In just 45 years, computers have dominated every aspect of people's lives. Computers that serve as a multifunctional machine change the way people live. People use it for pleasure, for study, for work. Surprisingly, digital computers were initially invented just for arithmetic. The people who invented the first “computer” never imagined how it could change the world. The magical combination of 0 and 1 has brought 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 develops. Looking back at history, it is the computing needs that motivated the invention of digital computers. Previously, people performed all the complicated calculations mostly by hand. Inevitably there would be many errors due to carelessness or varying accuracy. Then in the seventh century, calculating devices such as slide rules were invented to simplify calculations. Slide rules were primarily used for multiplication and division based on the concept of logarithm. But they weren't very accurate. Therefore some people have had to rely on the tables for greater accuracy. The problem is that every time a new version of the table was published, errors occurred. For example, in the nineteenth century it took an English teacher Shanks 28 years to calculate π equal to 707 places. Unfortunately, it was only correct up to the 〖527〗^(th) place. Shanks could make mistakes anywhere. He probably copied the wrong number from the tables. The new tables probably caused the errors. At the same time as Shanks the industrial revolution was underway with a boom in machine development. Engineers need precise numbers to build bridges, for na... middle of paper... n programming. These punched cards are “orders” for the machine, or, in a modern concept, they are software for the machine's hardware. However, the machine requires a space the size of a football field and he ended up with only a small model. Thus “Babbage fell from the status of national celebrity to that of national joke within a few years, and died embittered and unheralded.” (2) The invention of digital computers then suspended for almost 100 years. After one 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 performed by “teams of human computers equipped with desktop calculating machines.” (3) In 1939 the Second World War began. Unlike ancient wars, World War II was a scientific war