# Mathematician:Giuseppe Peano

## Contents

## Mathematician

Italian mathematician who contributed significantly to the founding of the fields of mathematical logic and set theory.

Invented many of the symbols used today in these fields.

Worked on the axiomatization of mathematics, and contributed greatly towards the method of mathematical induction.

Invented Latino sine flexione, a simplified version of Latin, intended as an international language. Peano's view was that Latin was already a universally-used international language, and there was no need to invent further such languages. (The recent ubiquity of English in its many forms has since rendered his argument obsolete.)

## Nationality

Italian

## History

- Born: 27 Aug 1858 in Cuneo, Piemonte, Italy
- 1881: Published first paper
- 1889: Appointed Professor First Class at the Royal Military Academy
- 1890: Appointed Extraordinary Professor of infinitesimal calculus at the University of Turin
- 1891: Made a member of the Academy of Science, Torino
- 1895: Promoted to Ordinary Professor
- 1901: Made Knight of the Order of Saints Maurizio and Lazzaro
- 1903: Announced Latino sine flexione
- 1905: Made Knight of the Order of the Crown of Italy.
- 1905: Elected a corresponding member of the Accademia dei Lincei in Rome
- 1917: Made an Officer of the Crown of Italy
- 1921: Promoted to Commendatore of the Crown of Italy
- Died: 20 April 1932 in Turin, Italy

## Theorems, Definitions and Other Creations

- Peano's Axioms, also known as the Dedekind-Peano Axioms (for Richard Dedekind who refined them)
- Peano Curve
- Peano Space
- Cauchy-Peano Theorem (with Augustin Louis Cauchy)

Results named for **Giuseppe Peano** can be found here.

Definitions of concepts named for **Giuseppe Peano** can be found here.

Axioms named for **Giuseppe Peano** can be found here.

## Books and Papers

- 1884: Contributed significantly towards
*Course in Infinitesimal Calculus*by Angelo Genocchi - 1887:
*Applicazioni Geometriche del Calcolo Infinitesimale* - 1888:
*Calcolo geometrico secondo l'Ausdehnungslehre di H. Grassmann* - 1889:
*Arithmetices principia, nova methodo exposita*, in which Peano's Axioms appear - 1891: Founded the journal
*Rivista di matematica* - 1892:
*Formulario Mathematico* - 1893:
*Lezioni di Analisi Infinitesimale*(2 volumes) - 1896:
*Formulario Mathematico, 2nd ed.* - 1908:
*Formulario Mathematico, 5th ed.*: project completed

## Sources

- 1910: Alfred North Whitehead and Bertrand Russell:
*Principia Mathematica: Volume 1*... (next): Chapter $\text{I}$: Preliminary Explanations of Ideas and Notations - 1951: Willard Van Orman Quine:
*Mathematical Logic*(revised ed.) ... (previous) ... (next): Introduction - 1959: A.H. Basson and D.J. O'Connor:
*Introduction to Symbolic Logic*(3rd ed.) ... (previous) ... (next): $\S 1.1$: Symbolic Logic and Classical Logic - 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): $\S 16$ - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.33$: Weierstrass ($1815$ – $1897$)