## Math Basics## All About Numbers |

## Who first came up with the idea of imaginary numbers? |

The origin of *i* is difficult to trace. Some historians give credit to Italian physician and mathematician Girolamo Cardano (1501-1576; in English, known as Jerome Cardan). In 1545, he is said to have started modern mathematics, first mentioning not only negative numbers but imaginary numbers in his Latin treatise, *Ars Magna (The Great Art).* But Cardano did not consider the imaginary numbers as the real mathematical objects we do today. To him, they were merely convenient “fiction” to classify certain polynomial properties, describing how their roots would behave when he pretended they even *had* roots.

Most agree that around 1777, Swiss mathematician Leonhard Euler (1707–1783) used “i” and “-i” (negative i) for the two different square roots of -1, thus eliminating some of the problems associated with notation when putting polynomials into categories. (He is also credited with originating the notation *a + bi* for complex numbers.) Much to the consternation of many past and present mathematicians, *i* and *-i* were called “imaginary,” mainly because the number’s function at the time of Euler was not clearly understood. When German mathematician, physicist, and astronomer Johann Friedrich Carl Gauss (1777–1855) used them for the geometric interpretation of complex numbers as points in a plane, the usefulness of imaginary numbers became apparent. (For more information or Gauss, Cardano, and Euler, see “History of Mathematics.”)