Abstract: Why mathematical knowledgement and what could it be

Michiel Hazewinkel

In this lecture I shall try to address the following two topics:

Why is mathematical knowledgement needed. How bad is the problem?
What can be done, what should be done, and to some extent what is being done.

In the first part I shall argue that the problem is far far worse than is generally assumed. There is an utter discrepancy between the funds there are devoted to finding/developing new results and the amounts being used for making sure that a result can be found if and when needed.

Here one question comes to mind: How to tell whether a result is new, or whether a problem has been solved (perhaps using different language). There are numerous examples where it was discovered many years later that some really good looking results were in fact dozen's of years old. I shall give some concrete examples of this.

Related matters are:

How difficult is it to find mathematical information?
How do we tell that we have found all of nearly all?
How large is the field anyway, and how fast does it grow?
....

The second and smaller part will be devoted to some remarks on what is being done, what should be done, and what can be done in the way of MKM. Basically, I believe, we are still at the problem defining stage, which has not prevented a lot of answers to, and techniques to deal with, questions which still have to be found.