Mathematics of the Italian Renaissance MAT 112-16 Summer 2011 Prof. Douglas Furman – Mathematics Dept. SUNY Ulster – International Programs Gambling, Betrayal & Murder: Cardano & The Italian Algebraists
The Italian algebraists of the Renaissance were able to accomplish what had eluded humanity for over three millenia!
Campaigns to be rector of the students, though he is not well liked.
“ This I recognize as unique and outstanding amongst my faults - the habit, which I persist in, of preferring to say above all things what I know to be displeasing to the ears of my hearers. I am aware of this, yet I keep it up willfully, in no way ignorant of how many enemies it makes for me.”
Recall in 1539 Tartaglia had refused Cardano’s request for the solution to the cubic.
Cardano mentions that he has been discussing Tartaglia’s ingenuity with the Governor of Milan
Tartaglia leaves Venice to visit Cardano in Milan…
Eventually Tartaglia shares his solution in the form of a poem and Cardano swears to keep it secret.
“ I swear to you, by God's holy Gospels, and as a true man of honour, not only never to publish your discoveries, if you teach me them, but I also promise you, and I pledge my faith as a true Christian, to note them down in code, so that after my death no one will be able to understand them.”
With Tartaglia’s solution to a depressed cubic, Cardano & Ferrari work for six years and discover methods to solve all the other cases of cubic equations, thus, in essence, they have discovered a general solution!
But the other cases hinge in the depressed cubic
x 3 + m x = n.
Cardano wants to publish his historic “discoveries” but is prevented by his oath to Tartaglia!