In the pantheon of geniuses who contributed to the emergence of the digital age, Alan Turing occupies a singular place, as do Ada Lovelace and Tim Berners-Lee. Born in 1912 in London, this exceptional mathematician established the theoretical foundations of modern computing long before the advent of the first computers. His numerous works on computability (capacity 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 disappearance.
The mathematical foundations of modern computing
The year 1936 marked a pivotal moment in the history of science with the publication of On Computable Numbers by Turing. This founding text responds to the Entscheidungsproblem posed by David Hilbert in 1928 – determining whether any mathematical proposition can be proven or refuted in a systematic way – Turing proposes a brilliant answer due to its conceptual simplicity.
He imagines a theoretical machine, similar to an infinite tape drive, capable of executing elementary instructions: read, write, erase, move. This abstraction, which would later be named “Turing machine”allows you to represent any sequence of calculations, no matter how complex. It’s as if Turing had created a universal score on which any mathematical melody can be written.
At Princeton, under the aegis of Alonzo Church, he deepened his research and established a remarkable bridge between different ways of thinking about calculus. He demonstrates that his theoretical machine and another mathematical approach, Church’s lambda calculus, are in reality two equivalent ways of describing the same calculation possibilities. This unification is comparable to the discovery that two seemingly 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 calculation, thanks to what he called “oracles”. He also developed the fixed-point combiner, a subtle mathematical tool that allows one to describe programs that analyze themselves, foreshadowing certain aspects of modern programming.
These theoretical works, seemingly abstract, in reality constitute the intellectual foundation of modern computing. Every time we use a computer or 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 reality in our modern processors, capable of running any computer program.
Engineering 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 find unlock the secrets of the Enigma machine between 1939 and 1945. This German encryption machine, similar in appearance to a typewriter, uses 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 directly guess the messages, 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, significantly reduces the number of combinations to test.
The “Bomb”, his most remarkable creation, is a true feat of engineering. This electromechanical machine, the size of a cabinet, contains dozens of rotating drums reproducing the operation of Enigma. It automates the search for daily settings used by the Germans, exploiting their procedural errors and certain system weaknesses.
For example, German operators often began their messages with predictable phrases like “ nothing to report » or weather forecasts. By knowing these message beginnings, the cryptanalysts could thus eliminate a large number of possible combinations for the Enigma settings, thereby speeding up the decryption process.
The challenge becomes particularly difficult in the face of German submarines. The Kriegsmarine (naval force of the Third Reich) actually used a more sophisticated version of Enigma, with stricter encryption procedures. Turing then developed specific methods to counter these reinforced defenses. In particular, he invented a system allowing machine settings to be deduced from minimal clues, such as the position of Allied ships or transmission times.
Collaboration with the United States amplifies the impact of these innovations. In Dayton, Ohio, Turing shared his expertise with American cryptanalysts. American industrial power makes it possible to manufacture hundreds of sophisticated “Bombs”. This multiplication of calculation capacities transforms decryption: from an artisanal activity carried out by a few mathematicians, it becomes 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 decrypted messages with other technologies such as ASDIC (Anti-Submarine Detection Investigation Committee) radar and sonar.
This information superiority allowed Allied convoys to avoid dangerous areas and warships to effectively track U-boatsfierce submarines of Nazi Germany. At the end of 1943, Admiral Dönitz, commander of the German submarine fleet, had to recognize the defeat of his “gray wolves” in the North Atlantic.
This success is based on an unprecedented synergy between theoretical mathematics, cutting-edge engineering and military intelligence. Turing’s “Bombs” prefigure modern computers : like them, they solve complex problems by breaking down the work into elementary operations repeated at high speed.
The precursor of artificial intelligence
Freed from the constraints of military secrecy, Turing embarks on an exploration of the frontiers of emerging computing. At the National Physical Laboratory, he designed the ACE between 1945 and 1947 (Automatic Computing Engine), a project that went beyond a simple electronic calculator.
The ACE embodies its vision of a universal machine: the very first programmable computer capable of performing any computable task. This revolutionary design integrates elements that we find in our current computers: rapid 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 Intelligence asks a provocative question: can machines think? Rather than getting lost in metaphysical debates on the nature of consciousness, he proposes an empirical approach that has become famous: the Turing test. The idea is deceptively simple – if a machine can converse indistinguishably from a human, shouldn’t we recognize it as a form of intelligence?
This test, still debated today, anticipates the questions raised today modern conversational assistants and generative artificial intelligence. Turing addresses objections that resonate surprisingly with our contemporary debates: artificial consciousness, machine learning, the limits of imitation. It 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 develops mathematical models to explain how complex patterns (streaks, spirals, spots) emerge in the living world. This work, published in The Chemical Basis of Morphogenesisestablish an unprecedented link between computer science and biology. THE Turing structures that he theorized are still used today in bioinformatics to model the development of organisms.
At the same time, he designed a sophisticated chess program, impossible to run on the computers of the time. His method, which already integrates concepts of position evaluation and tree search, lays 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 the judicial repression of his homosexuality and forced hormonal treatment, brutally deprived science of a rare spirit. The royal pardon granted by Elizabeth II in 2013 alone cannot repair this injustice, but finally recognizes her exceptional contribution to science and her country.
Turing’s intellectual legacy deeply irrigates our time. From compression algorithms in our smartphones to artificial neural networks, his mathematical intuitions have materialized into ubiquitous technologies. His particularly prescient thoughts on artificial intelligence feed into current developments in deep learning and cognitive robotics. Physics had Albert Einstein, computer science, mathematics had Turing; two geniuses who forever changed the face of the world.
- 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 Allied victory.
- A visionary, he explored pioneering concepts in artificial intelligence and mathematical biology, lastingly influencing science and technology.
