We all encountered this science at some point in our lives. In our youth, we all solved a quadratic equation or two. With "in our youth", one might as well mean the youth of civilisation; the oldest recorded solution of a quadratic equation is on a Babylonian clay tablet from 1700 BC. The problem dealt with on this clay tablet was the calculation of the length of the sides of a rectangular piece of land with given area and perimeter.
It is in such humble dwellings that the science of mathematics was born. Geometry arose out of the need to measure up rich agricultural land in a fair (or not so fair!) way after a river had made its periodic flooding. (Yet another phenomenon giving rise to a myriad of complex and mathematically extremely enticing models.). Algebra and number theory had their cradle in the world's first accountant's offices. Archaeologists had a serious disappointment when the mysterious Kretan clay discs written in Linear B were finally deciphered: instead of the expected stunning poetry, all they got was the bookkeeping of an olive oil trader.
So, mathematics, in different shapes and sizes has been with us for about as long as civilisation itself. Some mathematicians even claim to have the oldest profession in the world. This claim is of course heavily contested by bakers, brewers and goat herdsmen. Whatever the truth about the mathematicians claim to seniority, about all mathematics of these early days has one thing in common: its immediate applicability to everyday down-to-earth problems.
A tendency towards a more abstract, "l' art pour l' art" attitude first flourished in classical Greece. It was in this highly-refined culture that a number of schools were established which are often referred to as the first universities. Although, not quite. In the school of Pythagoras (yes, the one from the celebrated theorem), numbers were used to describe relations between individuals. A person was attributed a "prime character" and a sentence like "he stands to me like 4 to 7" was in standard use among the disciples of Pythagoras. When one of the students managed to prove that the square root of 2 could not be a rational number (i.e. a fraction of two integers), it seriously shattered the master's image of the world. Rumour has it that Pythagoras had the "unruly" disciple killed.
Since then, on the average, mathematicians have become a lot better behaved. And quite a lot of them have become more applied or application oriented. Mixture with other sciences is utterly commonplace. Albert Einstein is reputed to have said, "Since the mathematicians have invaded the theory of relativity, I don't understand it myself anymore". And this was only the very beginning! Since then, mathematics has successfully reshaped entire fields of research. The "obvious victims"- physics, engineering and computer science - have been joined by e.g. econometrics and theoretical chemistry. Not even the life sciences are safe anymore, as more then just one geneticist or population dynamics researcher will be able to testify.
It is in this line of "original motivation from outside the discipline" that both articles in this section can be situated. Motivation from outside is far from a one-way street as very often an original problem becomes generalised and embellished beyond the point of recognition, thereby giving rise to entirely new theory which eventually might end up (and very often does!) being useful for a completely different set of unrelated problems. Even some of the work of the famous G.H. Hardy (author of A Mathematician's Apology) has found applications, namely in coding theory. An astonishing fact for a man who declared with pride: "I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or for ill, the least difference to the amenity of the world. I have helped to train other mathematicians (...), but their work has been as useless as my own." If a clear-cut division between pure and applied mathematics ever made sense, it seems to have lost all credibility by now.
An interaction between virtually all the sciences and mathematics generates, luckily for mathematicians, an abundance of problems. This explosion of questions inevitably leads to an explosion of answers and thus it is estimated that about 200 000 "new" theorems are published yearly. In the following two papers, we present just a few of them.