Date: 
Wednesday, May 4, 2022 
Speaker: 
Prof. Daniel Curtin
Dept. of Mathematics
Northern Kentucky University
Email: danieljcurtin42 AT gmail DOT com

Title:

"A minus times a minus is minus", says Cardano. Why?

Abstract: 
Girolamo Cardano (15011576) was the most famous physician of his day, and also probably the greatest mathematician. In his Ars Magnaa, he laid out the solution for cubic and quartic equations, thus solving problems that had eluded the great mathematicians of the Islamic world. It thus comes as a bit of a shock that, late in life, he published two different articles, asserting that, contrary to the common usage, a minus times a minus should be a minus, not a plus. In all his previous works, he had taken the product to be positive. Why this turnabout? Pursuing this question, we will see Cardano considering the meaning of negative solutions to equations. Perhaps most importantly, we see him grappling with the fact that his solution to cubic equations can lead to expressions involving negative numbers under the square root, even in cases where the answer is in fact a real number, or an integer. Thus, from our point of view, he is attempting to understand the meaning of the concept of negative number.

