 # Intersection of mathematics and computing: The Birth of Computer Science

History has witnessed the birth of computing in a series of fascinating events marked by the abridgement of the human capability of solving problems. The invention of computing has transpired time and again when mathematics crossed paths with computing. We, computer enthusiasts, reminisce a great picture of Charles Babbage with his models of different engines and analytic engines when marked the history of computing, which were results of an adamant mathematician trying to reduce efforts in calculation promising better accuracy for the time. Ideas established dating way ahead of their time forming a breakthrough in the field of computing. A similar mathematical event marked the accidental birth of computer science, a monumental legacy conceived from trying to answer a very abstract question about the foundation of mathematics highlighting the interconnectedness between these two fields.

In the early 1900’s it had come to light an ambiguity about the very core of the mathematical study. No one seemed to be really sure what they were studying when they were studying mathematics. Mathematicians weren’t quite sure if math was a study of real-world objects or abstract entities. Did it exist in our minds or in some other realm of existence? A theory was already put forward by Plato describing that the mathematical entities and their relationships belong to their own ideal world separate from ours. A world of forms where these entities existed in perfect harmony. The modern-day mathematicians mostly discredited the theory trying to discover a definite answer. David Hilbert, a renowned mathematician tried to axiomatize whole mathematics into a formal system eliminating all the ambiguity and inconsistencies prevailing by answering these 3 questions:

1) Is mathematics complete?

i.e. a proof was required that all true mathematical statements which existed within the system could be proven within the system.

2) Is mathematics consistent?

i.e. no contradictions can be proven within the system.

2+2=4   and 2+2≠4 (contradiction mustn’t exist)

3) Is mathematics decidable?

i.e. there should exist and effective procedure for deciding the truth or falsity of any mathematical statement.

Hilbert wanted to construct a system that governed mathematics with a fixed set of rules which defines the term formal system. At the time the Euclidean geometry was famously defined as a formal system as it was designed under some fixed axioms and Hilbert wanted to do the same, constructing a foundational axiom for mathematics itself.

Alan Turing, a young mathematician alongside Hilbert was working on the decidability problem. The concept of effective procedure which we now famously term an ‘algorithm’, in the 30s was pretty vague. Turing firstly gave a clear picture of effective procedure defining it as anything a human computer could do by mindlessly following a list of instructions using no genius or insights was an effective procedure. Computers as a machine back then didn’t exist and were referred to as humans who performed calculations. Turing firstly divided the basic components of human computing as: