Peano , Giuseppe
(1858–1932) Italian mathematician and logician
Peano, who was born at Spinetta near Cuneo, in Italy, studied at the University of Turin and was an assistant there from 1880. He became extraordinary professor of infinitesimal calculus in 1890 and was full professor from 1895 until his death. He was also professor of the military academy in Turin from 1886 to 1901.
Peano began his mathematical career as an analyst and, like Richard Dedekind before him, his interest in philosophical and logical matters was awakened by the lack of rigor in some presentations of the subject. Peano was particularly keen to avoid all illegitimate reliance on intuition in analysis. His discovery in 1890 of a curve that was continuous but filled space went against intuition. A similar discovery was Karl Weierstrass's famous function that was everywhere continuous but nowhere differentiable. As with Weierstrass's function, Peano's curve shows that the concept of a continuous function cannot be identified with that of a graph.
His interest in rigorous and logical presentation of mathematics led Peano naturally to an interest in the mathematical development of logic. In this field he was one of the great pioneers along with Georg Boole, Gottlob Frege, and Bertrand Russell. Peano's achievement was twofold. First he devised, in his Notations de logique mathématique (1894; Notations in Mathematical Logic), a clear and efficient notation for mathematical logic which, as modified by Bertrand Russell, is still widely used. Secondly, he showed how arithmetic can be derived from a purely logical basis. To do this he formulated, in his Nova methodo exposita(1889; New Explanation of Method), nine axioms, four dealing with equality, and the remaining five, listed below, characterizing the numbers series:
1 is a number
The successor of any number is a number
No two numbers have the same successor
1 is not the successor of any number
Any property that belongs to 1 and the successor of any number that also has that property, belongs to all numbers (mathematical induction).
Peano's axioms had been proposed, in a more complicated form, by Dedekind a year earlier.
Peano also did notable work in geometry and on the error terms in numerical calculation. Among his extramathematical interests he was a keen propagandist for a proposed international language, Interlingua, which he had developed from Volapük.

Scientists. . 2011.

Look at other dictionaries:

  • Peano, Giuseppe — (1858–1932)    The son of a peasant family from a small village near Cuneo in Piedmont, Giuseppe Peano was one of the most important mathematicians of his day. He began his university career in 1876 at Turin, where he would continue to work and… …   Historical Dictionary of modern Italy

  • Peano, Giuseppe — ▪ Italian mathematician born Aug. 27, 1858, Cuneo, Kingdom of Sardinia [now in Italy] died April 20, 1932, Turin, Italy       Italian mathematician and a founder of symbolic logic (logic) whose interests centred on the foundations of mathematics… …   Universalium

  • Peano — Giuseppe …   Scientists

  • Giuseppe Peano — (* 27. August 1858 in Spinetta, heute Teil von Cuneo, Piemont; † 20. April 1932 in Turin) war ein italienischer Mathematiker. Er arbeitete in Turin und befasste sich mit mathematischer Logik, mit der Axiomatik der …   Deutsch Wikipedia

  • Peano — Giuseppe Peano Giuseppe Peano (* 27. August 1858 in Spinetta, Piemont; † 20. April 1932 in Turin) war ein italienischer Mathematiker. Er arbeitete in Turin und befasste sich mit mathematischer Logik, mit der Axiomatik der natürlichen Zahlen… …   Deutsch Wikipedia

  • Giuseppe Peano — Giuseppe Peano. Nacimiento 27 de agosto de 1858 …   Wikipedia Español

  • Peano — Giuseppe Peano Giuseppe Peano Giuseppe Peano (Spinetta di Cuneo (Coni), 27 août 1858 Turin, 20 avril 1932) est un mathématicien italien de la fin du XIXe et du début du …   Wikipédia en Français

  • Peano — Peano,   Giuseppe, italienischer Mathematiker und Logiker, * Spinetta (bei Cuneo) 27. 8. 1858, ✝ Turin 20. 4. 1932; Schüler von A. Genocchi, dessen Analysisvorlesungen er in Buchform herausbrachte, 1890 Professor in Turin. Peano trat zuerst als… …   Universal-Lexikon

  • Peano — (Giuseppe) (1858 1932) mathématicien et logicien italien …   Encyclopédie Universelle

  • Peano-Axiom — ℕ Die natürlichen Zahlen sind die beim Zählen verwendeten Zahlen 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 usw. Oft wird auch die 0 (Null) zu den natürlichen Zahlen gerechnet. Sie bilden bezüglich der Addition und der Multiplikation einen (additiv und… …   Deutsch Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”