Alan Turing – a Visionary Mathematician

Alan Turing – a Visionary Mathematician
The British mathematician and scientist Alan Turing died 70 years ago. Many people worldwide associate him with the decoding of Enigma in Bletchley Park northwest of London during World War II. In doing so, Turing helped shorten the war and indirectly saved the lives of many people. In addition, many are aware of his tragic suicide – after being forced to undergo cruel hormone treatment due to his homosexuality, triggering depression – thanks to the film “The Imitation Game”. However, his immense contribution to computer science, his visionary findings on artificial intelligence and not least his research in the field of theoretical biology are less well known.

For many of our colleagues all over the world and for me personally, Turing is among the most ingenious scientists of the 20th century. To this very day, his research forms the basis for inventions that not only influence our everyday work at our company, but also the lives of millions of people. 

The Turing machine sparks the computer revolution
Named after its inventor, the Turing machine is the theoretical foundation for the development of modern computers and triggered a computer revolution that in principle continues to this day and some say is even accelerating. With this, Turing proved that a simple, symbolic machine can perform every computable function. This also led to the realization that hardware and software should be viewed in isolation from each other. The design of the Turing machine, with an infinite tape and a head for reading and writing, inspired the computer architecture that is still used today with memory, processor and a sequence of instructions. His ideas advanced the development of logic and memory chips and thus also drove the need for highly innovative materials to manufacture the ever more complex hardware – for the development of which Merck KGaA, Darmstadt, Germany is now known worldwide.

The Turing test pointed the way forward for AI research
Turing was also one of the pioneers of artificial intelligence. In his 1950 essay “Computing Machinery and Intelligence”, he describes a method for testing whether a machine can show intelligent behavior and communicate in a similar way to a human. Like the Turing machine, the Turing test sparked a paradigm shift in the research and understanding of artificial intelligence. Turing’s ideas spurred the field of AI research to develop ever more complex systems that could imitate human behavior and thought. As such, the Turing test shifted the focus from an abstract definition of intelligence to observable behavior. Even modern AI assistants such as Siri, Alexa and ChatGPT essentially try to pass a variant of the Turing test in their interactions with humans. In this way, Turing gave AI research a new direction and a clear goal.

With the Turing patterns, the mathematical genius also helped us understand patterns in biology and beyond
The Turing patterns are lesser known than the Turing machine and Turing test. The British scientist was a universally talented mathematician who utilized his genius in mathematics to research various fields, including early developments in mathematical biology. In his 1952 paper “The Chemical Basis of Morphogenesis”, he developed a model for how systems such as diffusion and chemical reaction can produce patterns. In simple terms, two substances react with each other: One activates pattern formation, while the other inhibits it. This interplay results in stable and repetitive patterns, similar to the stripes or spots we also see in the natural world. Underscoring the broad applicability of Turing’s concepts, this interplay is alsoimportant for semiconductor processing materials. For instance, in its directed self-assembly technology Merck KGaA, Darmstadt, Germany uses block copolymers, which make up structures independently due precisely to activation over short distances and inhibition over long distances. This interplay leads to the formation of regular nanoscale patterns. We control these patterns by adapting the block lengths, the composition and the processing conditions. By also using an underlayer, we are creating what are currently the most technologically advanced patterns for semiconductors.

The halting problem recognizes the limits of computability
It often drives students to despair, but many mathematicians and computer scientists see Turing’s calculations on the halting problem as a work of genius. To this end, Turing asked whether an algorithm exists that can decide whether, based on any Turing machine and input, the machine will stop at some point or will continue to run forever. According to Turing, this problem is undecidable: No general algorithm exists that can predict this correctly. As such, the mathematician proved that there are limits of computability and that not all mathematical problems can be solved using algorithms, regardless of how much or how powerful hardware one throws at it.

Turing’s genius was not sufficiently acknowledged

In 1950, Alan Turing wrote: “We can only see a short distance ahead, but we can see plenty there that needs to be done.” Today we know that Turing could see much further ahead. Whether the Turing machine, Turing test, Turing pattern or halting problem – his visionary findings still influence important technologies such as artificial intelligence or semiconductors some 70 years after his death. His ingenuity and scientific achievements were acknowledged too late and too little. In part due to his introverted nature and the fact that he lived his life away from the limelight, Turing isn’t mentioned in the same breath as the geniuses of the 20th century even today. But he has surely earned it.