Re: [HM] Earliest priority dispute?
llusk@ccmail.gc.cc.fl.us
Tue, 25 May 99 11:31:18 -0600
First Prof. Lueneburg wrote:
> TARTAGLIA says that Cardano had sworn not to publish the result.
> This is in his Quesiti. But Lodovico Ferrari, apostrophied by
> Tartaglia as "il suo creato", says in his second Cartello di sfida
> that he was also present in the house of Cardano in Milan when
> Cardano and Tartaglia were talking to each other and that
> Tartaglia were telling lies. So it is not clear whether Cardano
> ever swore an oath. Ferrari also mentions in this cartello that he
> and Cardano went to Bologna where they saw a note book of Ferro's
> with the solution of the equation of the first type. And, after
> all, the result is one that must be made public, it has to be
> known by all mathematicians. Cardano has no right to withhold it.
> Moreover, Cardano had the solution for all types of cubic
> equations, no exceptions. .....
> Did Cardano swear an oath? We shall never know, I think.
Then Arturo Mena replied:
>> Quite clear, I believe.
>> Just one more question: Anyhow, Ferrari was a disciple of Cardano,
>> and there are reports that he (Ludovico) was, since fourteen years
>> old, a servant in Cardano's house. Do you think that his testimony
>> may have been biased?
Prof. Lueneburg, I assume, is referring to Ferrari's second letter
which was sent to Tartaglia on 1 April, 1547, which is known in the US
as "April Fool's Day." (Little pun intended.) He (Ferrari) claims to
have been present in Cardano's house when Tartaglia gave Cardano his
'inventiunculam', and as Prof. Lueneburg states, that no promises were
made, and, in effect or by implication, the gift was in return for
Cardano's hospitality. (Must have been a wonderful evening.)
As Arturo Mena points out, in assessing the value of this statement
one must not forget of Ferrari's strong partisanship towards Cardano.
In fact, in this same second letter he speaks of Cardano as "one whom
I owe everything."
Cardano and Ferrari are said to have later discovered the same or a
very similar formula in the hand-writing of Scipione del Ferro, the
man who had first made the breakthrough. And so, in this infamous
second letter, Ferrari accuses Tartaglia of having passed on to
Cardano as his own discovery the discovery of another. (Ferro's long
lost discovery is said to have returned to light some years ago by
Ettore Bortolotti - see page xix footnote 27 of Richard Witmer's
translation of Ars Magna.)
Cardano plays up the importance of, and gives credit to, Tartaglia's
revelation of the formula for solving the cases of the x^3 + ax = N
type. The praise is repeated often his works, but so much so one could
get the sense it might be written by the hand of guilt.
In any event, it is not hard to understand how Tartaglia felt. He
claims he wanted to and intended to work out all ramifications of his
discovery and have it published under his own name. Couple this with
Ferrari's remarks to Tartaglia, which were to the effect that Cardano
had saved Tartaglia's 'little discovery' from oblivion, planted it in
a rich garden, nutured it, expanded on it, and possibly made the name
of Tartaglia famous when he exclaimed that if it was not for his
(Tartaglia's) contributions, Cardano's garden would have remained a
forgotten woodlot.
In all it may be incorrect to speak of any of the principals (del
Ferro, Cardano, Tartaglia) as the discoverer of 'the' solution for
'the' cubic since none actually brought their results into the form of
a single formula.
History will eventually determine who the spoils belong to, and then,
as she often does, change her mind and reverse the decision. I think
what we need is a good mathematical psychologist to give us a new
slant on these folks.
I think I should stop as I've said more than my fair share.
Leo Andrew McCreary Lusk