The History of Imaginary Numbers

Once upon a time, in the imaginary land of numbers… Yes, numbers! I bet that would’ve never come to mind. Which brings me to the question: Who thought of them and why? In 50 A.D., Heron of Alexandria studied the volume of an impossible part of a pyramid. He had to find √(81-114) which, back then, was insolvable. Heron soon gave up. For a very long time, negative radicals were simply deemed “impossible”. In the 1500’s, some speculation began to arise again over the square root of negative numbers. Formulas for solving 3rd and 4th degree polynomial equations were discovered and people realized that some work with square roots of negative numbers would occasionally be required. Naturally, they didn’t want to work with that, so they usually didn’t. Finally, in 1545, the first major work with imaginary numbers occurred. In 1545, Girolamo Carding wrote a book titled Ars Magna. He solved the equation x(10-x)=40, finding the answer to be 5 plus or minus √-15. Although he found that this was the answer, he greatly disliked imaginary numbers. He said that work with them would be, “as subtle as it would be useless”, and referred to working with them as “mental torture.” For a while, most people agreed with him. Later, in 1637, Rene Descartes came up with the standard form for complex numbers, which is a+bi. However, he didn’t like complex numbers either. He assumed that if they were involved, you couldn’t solve the problem. Lastly, he came up with the term “imaginary”, although he meant it to be negative. Issac Newton agreed with Descartes, and Albert Girad even went as far as to call these, “solutions impossible”. Although these people didn’t enjoy the thought of imaginary numbers, they couldn’t stop other mathematicians from believing that i might exist. (The History of Complex Numbers)

Rafael Bombelli was a firm believer in imaginary numbers. However, since he couldn’t do anything with them people doubted him. He did understand that i times i should