Back in school I didn’t understand that mathematics isn’t a bunch of static, objective “facts.” Rather, mathematicians work out their ideas in conversation with each other, and invent new concepts in the process. The manuscript you are looking at here was one of the most important math texts in history. Its author, Gerolamo Cardano, thought so too.
Written in 1545, the _Ars Magna_ (originally _Artis magnae, sive de regulus algebraicis liber unus_) was really the start of a comprehensive theory for solving algebraic equations. In it, Cardano gave credit to Italians who had contributed some of the ideas (who themselves had borrowed from earlier scholars). But Cardano moved the knowledge of math forward in _Ars Magna_. In it, he gave an algebraic solution to cubic and quartic equations, and he discussed the concept of multiple roots.
The _Ars Magna_ was the first place imaginary numbers got invented. It was a real intellectual leap, because they aren’t in the number line. Remember, an imaginary number one with a negative when it is squared. Cardano called them “sophistic” in that they were not grounded in physical meaning. He wrote about them with the aside “dismissis incruciationibus” or “putting aside mental tortures,” because on one level they made no sense to him.
But imaginary numbers ended up having real-life applications. In the fields of electronics, radar, and brain wave studies they are used — any time a sine or cosine wave function is used. What started out as an abstract mental exercise eventually ended up truly shaping the physical world.
Source(s): Also _Veritasium_ “How imaginary numbers were invented” @veritasium. Mathatical Association of America (maa.org) “Mathematical Treasure: Cardano’s Ars Magna” by Cynthia J. Huffman. Wikipedia.
