Why software engineers need mathematics.

This article is translated from: ACM monthly newsletter 200 1/vol.44, issue 10.

Keith Defrin ((devlin@csli.stanford.edu is the executive director of the Center for Language and Information Studies at Stanford University.

Software engineers often claim that they have never used any math knowledge they learned in college. Speaking of this, they will also say that they don't even have much computer expertise in college. I have been engaged in mathematics for 30 years, so I let others talk about computer science, but as far as the use of mathematics is concerned, I have to admit that those software engineers are right: they just don't need the mathematics they learned in college.

But they are all wet. They use the math they learned in college every day.

In fact, it is not contradictory. The key is how to interpret the word "use". One kind of understanding is often encountered by software engineers in math class. For example, after learning the step-by-step integration method in advanced mathematics class, students use this method to solve the corresponding exercises and exams. This so-called "application" is the most common, and it is implied when software engineers say that they never use college mathematics. However, this understanding is based on the view that people's learning style is "stuffing ducks".

According to this "spoon-feeding" concept, education is mainly about pouring knowledge into the brain, and applying what you have learned is mainly about pouring out what you have poured in. I dare say that this view of education is highly simplified and wrong. However, under the current education system (I am also involved), people start classes and then set up a three-hour ruminant written test to test the effect of classes. It is this way that nourishes the idea that education is stuffing ducks again and again.

In contrast, a large number of studies on brain working methods and learning methods in the past few decades show that systematic steps such as mastering knowledge and algorithms are only appearances of people's learning process (we know those are appearances because we usually forget what we have learned in class soon after the final exam). This is not the real value of education. Our brain is probably the best example of an adaptive system in the world. When we educate the brain for a long time, the brain will change permanently. Physiologically, a certain part of the conducting nerve fiber chain in the brain grows further and is strengthened. From the perspective of function and experience, we have gained new knowledge and skills. The more times the learning process is repeated, the stronger and longer the above changes will be.

Repetitive learning plays a very strong role in mathematics, which is incomparable to other disciplines. Formal mathematics has a history of about five thousand years. 5000 years is only a blink of an eye in the long evolutionary history, and of course it is only enough for our brains to make the slightest changes. Therefore, although Semu people put forward abstract numbers 5000-8000 years ago, human mathematical thinking began earlier. We developed our ability to think about nature and society in the initial natural selection, but the new changes in mathematical thinking that should be born in human brain will integrate our ability, so that we can not only think about the concrete world, but also deduce the purely abstract world created by our minds.

It is extremely difficult for the human brain to deal with new levels of abstraction. This is why mathematicians can't handle zero and negative numbers freely until the18th century, and why many people can't accept that the cottage root of negative one is a real number until today.

However, software engineering is related to abstraction, and every concept, viewpoint and method is completely abstract. Of course, many software engineers don't think so, but this just illustrates my point of view. The biggest benefit they get from math class is that they strictly deduce purely abstract objects and structures. Moreover, math class is the only subject that gives them this experience. This kind of experience lies not in the important things taught in class, but in its own mathematics. In daily life, familiarity breeds contempt, but when learning how to work in a highly abstract field, familiarity breeds a feeling, well, a feeling of familiarity-that is, what once made people feel abstract begins to become concrete, so it becomes easier to deal with.

Although learning mathematics brings more rewards to computer professionals than ordinary people, everyone in today's society can benefit from it. For example, a study conducted by the U.S. Department of Education in 1997 (The Reilly Report) shows that students who have taken strict algebra or geometry courses in high school perform better in further study, even better after further study, no matter what they study in university. In other words, it seems that completing a rigorous math class-students don't even have to study hard-is an excellent way to improve people's thinking ability and become smart. This kind of thinking ability can benefit people in all aspects.

(In my own book "Mathematical Genes: How Mathematical Thinking Evolves, Why Numbers Are Like Eight Diagrams" (Basic Books, 2000), I analyzed the viewpoints in this paper more carefully and determined which survival advantages enabled human beings to have the ability of mathematical thinking. )

As I pointed out in this article, learning mathematics is more beneficial to software engineers than others. Actually, this is a basic premise. Although it is not formally mentioned in the requirement of compulsory mathematics course for engineering students, it is indeed the real reason why mathematics is useful.