Re: [HM] The Rainbow of Mathematics
Prof. Peter Schreiber (schreibe@rz.uni-greifswald.de)
Thu, 19 Nov 1998 12:37:48 MET
I return to Ivor Grattan-Guinness' two ways of producing history of
mathematics, "How we arrived in the present situation" or "What really
happened in the past". Of course, the second way is more interesting
for pure historians and seemingly a better and higher aim. But:
1. Most customers of the history of mathematics are not professional
historians but working mathemticians or teachers, and they have in
general only a need for answers to the first question.
2. Most people searching in history want to find arguments for opinions
and theses they have before the begin of the search. The answers we
can get from history, allways depend on the questions, and history
in the whole is too much and too complicated to give answers in advance
for all possible questions.
3. It is very difficult to find out what really happened in history.
Nobody can know all matters. Grattan-Guinness tries to realize some
of his aim in his rainbow-book, but even he is not defensed against
mistakes and errors. E.g. he makes a list of adherents of Newton and
Leibniz and in the list of Leibniz'adherents is Tschirnhaus. But
unless Tschirnhaus was in strong connection with Leibniz and for
some time there may have been a friendship, Tschirnhaus was a
consequent enemy of infinitesimals, like his "god" Descartes, and
in so far belongs not to the soldiers of Leibniz.
In a true history of what really happened I should like to read such
things as what J. J. Scaliger replied against the criticism of his
quadrature of the circle by Vieta, Snellius, van Ceulen and others:
"Why should I, a well-established professor of mathematics at Leidens
University, calculate in the same manner as some surveyors, lawyers
or else fighting masters!" This is indeed not interesting for the
further development of mathematics, but of course interesting for a
full understanding of the circumstances within Renaissance.
Peter Schreiber.