**Passport photo of Alan Turing at age 16**

When the fate of an entire nation, and even the entire *world*, rests on you talents as a gifted and skilled mathematician, it’s easy to see why modern-day presentations of Alan Turing are both numerous and in reverence to the man and his achievements. Popularised immensely by Cumberbatch’s portrayal of him in *The Imitation Game*, Alan Turing’s life has since been the subject of much interested from a more general public.

Who exactly was Alan Turing, though, and what was the nature and result of what is arguably one of the most prominent and important contributions to a conflict by any one man in modern history? It’s a subject so interesting that I felt compelled to write about it, from Turing’s love and loss at a young age to his resulting passion for and success in the field of Mathematics, and eventually his work on the Enigma code that cemented his place in the books of history as the genius mathematician whose thoughts and theories went on to form the basis of modern computing.

In this article, it is my intention to pay particular attention to the events in Turing’s life that firstly led to his passion in the field of mathematics. From his affection for a young childhood friend and the stoking of his passion for maths as a result of the tragic loss of his companion, through to his time at Cambridge, pure mathematics, his 1936 paper (now considered to be a text documenting the founding theory and ideas for modern computing), and of course his contribution towards breaking the German enigma codes, a feat that is widely regarded to have made a significant impact on the war effort and turned the tide in Britain’s favour.

The latter sections of this article will also take a look at the efforts of the codebreakers in general, as well as taking a look at the vital work undertaken at Bletchley Park (aka Station X) and its impact on the war.

### Then and Now: Modern Events: A Pardon for a crime that should never have Been and a Summary of Turing’s lasting Impact

I find it quite remarkable that it took the British government until 2013 to officially pardon Mr Turing for the despicable historical conviction imposed upon him for his homosexuality in the years before his death. That it has taken the ticking over of a century plus an additional 13 years for Turing to be fully recognised and pardoned is absolutely one of the greatest injustices of modern times.

Having been prosecuted in 1952 for homosexual acts under the notorious Criminal Law Amendment Act of 1885, Turing went on to commit suicide in 1954. The power of hindsight allows us to connect the dots between the two events, of course, but the words of Lord Sharkey, who pushed for the statutory amendment bill for the posthumous pardon for Turing, one of Britain’s most brilliant and impactful scientists, have never felt so powerful: “it (now) seemed extraordinary that he had been hounded for his homosexuality, and in the series of events leading to his suicide in 1954”. Sharkey isn’t alone in his admiration for Turing, either, nor was the call for the British nation and its powers to make amends for the 50 years of injustice following Turing’s death was nothing short of necessary.

After all, the impact of Turing’s work on breaking the German Enigma codes alone is worthy of knighthood and lifelong respect from each living person in the free world at the moment. But to boil down the achievements of Turing’s lifetime to that single feat of genius would in itself be an injustice. People often forget that the impact of Turing’s research and his ideas run much deeper, carving out ravines of progress that echo through the decades to the very concept of computing we have today. And that doesn’t even take into account his impact on the mathematics of biology and chaos.

The unjustness of the persecution of Alan Turing only serves to fester in the roaring heat of his lifetime achievements. Even today, the extent of the impact of Turing’s conceptualising of the modern computer – the idea that a simple machine that could be capable of completing complex tasks and running multiple programs - is still being revealed. Turing’s ideas were more than concepts, however. The proof of this lies within the work he carried out that led to the breaking of the German Enigma Codes, his contributions at Bletchley Park. This achievement, for which Turing is probably most known and commended, demonstrates Turing’s application of his work on mathematical and (early) computer theory into practice. It is this application of theory with view to breaking the enigma codes that is discussed below.

### Looming Clouds of War: The first Enigma and the Naval Enigma Problem

Boyle writes of two crucial encounters in *Unlocking the Enigma* that had bearing on his career and on him as a person, a mathematician, and a philosopher. The first was with Ludwig Wittgenstein, an Austrian philosopher that had quite an impact on Turing, frequently challenging him on his logical and mathematical principles; questions we raised about the application of Turing’s logical ideas and theories to the real world. These questions were to impact upon Turing in his work following the war. The second encounter was with the release of Snow White and the Seven Dwarfs, which interestingly garnered attention from other mathematicians such as Godel.

These encounters were significant, but most certainly overshadowed by the clouds of war gathering on the horizon in 1939. By this time, Turing’s name was well-known to the director of the government’s Code and Cipher school, Commander Alastair Denniston. Turing’s real work on the Enigma codes – work that has been the subject of many popular depictions of Turing and Bletchley Park over the years – was to take place soon after the war at sea began.

20 months after the declaration of war on Germany, German submarine U-110was defeated and boarded by the British, and retrieved from within was one of the elusive Enigma Machine. This machine was rushed to Bletchley Park – delivery of codebreaking machines and the corresponding code books were often expedited rapidly to Bletchley park, emphasising the importance of speed in the deciphering of the codes – where Turing, working as a temporary Civil Servant to the Foreign Office Department of Communication, worked on the machine.

Turing’s years at Bletchley park were some of the busiest he would ever encounter in his entire life. Of course he didn’t work alone, but formed part of a wider team. This team consisted of an array of professionals, from fellow mathematicians to linguists and statisticians. Make no mistake about it however: Turing was at the heart of the organisation tasked with the cracking of the Enigma Codes, and therefore instrumental in the war effort of the allies, his breakthroughs having direct consequences for allied land, sea, and naval forces.

**The Enigma and the “Bombe”**

The Enigma machine itself – there were many of these in existence, and the one retrieved from U-110 certainly wasn’t the first to fall into the possession of the allies – looked rather like a typewriter without the space for paper. Breaking the code was no easy task, either; the Enigma machine was once believed to be utterly impenetrable. After all, it was comprised of 3 rotors, which itself results in 17,000 possible combinations for finding a solution to the data coming from them. However, there were 6 ways of arranging these 3 rotors, which compounded the problem further, resulting in a staggering figure of 105, 000 possible solutions.

The possible combinations for the Enigma codes were already being calculated by the Polish. They used a system involving paper with punched holes, utilising lights to shine through the holes until one single light shone right through them. This system, as well as the machine used to facilitate it, was called the “bombe”. The bombe machine and system converged with Turing’s theories and ideas about computing in general.

Turing soon earned himself a nickname at Bletchley Park. He became known as “The Prof” relatively soon after his arrival there. No sooner than the problem of the Enigma codes made itself known did Turing get to work on theorising a solution to the complex problem.

### Turing’s Plans for Breaking the Enigma

The opening weeks of the war saw Turing devise a logical plan to break the Enigma codes. He theorised that the coded Enigma messages were reversible, and therefore could be used to reverse the process of the machine through which they are processed. His theory involved a 2-part solution. The first part involved the use of “Cribs” – pieces of code that were likely translations of the data – with these cribs being deciphered using an improved version of the Polish bombe machine.

The first crib-testing machine was built soon after these plans were devised. The machine itself was massive: 7ft long and 6 ft tall, in fact. It was known as “Victory”, and was shipped to Bletchley Park in an alarmingly non-covert fashion: on the back of a truck. Over 200 of these machines were eventually built in the effort to decipher the Enigma Codes.

These machines formed part of a comprehensive and extremely time-sensitive process. A rhythm of operation was developed. The initial messages were sent to be deciphered for pattern identification. Once the Cribs piled up, they needed to be processed in the machine rooms, with machines stopping when they either found a solution or encountered a problem. The deciphered codes were then translated and interpreted before being sent out. Turing’s and his team’s work on the initial Enigma codes was instrumental in pushing for victory during the Battle of Britain. However, the Battle of the Atlantic was already forming, and with it came a problem that was even more difficult to crack.

### The Problem of the Naval Enigma

The German Naval Enigma was even more difficult to decipher than the previous Enigma codes. The Naval Enigma formed a crucial part of German naval communication, and cracking them was essential for the allies, particularly in the lead-up to and after the commencement of the Battle of the Atlantic.

Previously-captured Enigma materials were instrumental in allowing Turing to develop a solution for cracking these more complex codes. The technique Turing used to eventually decipher the German Enigma Codes as known as Banburismus. Turing’s invention of this deciphering process was instrumental in Hut 8’s effort to decipher the German U-Boat transmissions; it effectively cut down the time it took the bombe machines to work, by positing high likelihoods of the positions of the right-most and centre wheels of the Enigma machine. The work at Hut 8 was crucial, leading to the allies being able to direct their fleets away from the packs of German U-Boats, thus saving thousands of lives and allowing allied advantage in the Battle of the Atlantic. Though not universally successful – German naval communications were indecipherable for a period in 1942 – Turing and his team’s efforts at Hut 8 were crucial in the allied war effort.

Turing’s contributions didn’t stop here, however. In 1942, he continued his work, which led to the development of another deciphering technique, this time a hand-deciphering technique known as Turingery (amusingly dubbed Turingismus by fellow mathematicians). Turingery helped to feed into the work at Bletchley Park that was focused on breaking the German Lorenz Cipher. He was also sent to liaise with the United States codebreakers after they entered the war. He helped the US with their efforts in enlightening them of the bombe machines, as well as furnishing them with knowledge about the Enigma codes and the machines that encrypted the messages. Following his return from the US, Turing furthered his work in cryptanalysis and later developed Delilah, which was a speech-scrambling machine.

### Paradoxical in Personality: The Enigma behind the breaking of the Enigma Codes

To fully appreciate, and indeed understand the motivations of the man behind the breaking of the Enigma codes, one must first comprehend a little about the man himself, namely his personality. In *Alan Turing: Unlocking the Enigma, *David Boyle writes that Turing was a man of paradoxical personality traits, as well as being a mixture of seemingly conflicting characteristics.

As one might expect, Turing was a man of great confidence in his own abilities, and outgoing in a charming and witty fashion when in the company of friends. In the company of strangers, however, he is said to have been much more reserved, shy even, with a certain scepticism about the so-called “specialness” of humankind. Boyle writes of Turing: “he was deeply English in his sheer practicality, for the literalism with which he turned intellectual ideas into practical projects”. In reading all that has been written about Turing, it is also patently obvious that he was influenced greatly by philosophers John Locke and David Hume, with a particular emphasis on the exclusion of all considerations aside from data that can be accurately attained from the senses.

Though a thoroughly logical man, Turing also displayed a fondness for fairy tales and even obsessed by Disney film *Snow White and the Seven Dwarfs*. So one can understand my choice of title for this section: Turing was indeed a man of paradoxes, making him the perfect candidate for the label of “Enigma”, but also unashamed in his logical approach to putting his theories into practise. This latter trait was no doubt a huge factor in his success with breaking the German Enigma codes.

### Formative Years: the making of the Enigma

Understanding where Turing and his theories ended up first requires an understanding of his background. Conceived in Chatrapur, India, to father Julius Turing and mother Sara, Turing was born after his parents returned home by to Paddington in 23rd June, 1912. Turing was said to have been quite a charming child, frequently inventing his own words, such as *Quockling (seagulls fighting over food).* Though clearly a bright child, he initially struggled with reading until he taught himself to do so within three weeks of reading a book called *Reading Without Tears*. It was clear that Turing, from this moment on, would prefer to work out puzzles and problems himself.

One particularly important moment highlighted by biographers of Turing was during his childhood, when he was given a copy of the book *Natural Wonders Every Child Should Know*, which is said to have fuelled his interest in numbers and mathematics from a young age. The book was written by Edwin Tenney Brewster, who himself subscribed to the notion that using the metaphor of a machine allowed for the explanation of the relationship between body and mind. One need only to read the previous sentence to realise that the idea of machine-as-metaphor was one that stayed with Turing, perhaps planting the seed for all of his work in the field of mathematics later in his life.

**Longing, Tragedy, and Obsession**

His parents returned to India, but Turing stayed in St Leonards-on-Sea, where he became increasingly introvert and withdrawn, and a market increase in what his guardians called “bookishness”. His obsession with mathematics was already established, and he was able (due to his mathematical intuition) to solve mathematical problems at school without the need for workings out.

He developed a particularly romantic friendship with a contemporary of his, Christopher Morcom, who was a significant influence on Turing (author David Boyle even suggests that Morcom was the love of Turing’s life). Morcom and Turing both promised each other that they would strive to interpret the world in an intellectual and logical fashion together. However, tragedy struck, as shortly after winning a place at Trinity College, Cambridge, Morcom died as a result of contacting Tuberculosis. It was Turing’s grief resulting from his love’s death that can certainly be attributed to his burning passion for mathematics that only intensified as the years went by. Turing secured a place at King’s College, Cambridge, where his success was undoubtedly motivated by his promise to Morcom, as well as his desire to live up to the intelligence of his erstwhile friend and love.

As a student, Turing is said to have been a rather peculiar character to those who don’t know him. Neurologist Sir Geoffrey Jefferson wrote of Turing: “Alan, as I saw him, made people want to help and protect him though he was rather insulated from human relationships”. He had a stammer, which tended to irritate people, and struggled to meet the gaze of others when in their company.

Turing also forged a number of sexual relationships with some male students, though it was obvious that no other man could take the place of Morcom. Academically. Turing was charging ahead with his studies. It was at Cambridge that Turing also discovered and developed a passion for pure mathematics. His dissertation on group theory was finished in 1934, and at the age of 22, he was elected as a fellow of the college. Hindsight allows us to see that his potential for mathematical genius was by this point somewhat of a certainty; it was the impact of these formative years that allowed Turing to produce and refine his logical and theoretical reasoning, applying them to the field of pure mathematics and, of course, going on to put these theories into practice for the benefit of the allied war effort.