Much of mathematics is driven by intuition, by a deep-rooted sense of what should be true. But sometimes instinct can lead a mathematician astray. Early evidence might not represent the bigger picture; a statement might seem obvious, only for some hidden subtlety to reveal itself.

Unexpectedly, three mathematicians have now shown that a well-known hypothesis in probability theory called the bunkbed conjecture falls into this category. The conjecture — which is about the different ways you can navigate the mathematical mazes called graphs when they’re stacked on top of each other like bunk beds — seemed natural, even self-evident. “Anything our brain tells us suggests the conjecture should be true,” said Maria Chudnovsky(opens a new tab), a graph theorist at Princeton University who was not involved in the new work.

But they were wrong. Last month, a trio of mathematicians announced a counterexample(opens a new tab), disproving the conjecture. The result offers fresh guidance on how to approach related problems in physics about properties of solid materials. But it also taps into deeper questions about how mathematics works. A lot of mathematical effort is spent trying to prove conjectures true. It’s lonelier to try to pull them apart. The team behind the new work failed many times before they finally found their counterexample. Their story suggests that mathematicians may need to question their assumptions more often.

...read more at quantamagazine.org