The history of computer science began long before the modern discipline of computer science that emerged in the twentieth century, and hinted at in the centuries prior. The progression, from mechanical inventions and mathematical theories towards the modern concepts and machines, formed a major academic field and the basis of a massive worldwide industry.

Algorithms
In the 7th century, Indian mathematician Brahmagupta gave the first explanation of the Hindu-Arabic numeral system and the use of zero as both a placeholder and a decimal digit.

Birth of computer science
Before the 1920s, computers (sometimes computors) were human clerks that performed computations. They were usually under the lead of a physicist. Many thousands of computers were employed in commerce, government, and research establishments. Most of these computers were women, and they were known to have a degree in calculus. Some performed astronomical calculations for calendars.
After the 1920s, the expression computing machine referred to any machine that performed the work of a human computer, especially those in accordance with effective methods of the Church-Turing thesis. The thesis states that a mathematical method is effective if it could be set out as a list of instructions able to be followed by a human clerk with paper and pencil, for as long as necessary, and without ingenuity or insight.
Machines that computed with continuous values became known as the analog kind. They used machinery that represented continuous numeric quantities, like the angle of a shaft rotation or difference in electrical potential.
Digital machinery, in contrast to analog, were able to render a state of a numeric value and store each individual digit. Digital machinery used difference engines or relays before the invention of faster memory devices.
The phrase computing machine gradually gave away, after the late 1940s, to just computer as the onset of electronic digital machinery became common. These computers were able to perform the calculations that were performed by the previous human clerks.
Since the values stored by digital machines were not bound to physical properties like analog devices, a logical computer, based on digital equipment, was able to do anything that could be described "purely mechanical." Alan Turing, known as the Father of Computer Science, invented such a logical computer known as the Turing Machine, which later evolved into the modern computer. These new computers were also able to perform non-numeric computations, like music.
From the time when computational processes were performed by human clerks, the study of computability began a science by being able to make evident which was not explicit into ordinary sense more immediate.
See also: Numerical analysis, Philosophy of mathematics, and Philosophy of lan
The theoretical groundwork
The mathematical foundations of modern computer science began to be laid by Kurt Gödel with his incompleteness theorem (1931). In this theorem, he showed that there were limits to what could be proved and disproved within a formal system. This led to work by Gödel and others to define and describe these formal systems, including concepts such as mu-recursive functions and lambda-definable functions.
1936 was a key year for computer science. Alan Turing and Alonzo Church independently, and also together, introduced the formalization of an algorithm, with limits on what can be computed, and a "purely mechanical" model for computing.
These topics are covered by what is now called the Church–Turing thesis, a hypothesis about the nature of mechanical calculation devices, such as electronic computers. The thesis claims that any calculation that is possible can be performed by an algorithm running on a computer, provided that sufficient time and storage space are available.
Turing also included with the thesis a description of the Turing machine. A Turing machine has an infinitely long tape and a read/write head that can move