Reprinted with permission from Quanta Magazine‘s Abstractions blog.
In math, sometimes the most common things are the hardest to find.Photograph by Vladyslav Danilin / Shutterstock
The first time I heard a mathematician use the phrase, I was sure he’d misspoken. We were on the phone, talking about the search for shapes with certain properties, and he said, “It’s like looking for hay in a haystack.”
“Don’t you mean a needle?” I almost interjected. Then he said it again.
In mathematics, it turns out, conventional modes of thought sometimes get turned on their head. The mathematician I was speaking with, Dave Jensen of the University of Kentucky, really did mean “hay in a haystack.” By it, he was expressing a strange fact about mathematical research: Sometimes the most common things are the hardest to find.
“In many areas of mathematics you’re looking for examples of something, and examples are really abundant, but somehow any time you try to write down an example, you get it wrong,” said Jensen.
The hay-in-a-haystack phenomenon is at work in one of the first objects that kids encounter in mathematics: the number line. Points on the number line include the positive and negative integers (such as 2 and –29), rational numbers…
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