Hacker News Reader

We didn't invent 'i' to "solve sqrt(-1)". This is an extremely common misconception about maths and how it progressed that unfortunately people get led into believing by lazy teachers every day

View on HN

So what did happen?

Square roots of negative numbers came up when solving cubic equations, even if the final solutions were all real. This meant the square root of a negative number was not something nonsensical the way you might claim for x^2 = -1, but actually...real in some sense.

Specifically I believe it involved a geometric construction for solving the cubics, which in some cases could not find a solution unless you allowed a square with "negative area".

There's a good YouTube video on it that includes an epic math battle.

Veritasium - How Imaginary Numbers Were Invented - https://youtu.be/cUzklzVXJwo

Solving the cubic was a physical thing back then. https://www.maa.org/press/periodicals/convergence/solving-th...

Reply on news.ycombinator.com