have been solved, new problems have been added, but the direction once set – identify the most important problems and focus on them – is still important.
As the year 2000 was approaching we started to wonder if something like that could be done for the new field of Computational Intelligence? Can we define a series of challenging problems that will give it a sense of direction, especially to our younger colleagues? Obviously the situation of a new, rapidly growing field, does not resemble that of the ancient queen of science, and noone has such a deep insight into its problems as David Hilbert had at his time, but without setting up clear goals and yardsticks to measure progress on the way, without having a clear sense of direction many efforts will be wasted. Some period of rather chaotic exploration of new mathematical techniques developed in neural, fuzzy and evolutionary algorithms was necessary, leading to many new directions and sub-branches of Computational Intelligence. Good mathematical foundations have been gradually introduced in the last decade. However, some of the problems CI experts attempted to solve as well as some of the methods used were of the same type as pattern recognition, operation research or some branches of statistics were working on 40 years earlier. For example, introduction of basic results from approximation theory has led to the development of basis set expansion techniques and Gaussian classifiers, and the old ideas of wide margins and kernels developed into the support vector machines. Although these ideas were known for decades they have been greatly developed on the theoretical, as well as on the practical algorithm and software fronts. |
