What do mathematicians hate most?
More than arithmetic : Math between school and beauty
Emotions are high: The Berlin maths tasks for the MSA secondary school diploma were probably particularly easy this year. Mathematics polarizes again. This is very typical: the subject hardly seems to leave anyone indifferent, some love it, others hate it. Who knows it? It's easiest to hate what you don't know at all or only know in very small parts.
Nevertheless, first of all, congratulations to everyone who passed the test! But what can they do then? What did they learn? Does the passed MSA test mean that the students can now “do math”? That they are equipped with “enough math for life”? Was that the goal at all? And how much math do you need for life?
And to make the whole thing one step more fundamental: What is mathematics? And why is it important, why should it be interesting for everyone?
Wikipedia gets grade 4 at best
Anyone who pecks at Wikipedia in the best student fashion will find that mathematics is “a science that emerged from the study of geometric figures and calculating with numbers”. O.k., the MSA exercises were about geometric figures and calculating with numbers. But science? Who Needs Science?
Wikipedia knows that mathematics is "usually described as a science that uses logic to examine abstract structures created by logical definitions for their properties and patterns". For this, Wikipedia gets a grade of 4 from me at best, sufficient: this is not a good description. If that's the math, it might be difficult, but I don't find it interesting! That's not why I became a mathematician. What is math?
Before taking final exams like MSA, it is important to look at the lessons. What is it actually about? What should it be about? What should the lesson convey? In my opinion, one answer is not enough, we need at least three. If you want it to be formal, you can imagine that we have three subjects, mathematics, with a separate curriculum and different teachers (and exams).
Mathematics is an essential part of our culture
Mathematics I would then be about mathematics as part of culture, history, mathematics as art and art as the result of mathematics. Mathematics I could also be combined with history or art classes. Mathematics is an essential part of our culture: human history begins with geometric patterns and then with numbers, long before the beginnings of writing.
Math is full of great puzzles, difficult problems, great discoveries, wonderful structures. I would tell about the icosahedron. On the competition for the formulas for the third-degree equations. From the Gaussian bell curve. Do you get to know mathematics as a science advanced by remarkable people? Euclid, Gauss, Euler, Weierstrass, Hilbert, Noether, Gödel, Grothendieck, Hirzebruch, Wiles, Tao - you have to hear the names! Mathematics is a science that is done by humans. (There are also Berliners among them!)
Mathematics produces art, the beauty of shapes and the beauty of formulas! And the heroic stories of the struggle with the really big problems, such as Fermat's Last Sentence or Kepler's problem. And the big puzzles that continue to occupy us, the Goldbach conjecture, for example.
There is mathematics behind weather reports, train timetables and chip design
The role of mathematics in the modern world - that is part of human history. Physics is inconceivable without mathematics, both of which have evolved over centuries as Siamese twins. Shouldn't every student know that there is a lot of complicated math in weather reports, in train timetables, in chip design and in telecommunications? This is general knowledge, even if the mathematics behind it is too complicated for school, you cannot explain it in Mathematics I: You can tell about it. Math is interesting!
If all these buzzwords mean nothing to you: Have you ever learned about mathematics? There is none of this in the Berlin MSA tasks. If one task had been “Name three famous mathematicians”, would you have failed? Or "Name an unsolved math problem" - what do you think of?
The school subject Mathematics II should equip each of us with the tools for daily life. We don't need a lot of math in everyday life. The basic arithmetic operations, percentages and interest, elementary geometry: all of this can already be found in Adam Ries' little arithmetic booklet in 1522, with which German merchants learned arithmetic, and thus became independent of the arithmetic masters, who were juicy for pre- and post-arithmetic operations Fees took (like today only the notaries for legal transactions). That was the basis for the economic boom in the 16th century and is still part of the basic equipment today, without a pocket calculator. Since Adam Ries, the probabilities have been added, and the interpretation of graphics, statistics and their pitfalls and pitfalls: mathematical tools, also for reading newspapers, indispensable! I also find all of this in the MSA exercises, Mathematics II is tested there.
The curve discussion is a prototype for analyzing relationships
And another school subject: Mathematics III provides an introduction to mathematics as a science. In Mathematics III one learns how mathematics works, the clean and watertight reasoning, the laws of logic, the proof of contradiction, the complete induction. To argue watertight, to formulate carefully, but also to deal with errors and round-the-clock errors and with limited calculation accuracy: these are skills that are not only needed for studying mathematics, but also for entering law or medicine; they are part of the ability to study . The "curve discussion" is not something we need in everyday life, but it is a prototype for analyzing relationships and an excellent training unit for understanding "necessary" and "sufficient" conditions. Every lawyer and every doctor should be able to argue with it! Mathematics III is therefore an essential part of preparing for a high school diploma and studying aptitude ...
Three separate school subjects Mathematics I – III? It was a mind game, which is of course not feasible, and neither useful nor desirable. Also because the three parts belong together. Mathematics classes in the middle school nowadays seem to concentrate on Mathematics II, on everyday mathematics, the toolbox. And that is then checked. But the motivation must also come from Mathematics I, and the “Mathematics for Key Technologies”, which the Berlin Research Center Matheon has been promoting since 2002, cannot be had without Mathematics III.
The most abstract formulas become art
No subject is reduced to the skin and bones of the curriculum like mathematics like mathematics. Overview knowledge, panorama, stories, perspectives - do they all get stuck in the toolbox? That would be a shame! The real beauty that lies in the numbers and figures can only be seen if you teach all the math, far beyond the knowledge of the toolbox. Yes, mathematics is difficult, that is part of it, that also makes mathematics interesting and exciting. And you don't have to understand all of that to see that mathematics is something special. Mathematics has many approaches, and there are just as many good motivations for wanting to see and know more.
Can you discover the beauty of mathematics in a completely different way? Experiencing mathematics as an art without studying it? Yes of course! The geometric figures in nature invite you to do this, but also in architecture. Each of the large domes over St. Peter's Basilica or the Reichstag, the glass roofs over the main train station or the inner courtyard of the Jewish Museum is a triad of mathematics, architecture and art. Geometry as art is produced by the architects and structural engineers, as are the geometers of the Berlin-Munich Collaborative Research Center “Discretization”. The most abstract formulas become art when they are reproduced in large format, placed in front of colored surfaces and allowed to work. The French sculptor Bernar Venet, to whom we owe the huge steel arch in front of the Urania in Berlin, has been producing great art since the 1960s!
Mistakes are part of it
But is it really art? The American critic Donald Kuspit wrote of Venet's mathematical graphics: “We are no longer afraid to be ignorant because the colors enable us to accept our ignorance as a path to emotional truth. We are no longer ashamed of our estrangement, the strangeness of mathematics becomes the point of entry to the emotional depths. ”Kuspit believes he can even see a“ sexual truth and depth ”in the mathematics graphics by Venet. Do you see them too? I am more profane there. I notice that Venet made mistakes when reproducing the formulas. I think they are part of it. To mathematics, and to art.
The author teaches mathematics at the Free University of Berlin. In 2013 he published “Mathematics - That's not art!” By Knaus-Verlag, in 2016 in the second edition: Ehrhard Behrends, Peter Gritzmann & Günter M. Ziegler (eds.): “? & Co. Kaleidoscope of Mathematics ”, Springer Spectrum.
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