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In the pantheon of geniuses who contributed to the emergence of the digital age, Alan Turing occupies a singular place, just like Ada Lovelace and Tim Berners-Lee. Born in 1912 in London, this mathematician exceptionally established the theoretical foundations of modern computinglong before the advent of the first computers. His extensive work on computability (the ability of a problem to be solved by a machine following a finite set of precise instructions) and artificial intelligence continue to influence our world, more than 70 years after his death.
Alan Turing, photographed in 1936 at Princeton University. © Unknown photographer/Wikipedia
The mathematical foundations of modern computing
The year 1936 marks a pivotal moment in the history of science with the publication of On Computable Numbers by Turing. This seminal text responds to the Entscheidungsproblem posed by David Hilbert in 1928 – to determine whether any mathematical proposition can be systematically proven or refuted – Turing offers a brilliant answer in its conceptual simplicity.
He imagines a theoretical machine, similar to an infinite tape reader, capable of executing elementary instructions: read, write, erase, move. This abstraction, which will later be called the “Turing machine”, makes it possible to represent any sequence of calculations, no matter how complex. It's as if Turing had created a universal score on which one can write any mathematical melody.
At Princeton, under the guidance of Alonzo Church, he furthered his research and established a remarkable bridge between different ways of thinking about computation. He demonstrated that his theoretical machine and another mathematical approach, Church's lambda calculus, are in reality two equivalent ways of describing the same computational possibilities. This unification is comparable to the discovery that two apparently different languages can express exactly the same ideas.
Turing introduced the concept of hypercomputing, imagining machines capable of solving problems beyond the limits of ordinary computing, thanks to what he called “oracles”. He also developed the fixed-point combinator, a subtle mathematical tool that allows the description of programs that analyze themselves, prefiguring certain aspects of modern programming.
These theoretical works, seemingly abstract, actually constitute the intellectual foundation of modern computing. Every time we use a computer or a smartphone, we unknowingly manipulate the heirs of this original Turing machine. His vision of a universal machine capable of simulating any other machine has become a reality in our modern processors, capable of running any computer program.
The Genius in the Service of Military Intelligence
At Bletchley Park, a Victorian mansion transformed into the nerve center of British intelligence, Turing, surrounded by a team of brilliant mathematicians, linguists, and cryptologists, leads a race against time to unlock the secrets of the Enigma machine between 1939 and 1945. This German cipher machine, similar in appearance to a typewriter, used a complex system of rotors to transform each letter into another, creating codes considered unbreakable by the Nazis.
Turing's approach then turned traditional decryption methods upside down. Instead of trying to guess the messages directly, he developed a systematic mathematical method. The “Banburismus”, which he invented, is based on the statistical analysis of the frequencies of appearance of letters and probable words. This technique, named after the town of Banbury where the analysis sheets were printed,allows to considerably reduce the number of combinations to be tested.
The “Bombe”, his most remarkable creation, is a true feat of engineering. This electromechanical machine, as big as a cupboard, contains dozens of rotating drums reproducing the operation of Enigma. It automates the search for the daily settings used by the Germans, exploiting their procedural errors and certain weaknesses in the system.
For example, German operators often began their messages with predictable formulas such as ” nothing to report ” or weather forecasts. By knowing these message beginnings, cryptanalysts could eliminate a large number of possible combinations for Enigma settings, thus speeding up the decryption process.
A replica of the Bomb, on display at the Bletchley Park museum. © Maksim/Wikipedia
200% Deposit Bonus up to €3,000 180% First Deposit Bonus up to $20,000The challenge becomes particularly difficult when faced with German submarines. The Kriegsmarine (naval force of the Third Reich) used a more sophisticated version of Enigma, with procedures for stricter encryption. Turing then developed specific methods to counter these strengthened defenses. In particular, he invented a system for deducing machine settings from minimal clues, such as the position of allied ships or transmission times.
Collaboration with the United States amplified the impact of these innovations. In Dayton, Ohio, Turing shared his expertise with American cryptanalysts. American industrial power made it possible to manufacture hundreds of advanced “Bombes”. This multiplication of computing capacities transformed decryption: from an artisanal activity carried out by a few mathematicians, it became an industrial operation capable of processing thousands of messages per day.
The consequences were spectacular in the Battle of the Atlantic. The Allies could now locate German submarines with formidable precision, combining the decrypted messages with other technologies such as radar and ASDIC (Anti-Submarine Detection Investigation Committee) sonar.
This information superiority allowed Allied convoys to avoid dangerous areas and warships to effectively track down U-boats, Nazi Germany's ferocious submarines. At the end of 1943, Admiral Dönitz, commander of the German submarine fleet, had to admit defeat to his “Grey Wolves” in the North Atlantic.
This success was based on an unprecedented synergy between theoretical mathematics, cutting-edge engineering and military intelligence. The “Bombs” Turing's prefigure modern computers: like them, they solve complex problems by breaking down work into elementary operations repeated at high speed.
The precursor of artificial intelligence
Freed from the constraints of military secrecy, Turingembarks on an exploration of the frontiers of nascent computing. At the National Physical Laboratory, he designs the ACE between 1945 and 1947 (Automatic Computing Engine), a project that goes beyond the simple electronic calculator.
The ACE embodies his vision of a universal machine: the very first programmable computer capable of performing any computable task. This revolutionary design incorporated elements that we find in our current computers: fast-access memory, stored instructions, parallel data processing.
In 1950, Turing published in the journal Mind an article on the border between philosophy and technology. Computing Machinery and Intelligenceasks a provocative question: Can machines think?? Rather than getting lost in metaphysical debates about the nature of consciousness, he proposes a now famous empirical approach: the Turing test. The idea is deceptively simple – if a machine can converse indistinguishably from a human, shouldn’t we recognize a form of intelligence in it??
This test, still debated today, anticipates the questions raised today by modern conversational assistants and generative artificial intelligence. Turing addresses objections that resonate surprisingly well with our contemporary debates: artificial consciousness, machine learning, the limits of imitation. He even suggests the possibility of computers that learn like children, an idea that deep learning is currently exploring.
In his later years, Turing turned to mathematical biology, particularly morphogenesis – the study of shapes in nature. He developed mathematical models to explain how complex patterns (stripes, spirals, spots) emerge in the living world. This work, published in The Chemical Basis of Morphogenesis, established a new link between computer science and biology. The Turing structures that he theorizedare still used today in bioinformatics to model the development of organisms.
At the same time, he designed a sophisticated chess program that was impossible to run on the computers of the time. His method, which already incorporated concepts of position evaluation and tree search, laid the foundations of modern machine learning. In May 1952, he manually simulated his program, taking half an hour to calculate each move – an early demonstration of the possibilities of artificial intelligence.
His tragic end in 1954 (Turing died of cyanide poisoning), following judicial repression of his homosexuality and forced hormone treatment, brutally deprived science of a rare mind. The royal pardon granted by Elizabeth II in 2013 alone cannot repair this injustice, but finally recognizes his exceptional contribution to science and to his country.
Turing's intellectual legacy deeply irrigates our era. From compression algorithms in our smartphones to artificial neural networks, his mathematical intuitions have materialized into ubiquitous technologies. His reflections on artificial intelligence, particularly prescient, feed current developments in deep learning and cognitive robotics. Physics had Albert Einstein, computer science, mathematics had Turing; two geniuses who changed the face of the world forever.
- Alan Turing laid the foundations of modern computing by conceptualizing a universal machine capable of solving all calculations.
- During World War II, he revolutionized codebreaking with mathematical methods and electromechanical machines that accelerated the Allied victory.
- A visionary, he explored pioneering concepts in artificial intelligence and mathematical biology, lastingly influencing science and technology.
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