Formulario mathematicoFormulario Mathematico (Latino sine flexione: Formulary for Mathematics) is a book by Giuseppe Peano which expresses fundamental theorems of mathematics in a symbolic language developed by Peano. The author was assisted by Giovanni Vailati, Mario Pieri, Alessandro Padoa, Giovanni Vacca, Vincenzo Vivanti, Gino Fano and Cesare Burali-Forti. The Formulario was first published in 1894. The fifth and last edition was published in 1908. Hubert Kennedy wrote "the development and use of mathematical logic is the guiding motif of the project".
Latino sine flexioneLatino sine flexione ("Latin without inflections"), Interlingua de Academia pro Interlingua (IL de ApI) or Peano's Interlingua (abbreviated as IL), is an international auxiliary language compiled by the Academia pro Interlingua under the chairmanship of the Italian mathematician Giuseppe Peano (1858–1932) from 1887 until 1914. It is a simplified version of Latin, and retains its vocabulary.
Mathematical inductionMathematical induction is a method for proving that a statement is true for every natural number , that is, that the infinitely many cases all hold. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: Mathematical induction proves that we can climb as high as we like on a ladder, by proving that we can climb onto the bottom rung (the basis) and that from each rung we can climb up to the next one (the step). A proof by induction consists of two cases.
LogicismIn the philosophy of mathematics, logicism is a programme comprising one or more of the theses that — for some coherent meaning of 'logic' — mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and Alfred North Whitehead championed this programme, initiated by Gottlob Frege and subsequently developed by Richard Dedekind and Giuseppe Peano.
Space-filling curveIn mathematical analysis, a space-filling curve is a curve whose range reaches every point in a higher dimensional region, typically the unit square (or more generally an n-dimensional unit hypercube). Because Giuseppe Peano (1858–1932) was the first to discover one, space-filling curves in the 2-dimensional plane are sometimes called Peano curves, but that phrase also refers to the Peano curve, the specific example of a space-filling curve found by Peano.
ItaliansItalians (Italiani, itaˈljaːni) are an ethnic group native to the Italian geographical region. Italians share a common culture, history, ancestry and language. Their predecessors differ regionally, but generally include native populations such as the Etruscans, the Rhaetians, the Ligurians, the Adriatic Veneti, and the Italic peoples, including the Latins, from which the Romans emerged and helped create and evolve the modern Italian identity.
Louis CouturatLouis Couturat (kutyʁa; 17 January 1868 – 3 August 1914) was a French logician, mathematician, philosopher, and linguist. Couturat was a pioneer of the constructed language Ido. Born in Ris-Orangis, Essonne, France. In 1887 he entered École Normale Supérieure to study philosophy and mathematics. In 1895 he lectured in philosophy at the University of Toulouse and 1897 lectured in philosophy of mathematics at the University of Caen Normandy, taking a stand in favor of transfinite numbers.
Alessandro PadoaAlessandro Padoa (14 October 1868 – 25 November 1937) was an Italian mathematician and logician, a contributor to the school of Giuseppe Peano. He is remembered for a method for deciding whether, given some formal theory, a new primitive notion is truly independent of the other primitive notions. There is an analogous problem in axiomatic theories, namely deciding whether a given axiom is independent of the other axioms.
Mario PieriMario Pieri (22 June 1860 – 1 March 1913) was an Italian mathematician who is known for his work on foundations of geometry. Pieri was born in Lucca, Italy, the son of Pellegrino Pieri and Ermina Luporini. Pellegrino was a lawyer. Pieri began his higher education at University of Bologna where he drew the attention of Salvatore Pincherle. Obtaining a scholarship, Pieri transferred to Scuola Normale Superiore in Pisa. There he took his degree in 1884 and worked first at a technical secondary school in Pisa.
Hilbert curveThe Hilbert curve (also known as the Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891, as a variant of the space-filling Peano curves discovered by Giuseppe Peano in 1890. Because it is space-filling, its Hausdorff dimension is 2 (precisely, its image is the unit square, whose dimension is 2 in any definition of dimension; its graph is a compact set homeomorphic to the closed unit interval, with Hausdorff dimension 2).
