History of Mathematics at CMUC: Description


This thematic line gathers CMUC researchers working on the History of Mathematics. The subject is understood in the precise sense of the history of mathematical ideas, so it does not include, unless mathematical content is involved, the history of teaching, the history of institutions, or biographies.

It is natural that emphasis is given to the History of Mathematics in Portugal. Our work concentrates on the few Portuguese mathematicians of the past who made relevant contributions to the progress of Mathematics.

The main examples, among others, are the following:

  • Pedro Nunes (1502-1578), one of the important names in European 16th century Mathematics, who founded the modern science of navigation, distinguishing rhumb-lines from great circles and making explicit the requirements for the later (so-called) Mercator chart. Apart from many other contributions, it is quite remarkable that he gave the complete solution to the problem of the shortest twilight, and presented a mathematical description of points on a loxodrome, more than a century before the creation of the calculus.
  • José Monteiro da Rocha (1734-1819), who did extensive work on celestial mechanics and astronomy and was a forerunner in the study of the parameters describing the orbits of comets.
  • José Anastácio da Cunha (1744-1787), who long before Bolzano and Cauchy saw the need for rigour in the foundations of Mathematics. This is most interesting and original when, in a treatise entitled Principios Mathematicos, he deals with the controverted matters of infinite series and the calculus. His efforts to put infinitary processes on solid logical ground are remarkable. He gave the first general definition of powers, and this work was much later praised by none other than C. F. Gauss.

We try to adopt rigorous scholarship methodologies, concentrating on primary sources. Expository work based on secondary sources, and non-mathematical historical material, are part of the Outreach thematic line.

The work in this line also involves publishing modern editions of writings of the above-mentioned mathematicians, including previously unknown manuscripts, with extensive comments. Much of this is done in collaboration with other groups in Portugal, especially in the Universities of Minho, Porto and Lisbon.