> One of the earliest and probably the most acrimonious, was that between
> Tartaglia (c. 1499-1557) and Cardano (1501-1576) over the algebraic
> solution of the cubic. Archimedes had produced a geometric solution in
> his work 'On the sphere and cylinder' and there is little doubt that
> Tartaglia was familiar with this work. But Tartaglia certainly
> independently found an algebraic solution about 1535.
I think the methods used by Tartaglia and his competitors to solve the
cubic equation or better certain types of it had nothing to do with
Archimedes' solution of the cubic problem in 'On the sphere and cylinder'.
There is no question that there was a dispute between Tartaglia and
Cardano, but no priority dispute, since the question who had contributed
when and what to the algebraic solution of types of the cubic equation had
been settled in this dispute from the very beginning.
> Tartaglia was furious, not only for moral and intellectual reasons, but
> also because there were material gains associated with being the sole
> possessor of mathematical knowledge. He published diatribes about
> Cardano's perfidy, and tried to challenge him to mathematical contests.
> Cardano remained above the fray, sending his pupil Ferrari instead. The
> latter defeated Tartaglia, who died an embittered man.
I agree with "furious", "moral" and "economical" for the "material gains"
mentioned but I would skip "intellectual".
Ivo Schneider