Abstract: – An unsung hero of World War II was born on June 23, 1912 in London, Alan Mathison Turing was an innovative thinker, computer scientist and mathematician. He was not recognized for his contributions to our society until after his death and many pardons later. He was especially prominent in the development of theoretical computer science. He is widely known for his 1936 paper which introduced the “Turing Machine. ” His work also made substantial contributions in the area of artificial intelligence and has set the foundation for research in this area.

Other areas of interest which he ontributed to included cryptology and theoretical biology. Key-Words: – Computer Science, Enigma Machine, Mathematician, Turing Test, Artificial Intelligence 1 Introduction Alan Mathison Turing (see Fig. 1) was born in Maida Vale, London, England. As a young child, he portrayed signs of intelligence. Although, his intelligence was recognized, some of the teachers did not respect it. As a young student he became specifically interested in the field of mathematics and science.

From 1931-1934, Turing attended University of Cambridge where he proved the central limit theorem in his dissertation. In 936, he presented the idea of a universal machine known as the “Turing Machine” in his paper “On Computable Numbers, with an Application to the Entscheidungsproblem. ” “The Turing Machine moved from one state to another using a precise finite set of rules (given by a finite table) and depending on a single symbol it read from a tape” (O’Connor and Robertson).

Ultimately, Turing studied mathematics and cryptology at Princeton University where he received his Ph. D. Following this accomplishment, he returned to Cambridge, where he accepted a position with the Government Code and Cipher School (GCCS) t Bletchly Park. His work made significant contributions in breaking the German Egnima Code. Turing further addressed the issue of artificial intelligence in his 1950 paper, “Computing machinery and intelligence. ” He’s laid the foundation for the study of artificial intelligence research. He was, ultimately, charged with indecency for being a homosexual. This resulted in the removal of this security clearance and was prohibited to continue his work at the GCCS.

Fig. 1 Alan Mathison Turing [2] 2 Early Life During Great Britain’s rule over India, the elite group named the Imperial Civil Service or Indian Civil Service kept the control over India. Alan Turing’s father, Julius Mathison Turing was part of this elite group of men and an official of in India, consequently, he was abroad most of Alan Turing’s life. Alan’s mother, Ethel Sara Stoney, left Alan and his older brother behind in England with friends of the family when Alan was about one-year-old to join her husband. Ethel’s father and Alan’s grandfather, was an engineer in India.

Alan grew up away from his parents and in the care of a retired colonel in Hastings. In 1922, Alan was sent to a preparatory school in Hazlehurst Sussex [2]. peace and 3 Schooling While Turing attended Hazlehurst Preparatory School where he was considered an average to good pupil that would follow his own ideas. His headmaster stated that “if he is to be solely a scientific specialist, he is wasting his time at a public school”” [1]. In 1926, at the age of 13, Alan attended Sherborne School in Dorset. Alan had to cycle 60 miles to get to school because of a general strikes going on in those days in Britain.

He was a great athlete throughout his life and enjoyed running [2]. He was eager to go to school and was part of the chess team and the ebate team. His mother insisted he should get a public education even if he as capable of learning more on his own. Turing studied advanced mathematics and science on his own and was always running ahead of the school syllabus. It was at Sherborne that he met Christopher Morcom, a friend that inspired many of Turing’s future ideas. In 1931, he attended King’s College, Cambridge. There he received first class honors for his works in mathematics.

At the age of 22 he was even elected fellow for his proof of the central limit theorem even if Lindeburg had proven it about ten years earlier. He was set with a career in mathematics but he had an interest in putting his mathematics to use and wrote a paper that is now known as the foundation of computer science. 4 Treatise Alan Turing wrote many papers about his ideas and some of his most well known published works are, On Computable Numbers with an application to the Enthscheidungsproblem (decision problem), Computing machinery and intelligence and his dissertation titled Systems of Logic Based on Ordinals. . 1On Computable Numbers with an application to the Entscheidungsproblem (decision problem) Alan Turing wrote On Computable Numbers With an Application to the Entscheidungsproblem in 1936.

In this paper he answers some questions of his time. The Entscheidungsproblem or decision problem was a challenge posted by David Hilbert in 1928 in which he challenges mathematicians to find a universal algorithm that takes as input a statement of a first-order logic and answers Yes or No to whether it is universally valid and can be proven through axioms and rules of logic.

If this algorithm is found, there is no problem that is unsolvable. An American named Alonzo Church also wrote about this problem and greed with Turing that the entscheidungsproblem is unsolvable in general. Turing goes on to define computability and algorithm. He writes about a hypothetical machine that can be made to solve any solvable problem using simple logic rules and is later known as the Turing machine. He also states that if one problem can be solved by one system, then it should be solvable by all systems or machines [4].

In this paper he defines computable numbers as numbers with decimals that can be computed in finite time. He expresses that humans are limited to computing large numbers and machines can calculate large umbers for us. He starts basing his machine on the model of a human solving a problem. In this paper he starts defining the memory of a computer by defining the states of a machine. He describes a tape that is divided into squares that holds a symbol that gets scanned. This describes computer instructions and computer memory.

He describes an automatic machine capable of having two types of output symbols. The first types of symbols are either a zero or a one and the other type of symbols are help symbols. This idea is later called a computing machine or computer [4]. 4. 3Systems of Logic Based on Ordinals Alan wrote Systems of Logic Based on Ordinals in 1938, and he explores incompleteness theorems. He wrote about effective calculability, number theoretic theorems, types of problems that mal math systems after Kurt Godel’s are not number theoretic, logic formulas, ordinal numbers and completeness problems.

This and his major works have been influential in the fields of mathematics and computer science [5]. 4. 2Computing machinery and intelligence Turing wrote Computing machinery and intelligence in 1950. This paper introduces what is now known as the Turing test. The paper looks to answer the question “Can machines hink? ” [3]. In order to answer this question, he explains what he means by the word think and defines the kind of machine he is thinking of. He proposes we ask instead if a computer can win a game, which he calls the imitation game. The game consists of three players.

Player A, a human, player B, a computer, and player C, a human judge. The object of the game is for Players A and B to convince the judge they are the human by answering a series of questions. The question then turns from “Can machines think? ” to “Can machines do what humans can do, in this case decide which player is the real human. In his paper he also addresses nine objections to defend his machine. He begins defending the concept of artificial intelligence. He rebutted objections about religion by comparing making machines to procreating of children.

He also disagreed with Ada Lovelace when she said Charles Babbage’s analytical engine would never be capable of originality. He clarified many mathematical objections, arguments from consciousness, arguments involving the nervous system, and extra sensory perception. He concludes with learning machines, where he writes his thoughts about the learning machine that would one ay win the imitation game [3]. 5 Cryptanalyst Alan Turing had a great career in mathematics and had a job set in academia at Princeton but he wanted to apply his mathematics.

In 1936, he returned to Great Britain and worked with the government as a code breaker. Alan joined the Government Code and Cipher School (GCCS) at Bletchly Park. World War II was underway and Germans used the encrypting Enigma machine to send messages and coordinates of their strategic locations. German U-boats were bombing any ships with supplies headed to help the Allied forces and were winning the war. It was not until Alan Turing and his colleagues at Bletchly cracked the code and changed the course of events. He developed the machine he called the Bombe (see Fig. ), which consisted of cogs and wheels that were capable of breaking Enigma messages.

His machine broke two messages a day, which was by far faster than the human. Breaking these codes allowed the Allied forces to statistically and strategically win key battles during World War II. Many believe the code breaking cut the war short by four years. The machine deciphered faster than the human and brought about questions such as, “was this machine cleverer than a human? [1]. The German navy had better cypher machines nicknamed Tunny by the British and Turing was determined to break their code.

In 1942 he broke the messages using a strategy nicknamed Turingery by his colleagues at Bletchly Park. With this strategy they could break any codes the Germans would use. It is estimated that 14 to 21 million people might have died if the Turing would not have broken the code. He proposed to Joan Clarke, a fellow mathematician at Bletchly, but told her he had homosexual tendencies and the engagement was brief. This gave him confidence to begin a homosexual life. Fig. 2: Bombe 6 Conviction In 1952 Alan was in a relationship with a man named Arnold Murry.

There was a break-in at Alan Turing’s home that year and Arnold told Alan who the burglar was. Alan decided to go to the police since he knew who the culprit was. During his testimony against the thief, he confessed he had homosexual relations with a man. Alan was quickly arrested in Manchester for having a relationship with another man, despite all the great work he had done for the country. He was convicted of gross indecency and was not allowed to work for the government. In order to avoid jail, Alan was forced to have hormone treatments or injections to decrease his libido.

The treatment made him impotent and two years after his conviction Turing made the choice to poison himself with cyanide. Fig. 3: Alan Mathison Turing Statue [2] 7 Tribute and Pardon In 1994 Manchester saw the first tribute done in the name of Turing, which was that the city’s leaders renamed part of the inner road Alan Turing Way. This was something great, but the people who lived around that area did not recognize his name. A little after it was decided to bring some light to his name and what he had contributed and this was done through a play about his life.

In 2001 a statue of Alan Turing sitting on a bench (see Fig. 3) was placed in the Manchester’s Sackville Garden as a memorial. This statue is a popular attraction for the tourist. Turing had not been properly recognize for all the contributions because he was a homosexual; therefore, Williams Jones began a petition for a posthumous pardon, Dr. John Graham-Cumming requested for an official apology from the Prime Minister, and Mr. Leech who tabled a motion in Parliament. Mr. Leech said, “Alan Turing’s contribution to Manchester was enormous as well as his efforts in bringing the what to an early conclusion.

He is a national hero. ” Finally, in December of 2013, Alan Turing was granted a posthumous royal pardon, formally cancelling his criminal conviction of being homosexual. Also on the twentythird of December the Queen (see Fig. 4) visited Bletchley Park where she studied the Enigma machine [1]. Fig. 4: Queen and Enigma Machine [1] 8 Contributions Alan Turing worked out a major puzzle in our history and impacted the results of World War II by creating the bombe and Turingery. He also produced a detailed design of the ACE or Automatic Computing Engine. This computing machine stored programs in its memory.

He reported this machine should have unlimited range of applications and wrote about software development. The prototype was never finished because he quit the company before it was piloted. He laid the groundwork for all computers we use today. Alan opened up the ideas of Artificial Intelligence and the thought that a computer could one day think for itself. The Turing test for Al is used today and is thought it will be used for many years to come. Turing also explored biological patterns, spots, stripes and flower petals and patterns in nature during his last years.

Conclusion Our current knowledge of mathematical problems and concepts is one that has derived from the many contributions and efforts of past scholars. Alan Turing is one of these great scholars who has made significant contributions in the field of mathematics and computer science. His work and efforts in cryptology allowed the significant contribution of breaking the German enigma code during World War II. Furthermore, his work has set the foundation for research in Artificial Intelligence.