In May 1926, a thirteen-year-old boy set off from Southampton on his bicycle, heading towards the rolling hills of Dorset and his new school. The General Strike had disrupted transport, so he cycled the more than sixty miles to Sherborne School. His name was Alan Turing, and his mathematical ideas would help shape the world we live in today.
But what can we learn from him that might inspire us to follow his example?
Much has been written about Alan Turing: his life, his mathematics, his work at Bletchley Park, the birth of the computer and his ideas about artificial intelligence. Yet another story deserves our attention: how he tackled problems when he did not know the answer. Again and again, he stripped away unnecessary complications, looked at problems from a fresh angle and found simple ideas that revealed something others had missed.
By looking at how Turing approached the problems he worked on, we can discover five steps that anyone can use.
1. Question the problem
Before trying to solve a problem, ask whether you are looking at it in the right way. Could you frame it differently? Are you making assumptions that you do not need to make?
Turing’s work on computation began with a straightforward question: What does it mean to calculate?
Rather than starting with existing calculating machines, he imagined a person following a set of instructions, step by step. He asked how this process could be described in a simple, precise way. From this idea, he developed what became known as the Turing machine, a mathematical model that helped him investigate fundamental problems in logic and computation.
He took a similar approach to artificial intelligence. The question Can a machine think? is difficult to answer without first deciding what we mean by think. Turing suggested a different question: could a machine hold a conversation so convincingly that we could not reliably tell it apart from a human? This gave researchers a more practical way to explore the question.
Sometimes, the first step towards solving a problem is to ask a better question.
2. Simplify
Once you have questioned the problem, look for its essentials. Ask yourself: What is the simplest explanation that could work?
Turing applied this approach to biology. Living organisms are enormously complicated. Their cells contain countless interacting processes involving genes, proteins and chemical reactions. Rather than trying to explain everything at once, Turing asked a simpler question: Could a small number of basic processes explain how patterns develop in living things?
He developed mathematical equations to describe how chemicals react and spread through a substance. His work showed how these simple processes could interact to produce patterns across a much larger area.
The lesson is important. You do not always need to understand every detail of a complicated problem before you can begin to understand how it works. Sometimes, finding the right simple model is the key to making progress.
3. Explore possibilities
Do not dismiss an idea simply because it seems unlikely. Explore it. Ask what would happen if it were true.
Turing’s work on biological patterns provides a striking example. We might expect an orderly pattern to need something to organise it, like a gardener arranging plants in a flower bed. Turing showed mathematically how patterns could arise through the interaction of chemicals, without an external organiser laying them out.
This was a surprising idea. The chemicals did not need to follow a plan for a pattern to emerge. Their interactions could produce one.
When faced with a difficult problem, do not assume that something is impossible just because you cannot yet see how it could happen. Explore the possibility, work out its consequences and see where the reasoning leads.
4. Persist
Some problems cannot be solved at the first attempt. When one approach fails, look for another. Be prepared to change your thinking and try again.
Turing’s work on Enigma, the German cipher machine used during the Second World War, shows why persistence matters. Enigma could produce an enormous number of possible settings, making it impractical to test every possibility one by one.
Turing and his colleagues at Bletchley Park looked for clues and mathematical patterns that could help eliminate possibilities and narrow the search. Their work helped them find ways through a problem that had seemed impossibly difficult.
Persistence does not mean repeating the same action and hoping for a different result. It means continuing to work on a problem, learning from what fails and looking for a better approach.
5. Make it work
Finally, put your ideas into practice. A solution is not necessarily complete just because it looks convincing on paper. You need to find out whether it works.
Turing combined abstract mathematical thinking with practical problem-solving. His work at Bletchley Park helped turn mathematical ideas into methods that could be used to break German codes. His ideas about computation also helped lay the foundations for the computers we use today.
This lesson matters particularly in the age of artificial intelligence. An AI system can produce an answer that sounds convincing. But sounding convincing does not prove that the answer is correct. We still need to test ideas, examine the evidence and find out whether they work in practice.
Understanding an idea is important. Putting it to the test is equally important.
In 1926, Alan Turing set off on his bicycle for a school in Dorset. He could not have known what he would go on to achieve. His importance lies not only in his mathematical discoveries, but also in the way he approached problems.
He questioned what others took for granted. He stripped complicated problems back to their essentials. He explored ideas that seemed unlikely, persisted when answers were hard to find and put his ideas to the test.
These are not skills reserved for great mathematicians. They are skills we can all develop.
The next time you face a difficult problem, whether at school, at home or with something you want to achieve, try asking a different question. Look for a simpler explanation. Explore possibilities, keep going when your first attempt fails and test whether your ideas work.
You don’t have to be Alan Turing to solve problems like Alan Turing.