People, Places, Practices: Joint BSHM-CSHPM/SCHPM Conference: Symposium Real Numbers in Transition: Aspects of the 18th and 19th Centuries

0548821 - FLÚ 2022 RIV eng U - Uspořádání akce
López, E. D. - Fuentes Guillén, Elías
People, Places, Practices: Joint BSHM-CSHPM/SCHPM Conference: Symposium Real Numbers in Transition: Aspects of the 18th and 19th Centuries.
[Online, 15.07.2021-15.07.2021, (K-WRD 20/18)]
Institucionální podpora: RVO:67985955
Klíčová slova: History of mathematics in the 18th century * History of mathematics in the 19th century * Real Numbres * Heinrich Lambert * Bernard Bolzano * Martin Ohm
Obor OECD: Philosophy, History and Philosophy of science and technology

It is usually accepted that the notion of real numbers was more or less there, prior to the publication of detailed theories (often called constructions) in the 1870s. However, a closer look indicates that the extent of the domain of real numbers was far from well determined, or well understood, in the 18th and early 19th centuries. Up until 1800 it was still common to understand by irrational numbers only the radicals such as √3 or√1 −√5, but gradually there was a transition from the conception of decimal fractions (or continued fractions, etc.) as a tool for approaching irrationals, to their conception as mathematical objects. Meanwhile, the preeminence of analytic methods introduced in the 17th century made possible some proofs of the irrationality of transcendental numbers during the 18th century. At the turn of the 19th century the need for a clear conceptual characterization of the continuity of the real-number domain was not yet been envisioned and indeed crucial ingredients of a mature theory of real numbers were still lacking, as evidenced by the sporadic introduction of irrationals. But this is not to deny some groundbreaking features contained in the works of mathematicians of the first half of that century. The aim of this symposium will therefore be to throw light on that transitional period, before the 1870s, by examining the relevant contributions due to key authors of the German-speaking area, namely Lambert, Bolzano, M. Ohm and Grassmann. In doing so, and partly by paying attention to their biographies, we intend to address the ways in which those mathematicians and some of their contemporaries worked during that period.
Trvalý link: http://hdl.handle.net/11104/0325045