One of mathematics' strengths is the high degree of abstraction of modern mathematics that enables us to write complicated things in a simple and clearly expressed form. Unfortunately, this is also something that estranges mathematicians from many people who are not capable of decoding these formulas. This is the reason why we cannot use formulas to communicate on mathematics with the public at large. There is a world congress of mathematicians every four years and there was an easily understandably written essay on mathematicians and mathematics by the poet Hans Magnus Enzensberger at the world congress in Berlin in 1998. It bore the title "Drawbridge up: Mathematics - a cultural anathema". In it, Enzensberger points out that people rarely brag that they don't understand anything about painting, poetry or music. However, one thing most people agree about is the fact that they don't like mathematics. And the mathematician probably has a fair share of the blame for this.


The German Association of Mathematicians undertakes great efforts to improve the image of mathematics in the public eye. There has to be mathematical education in schools that schoolchildren enjoy and that is focused on interesting and everyday questions in spite of the difficulty of the material. Einstein once said that we should make things as simple as possible, but not simpler. If we take a look at a score of Johann Sebastian Bach, the first thing you see is the formal language of notes that many people simply don't understand, a cornucopia of formal structures as in a fugue. But, Bach's music is a great deal more. It makes your soul vibrate, and that's how the mathematician feels about his or her science. Mathematics is a valuable part of human culture just like painting, poetry and music.

It is not only the fundamental forces that play a key role in nature, but also passing on information in such things as hereditary information. In 1948, the American electrical engineer and mathematician Claude Shannon (1916-2001) created a new branch of mathematics, namely information theory. Shannon dealt with the question of efficiently transferring information in communication channels. The magic formula



is at the top of the standard model of information theory, that strangely enough is based upon the notion of probability. The numberk is a normaling constant. An experiment in probability is carried out in this model that has exactly n possible outcomes A1,...,An, realised with the corresponding probabilities p1,...,pn. For n = 2 we could imagine tossing a coin with the outcomes of "heads" or "tails" and they have the probability p1=p2=1/2 . Shannon maintains that you have gained the informationS when you know the outcome of the experiment. However, that doesn't seem to have a great deal to do with our intuitive idea of what information is. But, it can be shown that this concept of information is a measure of the average number of questions with yes-no answers necessary for finding out what the outcome of the experiment is. For instance, it is sufficient in our coin experiment to pose one single question. Physicists have been familiar with the concept of information for more than one hundred years, but in a completely different framework. There they called it entropy. In 1824, the French engineer Sadi Carnot (1796-1832) calculated the optimal efficiency of steam engines when transforming heat energy into mechanical energy. In this process, he came upon a concept that Rudolf Clausius (1822-1888) called entropy in 1865. The second main theorem of thermodynamics formulated by Clausius states that the entropy of the universe strives towards a maximum, meaning that all structures disintegrate. An example was given of this recently when astrophysicists simulated the behaviour of a white dwarf star with a supernova explosion on computers using methods of turbulence theory so that supernovae explosions of white dwarves can be used to determine the distance of galaxies in the depths of the universe. This also allows us to measure the red shift in the spectra of galaxies. The observations ascertained by the Hubble Telescope in this framework show that our universe will accelerate its expansion and never contract again. There have been about 15 billion years since the Big Bang. All stars will have been extinguished in 100,000 billion years, which satisfies the requirements of Clausius' thermal death. Of course, there is the theoretical possibility that a new Big Bang might be ignited in a far-off future if there are sufficiently great quantum fluctuations of the ground state of our universe.