What is the Relationship Between Chess and Mathematics?

The foreword of the book Chess and Mathematics, written by scholars in the former Soviet Union, says: "The board, pieces, and moves of chess are often used to express various mathematical concepts and solutions. Chess plays an important role in developing modern methods of computer programming." Many chess terms also appear in books on cybernetics, game theory, computational mathematics, campaign research, graph theory, and combinatorial analysis.

Chess and mathematics have a lot in common. The outstanding mathematician Halji wrote in his paper "Confessions of Mathematicians": "Disassembling chess problems is like solving mathematical problems, and playing chess is like performing mathematical operations." This is Haley's conclusion after comparing chess and mathematics.

The thinking form of chess and mathematics is very similar, so people with mathematical talent often can play chess well. Of course, not all the top students in the mathematics department will study chess, because it is very difficult to master both.

A generation of chess king Karpov once said when he was in college: "My mind is suitable for learning mathematics, and I hope to conquer the cutting-edge. Therefore, I study mathematics mechanics. I find that there is something in common between chess and mathematics. The problem is that I often participate in chess competitions, and I have no time to practice mathematics. Mathematical theory can also take a break from time, but what's the benefit of not doing exercises? Chess is more important!" As a result, Karpov decided to transfer to economics to spare more time and energy for chess activities.

Mathematics and chess have another thing in common, that is, they both have a popular and fascinating mathematical form. Mathematical games, problem-solving and intelligence tests on the chessboard belong to this form of mathematics. We call this mathematics chess mathematics. In almost every set of Olympic mathematical exercises, intellectual games, and interesting mathematical books, you can find wonderful problems related to chess boards and pieces. Many of the questions contained interesting historical stories, which attracted the attention of some famous scholars.

The great Swiss mathematician Oyler solved the chess problem about the route of the horse ("Knight Tour"), while the great German mathematician solved eight chess problems later. It is worth noting that Oyler was obsessed with chess in the 18th century, while Gauss was in the 19th century. During the whole 100 years, mathematical authorities did not seem to have carefully studied chess (here it refers to the scientific nature of chess moves). Due to the rapid development of cybernetics and computing technology, the situation has changed dramatically in the middle of this century. Chess has become the most convenient model to use mathematics to analyze modern methods of computer programming. Outstanding scholars, such as Vinier, Qiu Lingge, and Shen Nong, often involve chess in their works.

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