> As Avinoam Mann reminds us, mathematicians (like other humans) are not
> above petty disputes over priority. And that raises the question: What
> is the earliest such dispute on record? (I'm not referring to disputes
> among *historians* over who deserves credit for discovering particular
> results, but disputes among the principals themselves.)
>
In the prefatory letter to Book I of the CONICA, Apollonius says
that "The third book contains many incredible theorems of use for the
construction of solid loci and for limits of possibility (tous
diorismous) of which the greatest part and the most beautiful are new
(xsena). And when we had grasped these, we knew that the three-line and
four-line locus had not been constructed by Euclid, but only a chance
part of it and that not felicitously. For it was not possible for this
construction to be completed without the additional things found by us."
About this, Pappus says "[Apollonius] was able to add the missing
part to the locus because he had Euclid's writings on the locus already
before him in his mind, and he had studied for a long time in Alexandria
under the people who had been taught by Euclid, where he also acquired
this so great condition (of mind), which was not without defect.
"The locus on three and four lines that he [Apollonius] boasts of
having augmented instead of acknowledging his indebtedness to the first
to have written on it, went like this..." (Hultsch 678, A. Jones'
transl.).
In the sentence following his remarks about the third book,
Apollonius claims that "The fourth book shows in how many ways the
sections of a cone intersect with each other and with the circumference
of a circle, and contains other things in addition none of which has
been written up by our predecessors, that is in how many points the
section of a cone or the circumference of a circle and the opposite
branches meet the opposite branches." And in the preface to the fourth
book, Apollonius elaborates and says "Conon of Samos presented the first
mentioned [question] to Thrasydaeus without giving a correct
demonstration, for which he was rightly attacked by Nicoteles of
Cyrene. As for the second [question], Nicoteles, in replying to Conon,
only mentions that it can be demonstrated, but I have found no
demonstration either by him or by anyone else. Regarding the third and
similar [questions] [namely, in how many points opposite sections can
meet one another], however, I have not found them even noticed by
anyone. And all these things just spoken of, whose [demonstrations] I
have not found anywhere, require many and various striking theorems, of
which most happen to be presented in the first three books [of my
treatise on conic sections], and the rest in this book."
I suppose these examples from Apollonius could be taken as "disputes
over priority." They show, at least, a *concern* over priority.
Michael N. Fried