John Von Neumann and the Mathematician's Trap

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John Von Neumann and the Mathematician's Trap

Summary

The article recounts a famous anecdote about the legendary mathematician John von Neumann to illustrate how even brilliant experts can become trapped by their own habits of thinking. In the classic puzzle, two trains travel toward each other while a fly repeatedly flies back and forth between them until they collide. Most mathematicians instinctively solve the problem by calculating an infinite series of distances, but there is a far simpler approach: determine the time until the trains meet and multiply it by the fly’s speed. 

The surprise is that von Neumann produced the correct answer almost instantly, yet not by using the shortcut. When asked how he avoided the “mathematician’s trap,” he replied, “By infinite series, of course!” The story highlights von Neumann’s extraordinary mental abilities, showing that he could compute the complex infinite series in just a few seconds. More broadly, the article emphasizes that expertise can sometimes encourage unnecessarily complicated thinking, while creative problem-solving often comes from stepping back and looking for a simpler perspective. 

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