In just 45 years, computers have dominated every aspect of people's lives. Computers serving as multifunction machines are changing the way people live. People use it for fun, to study, to work. Surprisingly, digital computers were first invented primarily for arithmetic. The inventors of the first “computer” would never imagine how much it could change the world. The magical combination of 0 and 1 has led the world into a new era. This article focuses on the relationship between mathematics and digital computers; how mathematics triggers the invention of digital computers and how digital computers change the way mathematics is developed. Looking back, it was the computational requirements that drove the invention of digital computers. Before, people did all the complicated calculations mostly by hand. Inevitably, there would be many errors due to negligence or differing accuracy. Then calculating devices like slide rules were invented to simplify calculations in the 7th century. Slide rules were mainly used for multiplications and divisions based on the concept of logarithms. But they weren't very precise. So some people had to rely on tables to get greater accuracy. The problem is that every time a new version of the table was released, errors occurred. For example, in the 19th century, Shanks, an English professor, spent 28 years calculating π to 707 places. Unfortunately, it was only correct up to 〖527〗^(th) place. Shanks could make mistakes anywhere. He probably copied the wrong number into the tables. The new tables are probably causing the errors. At the same time as Shanks, the industrial revolution was underway with a dazzling development of machines. Engineers need precise numbers to build the bridges, to get to the middle of paper......and programming. These punch cards are "commands" for the machine or, in a modern concept, software for the hardware machine. However, the machine requires a space as large as a football field and he ended up with only a small model. Thus, “Babbage went from national celebrity to national joke in a matter of years, and he died a bitter and unsung man.” (2) The invention of digital computers was then put on hold for almost 100 years. After a hundred years, technology has moved from the steam engine to the oil burner, from vehicles to airplanes, from letters to telephones. But there is little progress in computing devices. Most calculations are done by “teams of human computers equipped with desktop calculating machines.” (3) In 1939, the Second World War broke out. Different from ancient wars, World War II was a scientific war