Science is possible without mathematics

Between hatred and enthusiasm

Mathematics is something that some people really love, mathematicians like Ehrhard Behrends for example:

"Yes, it started in school that I was particularly interested in mathematical questions. On the one hand, it is intellectually demanding, you can reach truths that in a certain way have a more objective value than the truths of other sciences. It is a science that enables one to understand facts in philosophy, in the natural sciences, better than one can understand without mathematics, and it is an area that is so extensive that it is never boring to grapple with exciting new questions. "

Also the mathematician Christine Scharlach:

"What has always excited me is this feeling of solving a problem. Yes, when you have understood something apparently very difficult, very abstract, this feeling, I can grasp it, it's just beautiful. So it gives me a sense of security that I ultimately know that I can either answer most of the questions that come my way or that I can sit down and find out in a certain amount of time. And I enjoy being able to help someone by helping them, to structure your problem, to see what is my problem and then to be able to solve it a little further. That might even go towards the therapist, yes. "

Mathematics is something that some people at least approve of:

"In any case, it always comes up as the first stumbling block in all science-oriented courses of study, nowadays you simply can't get by without the tool of mathematics in most of the sciences."

"It played a very big role, and a much bigger one than I thought before, mathematics is the language of physics."

"Physics, biology and chemistry play an essential role in medicine, at least marginally, and mathematical knowledge is also required for these subjects, certainly not at a university level."

"For me as a musician, mathematics first aims at thinking, at the mind, while music is primarily concerned with emotions - although, there is such a connection, you have to count when you play pieces of music, yes, the relationships of the tones to one another, which are also expressed in relationships, in mathematical relationships, that is, Bach comes to mind. "

For most people, however, mathematics is something that they shudderingly turn away from, or as the German mathematician Paul Epstein put it:

"The majority have feelings towards mathematics as Aristotle said they should be awakened by tragedy, namely pity and fear. Pity for those who have to struggle with mathematics, and fear: that one might end up in this dangerous situation oneself . "

"Yes, there are exactly two sides to it, either you can do it very well or you can do it very badly."

Mathematics - the very word often leads to violent reactions in many people. Bad memories from school come back. Many people here have suffered major defeats in their otherwise quite successful professional life. And some even seem to understand mathematical ignorance as a prerequisite for being a real esthete or philanthropist

Hans Magnus Enzensberger sees in an essay on the occasion of the World Congress of Mathematicians in Berlin 1998 "Mathematics in the Beyond Culture" - and finds it "downright perilous",

"Because never before has there been a civilization that has been so permeated with mathematical methods and so dependent on them as ours". "

Mathematics in the actual ancient Greek sense of the word means "the art of learning", or as the mathematician Ehrhard Behrends puts it:

"" Mathematicians are concerned with creating structures that are necessary in order to be able to produce models for understanding the world. Whether these are numbers or vectors or probability spaces, you can use them to describe phenomena that are important for human life. "

Structure thoughts, explain the world, describe vital phenomena - and what about arithmetic?

"Mathematics is of course based on arithmetic", "

says Christine Scharlach, mathematics professor at TU Berlin, and her colleague from Freie Universität, Ehrhard Behrends, adds:

"" Today it is still very important to have invoices for the concrete finding of solutions, but of course the computers do that. And that is why: arithmetic is not of great temporal importance for what mathematicians understand by mathematics. And it is the very least that interests them. "

Scharlach: "Whereby everyone certainly has to learn to calculate in order to understand mathematics for the first time."

For mathematicians, mathematics is "the art of avoiding arithmetic", as someone once said, the often annoying, unpopular accessory when it comes to the real thing. Because: The essence of mathematics is the formation of theories to solve fundamental problems. But: Which science do these questions belong to? Are mathematicians natural scientists or humanities scientists?

"Mathematics is the alphabet with which God wrote the world", "

believed Galileo Galilei. So mathematics would be a natural science

Ehrhard Behrends and Christine Scharlach:

"" History, especially since the beginning of modern times, is full of situations where mathematical methods have succeeded in making really fundamental contributions to the understanding of the world. Newton's fundamental laws of mechanics, where the attempt is made to reduce the gigantic structure of all possible movements in this world to a common denominator by means of less elementary terms and less fundamental assumptions. "

"So theoretical physics, for example, or theoretical computer science, the boundaries are often difficult to draw, what is mathematics there and what is computer science or physics? I think that of course this will change a lot in the historical context has: Especially where applied mathematics has become more and more popular, the proximity to natural science has of course become much greater. Otherwise, however, I think that the proximity to the natural sciences absolutely does not equate. "

No question about it: with the rise of the experimental natural sciences, the importance of mathematics as a science also grew. Calculations, the formalization of observations and thoughts, the exact derivation of a theory through proof - these mathematical methods form a large part of scientific research.

Conversely, however, scientific methods are not part of the mathematician's tools: They do not observe natural phenomena and they do not experiment. Your research object is not the world as it really is. The mathematician, computer specialist and computer critic Joseph Weizenbaum described this very clearly at a congress a few years ago with the following story:

"There's a man with a little child by his hand, and over there you can see a hill like that, a mud hill, and there is an elephant up there. And then the child says: 'Daddy, how long would it be if that Elephant slipping down there? ' The father thinks for maybe half a minute and then he says, 'About 90 seconds, it could be 92 or 88.' What did the father do, especially when he is a mathematician and studied at MIT? He made a mathematical model in his head. "

This model contains everything that is important to answer the boy exactly to his question: the elephant as a mass point, the hill as an incline, the slip angle and a few more physical data and arithmetic formulas.

"But what's not in this model? For example, that the sun is shining, or how the elephant smells, or that the elephant is a living being, or how old the son is. Now if I try to make an extensive list of I would never come to the end of all the things that are not included in the model. The whole world, everything that you can and would like to say about this world, is not there. "

Some even deny that math wants to be useful at all. The theoretical physicist Richard Feynman once said:

"Math is like sex, sure there are some useful results, but that's not why we're doing it."

There is an old argument as to whether a mathematical theory will be invented or found. For example, where do the numbers exist? Does mathematics deal with phenomena that are in principle there, just need to be discovered? Or are the objects of mathematics only created through pure thinking, through the activity of a brain? Ehrhard Behrends:

"At first one is just as correct as the other, because neither of these claims can be proven. At the beginning of this century, a lot of thought had been given to it, but the caravan moved on, and I myself have the feeling that I am discovering something rather than constructing it . "

"Mathematics is the most radical of all humanities", "

wrote Gero von Randow in an essay in "Die Zeit".

Scharlach: "" I think that for most mathematicians, mathematics actually only exists in the mind, they are abstract formalistic objects with which we then continue to manipulate. That's why I think everyone should learn math because it's just a certain state of mind. "

So really more of a humanities? At least the basic working methods are similar, says Christine Scharlach:

"In principle, I just need a piece of paper and a pen to work - which unfortunately you don't have that often, maybe the computer, but otherwise, like a humanities scholar, I don't need any tools, I'm alone able to do math with my mind. "

On the other hand ...

"There are big discussions about how to describe the humanities, so we as mathematicians do not usually deal with any cultural phenomena, yes. Or these working methods in the sense of unambiguity there is then again a huge difference. So as a humanities I would not label it. "

Maybe mathematics is more of a philosophy? Ehrhard Behrends:

"It is true that mathematics also played an important role in all great philosophies. Whether you take Plato, Aristotle, Descartes, Kant - all of them assigned mathematics a predominant role."

Only those who mastered mathematics were accepted into Plato's philosophy school. For Immanuel Kant, geometry and arithmetic were considered "examples of absolutely certain knowledge". Both philosophers and mathematicians have to deal with logic. Both work with terms like "infinite", "rational", "irrational" or "imaginary". And the mathematical zero is just as difficult to grasp and controversial as the philosophical zero.

The philosopher and mathematician Leibniz even wanted to combine the two sciences with a stroke of genius, says philosophy professor Sybille Krämer from the Free University of Berlin:

"Leibniz had the idea of ​​a universal calculus of thinking for the first time, this idea that all problematic questions can be solved with a method that is analogous to arithmetic. No one before him has said with such clarity that thinking is arithmetic. So the beginning Modern thinking in the 17th century was the attempt to develop a cognition that no longer needs divine revelation or any reference to God, and that means that thinking is a regulation, there is a set of rules, keep it and you will come to the truth. "

In the meantime, however, mathematics is no longer a guarantee for "truth". There was a fundamental crisis in the last century when it turned out that not all mathematical theories can be proven beyond doubt. This even makes some scoffers ask whether mathematics is not more of a question of faith than a science today.

In any case, mathematics has lost its earlier fame as the mother or queen of all sciences. It seems to be there everywhere, but that gives it the status of an auxiliary science for many today. Of course, the mathematician Behrends attaches a little more weight to her:

"When I look at mathematics as it is used as a science in other sciences, for me it is a kind of bridge science, yes, it stands as a bridge between the world that interests us and the sciences that deal with theories care about this world. "

Still others count mathematics among the structural sciences, a term coined by the physicist Carl-Friedrich von Weizsäcker. They are not concerned with researching specific objects or questions, but rather develop a wide variety of methods for the sciences as a whole. For math professor Christine Scharlach, that's not the case. She definitely sees mathematics as something very special:

"I believe mathematics is a certain way of thinking, a certain way of solving problems: I actually like 'the science of problem-solving'."

And mathematics is an enormously important science for society.

"You can say that we live in the age of mathematics. Our culture is mathematized", "

says a report published by the American Mathematical Society in 1984.

Scarlet fever; "" For me, a wonderful example is our time: Who can imagine living without a time. You can also see that this linearization, this way of imagining yourself every minute the same length, does not necessarily correspond to the real feeling, but in fact it is the way we interact with each other, even agree to meet the time and so on. "

The large areas of our society: economy, technology, science cannot do without mathematics.

Behrends: "When an engineer builds a bridge, support loads are calculated, material constants are inserted into the equations in order to be able to check load-bearing capacities at the end, that is, to put it bluntly, the kind of mathematics already carried out by the Egyptians and Babylonians So in this first sense, mathematics is essential for all engineering sciences, but also because of the stochastic components for psychology, social sciences, medicine and so on. "

In almost all areas of science, statistical methods and / or models are used, counting and calculation, and connections are logically derived. Even in German studies, with linguists or in musicology. And economics is no longer conceivable without a solid arithmetic background and partly without mathematical theories. For example, the American mathematician John Nash and two economists received the 1994 Nobel Prize in Economics for their joint achievements in the field of game theory.

Professor Christine Scharlach even believes that mathematics can have a certain meaning in social life:

"When I talk to people about very personal problems, relationship problems, it is often important to untangle this tangle of mathematics - pull apart, see what it's all about, structure, use. But then of course it is always important to instead of just including the head, always including the emotional levels, which I believe are very difficult to describe mathematically. You should certainly also focus more on where it is and what you can really use it for. "

To convey this deeper interest in mathematics is one of the tasks of the school - which apparently still has a hard time with it. So it doesn't help that some didacticians repeatedly point out that, in addition to dealing with numbers, you can learn a lot more for life by studying mathematics: Mathematics enables you to analyze problems and find strategic solutions; you learn that it is sometimes important to be precise, even in the language - and to argue well.

And yet: Most people are not interested in mathematics, not even in everyday things: They may just be able to calculate the size of their living room to know what the price per square meter on the large carpet roll at the retailer means for their wallet. But what happens when you search for a recipe for Sour Spicy Soup and enter the word on Google, you don't want to know anymore. This is called "black box thinking". A behavior that Professor Ehrhard Behrends finds regrettable, not only from a mathematical perspective:

"Yes, that is the question of what you see as education. If you are satisfied with pressing a button and then something happens, you don't have to know anything. Then you just have to be able to push buttons. But I think so that someone who has satisfied these elementary needs should also think about why something is the way it is.What do we know about the world today? And then there is no getting around mathematical theories, and I think it is at least as important to know how modern cryptography methods work, which are fundamentally important if you are making bank transfers or want to be sure that your Eurocard is not being used without authorization how it is important to know, for example, what Stravinsky composed. But that's almost a different story about what is seen as important and interesting in different cultures. "