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The Four Color Theorem is a famous problem in mathematics that states that any map can be colored with only four colors so that no two adjacent regions have the same color. This theorem was first proposed in the mid-19th century by Francis Guthrie and his brother Frederick, and it quickly became one of the most famous mathematical problems of the era. Over the years, many mathematicians attempted to prove or disprove the theorem, but it wasn't until the 1970s that a proof was finally discovered. The proof of the Four Color Theorem is quite complex, involving detailed arguments about the properties of planar graphs and the relationships between various types of maps. The first successful proof was published in 1976 by Kenneth Appel and Wolfgang Haken, using a computer program to verify the validity of their arguments. While some mathematicians were initially skeptical of this approach, the proof has since been widely accepted as correct. The Four Color Theorem has many interesting applications in fields such as cartography, where it is used to ensure that maps are easily readable and aesthetically pleasing. It has also led to the development of new mathematical tools and techniques that have been useful in other areas of research. In conclusion, the Four Color Theorem is a famous mathematical problem that has intrigued and challenged mathematicians for over a century. While its proof is complex and relies on advanced mathematical concepts, it has many practical applications and has led to important advances in the field.

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Mathematics is a rapidly growing field with more research being done than ever before, yet many people still view it as a static, completed subject. A new book aims to reveal the beauty and power of mathematics, providing a survey of many areas of current research in non-technical terms. It describes the problems that mathematicians are currently trying to solve, where they come from, how they are solved, and how solving them or failing to solve them can change people's views of mathematics and the way it is advancing. The book covers topics such as prime numbers, non-Euclidean geometry, infinity, probability, chaos, and algorithms, all developed within a historical context. The book also explores the relationship between mathematics and its applications. Each topic is accessible to the general reader, and many recent breakthroughs are presented for the first time in layman's terms. The book aims to open the door to the rapid modern growth of mathematics and its beauty and power.