Numbers thought to have no analogue in the real world have meaning at quantum scales. When you purchase through links on our site, we may earn an affiliate commission. Here’s how it works.

Mathematicians were disturbed, centuries ago, to find that calculating the properties of certain curves demanded the seemingly impossible: numbers that, when multiplied by themselves, turn negative.

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William Ross does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their ...