This famous probability theory was intuitive, even obvious. It was also wrong.
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.
In many of the examples it spat out, they found that a bottom-bunk path was only the tiniest bit more probable than its top-bunk alternative. But the model didn’t uncover any graphs where the reverse was true. There was another problem. Each graph the neural network came up with was still so large that the mathematicians couldn’t possibly investigate every single outcome of the coin-flipping step.
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