TLDR: In the Rennaissance Italy, Maths Duels were a thing. (Mathematicians would be challange eachother to maths duels, their pride and honor on thr line.)
Antonio Fior was thaught by Scopione del Ferro (who also was Da Vinci’s teacher) how to solve the cubic equation. Del Ferro never published his discovery, because he needed it as a trump card, should he be challanged to a duel.
With this trump card in hands Fior challanged Tartaglia to a duel.
Fior failed misserably as he could not solve a single problem Tartaglia had given him, while Tartaglia himself had come up with a solution for the cubic equation and solved every single problem Fior had given him.
It’s better than that. Tartaglia won becuase he discovered imaginary numbers. At this time, mathematicians were called Geometers because they used geometry to solve complex math problems instead of directly working with the numbers themselves, and a huge number of cubic equations can’t be solved geometrically without producing squares with negative areas. del Ferro discovered a solution for the depressed cubic, which is an equation with no squared variable (ax³+bx+c) and as a result do not create squares with negative areas when solved geometrically. Tartaglia found that if you just deal with the weird negative areas, usually they just factor out at the end and there’s no problem.
TLDR: In the Rennaissance Italy, Maths Duels were a thing. (Mathematicians would be challange eachother to maths duels, their pride and honor on thr line.) Antonio Fior was thaught by Scopione del Ferro (who also was Da Vinci’s teacher) how to solve the cubic equation. Del Ferro never published his discovery, because he needed it as a trump card, should he be challanged to a duel. With this trump card in hands Fior challanged Tartaglia to a duel. Fior failed misserably as he could not solve a single problem Tartaglia had given him, while Tartaglia himself had come up with a solution for the cubic equation and solved every single problem Fior had given him.
It’s better than that. Tartaglia won becuase he discovered imaginary numbers. At this time, mathematicians were called Geometers because they used geometry to solve complex math problems instead of directly working with the numbers themselves, and a huge number of cubic equations can’t be solved geometrically without producing squares with negative areas. del Ferro discovered a solution for the depressed cubic, which is an equation with no squared variable (ax³+bx+c) and as a result do not create squares with negative areas when solved geometrically. Tartaglia found that if you just deal with the weird negative areas, usually they just factor out at the end and there’s no problem.