How Imaginary Numbers Were Invented

How Giving Up Reality Solved the Cubic Equation

For centuries, a general solution to the cubic equation was considered impossible—until mathematicians embraced complex numbers, abandoning the strict requirement that math reflect physical reality.

References:

• Videos:
  • 500 Years of Not Teaching the Cubic Formula – YouTube
  • Imaginary Numbers are Real – YouTube
• Books and Papers:
  • Dunham, W. (1990). Journey Through Genius: The Great Theorems of Mathematics. Link
  • Toscano, F. (2020). The Secret Formula, Princeton University Press. Link
  • Bochner, S. (1963). The Significance of Some Basic Mathematical Conceptions for Physics, Isis, 54(2), 179–205. Link
  • Muroi, K. (2019). Cubic Equations of Babylonian Mathematics, arXiv:1905.08034. Link
  • Branson, W. (2014). Solving the Cubic with Cardano. Link
  • Rothman, T. (2013). Cardano v Tartaglia: The Great Feud Goes Supernatural, arXiv:1308.2181. Link
  • Siadat, M. V., & Tholen, A. (2021). Omar Khayyam: Geometric Algebra and Cubic Equations, Math Horizons, 28(1), 12–15. Link
  • Merino, O. (2006). A Short History of Complex Numbers, University of Rhode Island. Link
• Historical Works:
  • Cardano, G. (1545). Ars Magna (Dover reprint, 1993). ISBN: 0-486-67811-3
  • Bombelli, R. (1579). L’Algebra. Link
• Software:
  • Manim Community Developers. (2021). Manim – Mathematical Animation Framework (v0.13.1). Link