Mathematical Impossibility in History and in the Classroom

Theorems stating that something is impossible are notoriously difficult to understand for many students and amateur mathematicians. In this talk I shall discuss how the role of such impossibility statements has changed during the history of mathematics. I shall argue that impossibility statements ha...

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Autor Principal: Lützen, Jesper
Formato: Artículo
Idioma: Español
Publicado: Universidad de Costa Rica 2014
Acceso en línea: http://revistas.ucr.ac.cr/index.php/cifem/article/view/14723
http://hdl.handle.net/10669/18810
Sumario: Theorems stating that something is impossible are notoriously difficult to understand for many students and amateur mathematicians. In this talk I shall discuss how the role of such impossibility statements has changed during the history of mathematics. I shall argue that impossibility statements have changed status from a kind of meta-statement to true mathematical theorems. I shall also argue that this story is worth telling in the classroom because it will clarify the nature of impossibility theorems and thus of mathematics. In particular it will show to the students how mathematics is able to investigate the limits of its own activity with its own methods.