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"A Brief History of Geometry” is a overview of the main historical steps of Geometry, from Euclid to Perelman, via Descartes, Gauss, Riemann, Ricci, Poincaré and Einstein… This conference was given by Jean-Pierre Bourguignon (IHES, France) at the Academy of Sciences of Lisbon the November 2nd, 2017, at the invitation of the Centro de Matemática, Aplicações Fundamentais e Investigação Operacional da Faculdade de Ciências da Universidade de Lisboa, Portugal.

Through works by renowned architects such as Antoni Gaudí, Felix Candela and Oscar Niemeyer, this film intends to show the natural way in which the formulas, the geometry of forms and their concretization are intertwined.

Através de obras de arquitetos de renome como  Antoni Gaudí, Felix Candela e Oscar Niemeyer, este filme pretende evidenciar a forma natural como se entrelaçam as fórmulas, a geometria das formas e a sua concretização.

O vídeo insere-se no projeto Geometria Intuitiva e Interativa (GI2). Mais informações em http://www.gi2.pt/ .

On Goodman realizability

Emanuele Frittaion
CMAFCIO, Universidade de Lisboa

Abstract: Goodman's theorem (after Nicholas D. Goodman) asserts that adding the axiom of choice to intuitionistic arithmetic in all finite types yields a system which is conservative over Heyting arithmetic. This is in contrast with classical arithmetic in all finite types. In fact, the combination of choice with classical logic results in a system as strong as full second-order arithmetic.

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