Giuseppe Peano (August 27, 1858 – April 20, 1932) was an Italian mathematician and philosopher.

Giuseppe Peano was born on a farm near the village of Spinetta in Piedmont, Northwestern Italy.

In 1876 he enrolled at the University of Turin in the same region of Italy.

He graduated in 1880 with 'High Honours' and began his teaching career. Peano was a University assistant between 1880 and 1882, first to Enrico D'Ovidio and then to Angelo Genocchi (the chair of Infinitesimal Calculus). In 1881 Peano published his first paper. In the course of his life, Peano had over two hundred papers and books published (most of them on mathematics).

By 1882, due to Genocchi's ill health, Peano was in charge of the Infinitesimal Calculus course where the students made fun of him because of an inability to pronounce the letter 'r'.

His first major work, a text book on calculus, credited to Genocchi, was published in 1884. On the July 27, 1887 he married Carola Crosio. The following year Peano's father died. Peano also published his first book dealing with mathematical logic. This book was the first to use the symbols for union and intersection of sets as we now know them.

In 1889 Peano was appointed 'Professor first class' at the Royal Military Academy in Turin where he also taught. Peano's famous space-filling curve appeared in a publication of his as a counterexample in 1890. He used it to show that a continuous curve cannot always be enclosed in an arbitrarily small region. In the same year he was also appointed 'Extraordinary Professor of Infinitesimal Calculus' at Turin University.

The following year he became a member of 'The Academy of Science' in Turin. This year (1891) saw Peano begin his ambitious task of creating an 'Encyclopedia of mathematics'. Known as the 'Formulario Project' it was to be a collection of all known formulae and theorems of mathematical science using a standard notation invented by Peano.

In 1895 he was promoted to 'Ordinary Professor' at Turin University.

The First International Conference of Mathematics was held in Zürich in 1897 where Peano was a key participant, presenting a paper on mathematical logic. At this time Peano started to become increasingly occupied with 'Formulario' to the detriment of his other work.

In 1898 he presented a note to the 'Academy' about binary numeration and its ability to be used to represent the sounds of languages. He also became so frustrated with publishing delays (due to his demand that formulae be printed on one line) that he purchased a printing press.

Paris was the venue for the Second International Conference of Mathematics in 1900. The conference was preceded by the First International Conference of Philosophy where Peano was a member of the Patronage Committee. He presented a paper which posed the question of correctly formed definitions in mathematics (i.e. how do you define a definition?). This became one of Peano's main philosophical interests for the rest of his life. Peano met Bertrand Russell and gave him a copy of 'Formulario'. Russell was so struck by Peano's innovative logical symbols that he left the conference for home where he studied Peano's text. Peano's followers presented papers (using Peano's teachings) at the mathematics conference but Peano didn't. A resolution was raised on the formation of an International Auxiliary Language that would make the spread of new mathematical (and commercial) ideas easier. Peano was in full support.

By 1901 Peano was at the peak of his mathematical career. He had made advances in the areas of analysis, foundation and logic. Peano had made many contributions to the teaching of calculus. He also contributed to the fields of differential equations and vector analysis. Peano played a key role in the axiomatization of mathematics and was a leading pioneer in the development of mathematical logic. In recognition of this Peano was made a "Knight of the Order of Saints Maurizio and Lazzaro". Peano had by this stage become heavily involved with the 'Formulario' project and his teaching began to suffer. In fact he became so determined to teach his new mathematical symbols that the calculus in his course was neglected. As a result he was dismissed from the Royal Military Academy but retained his post at Turin University.

1903 saw Peano announce his work on an international auxiliary language called "Latino sine flexione" (Latin without flexions, and later called Interlingua). This now became an important project (along with finding contributors for 'Formulario').

In 1905 Peano was made a "Knight of the Crown of Italy" and was also elected a Corresponding Member of the "Accademia dei Lincei" in Rome, the highest honour for an Italian scientist (Galileo was also a member in his time).

1908 was the year in which the final (5th) edition of the 'Formulario Project', titled "Formulario Mathematico", was published. It contained 4200 formulae and theorems, all completely stated and most of them proved. The book received little use and most of the content was dated by this time. The comments and examples were written in "Latino sine flexione" which put most mathematicians off using the book. However, it was (is) a significant piece of mathematical literature. Also in 1908, Peano took over the Chair of Higher Analysis at Turin. This lasted for only two years.

He was elected as the director for Academia pro Interlingua (the "Academy" was the former Kadem bevünetik volapüka (International Academy of Volapük) created at a congress in Munich in August 1887, and which under Rosenberger, who became the Academy’s director in 1892, changed its name to Akademi Internasional de Lingu Universal in 1898). When the Akademi which had created Idiom Neutral effectively chose to abandon it in favor of Latino sine flexione, Peano was appointed the director, and the name was changed to Academia pro Interlingua (since Interlingua was an alternative name for Peano's language).

In 1910, Peano's mother died. For the next twenty-four years, Peano divided (not equally however) his energies between developing and promoting his and other artificial languages (he became a revered member of the international auxiliary language movement), teaching, and working on texts aimed for secondary schooling (including a dictionary of mathematics). He used his membership of the Accademia dei Lincei to present papers written by friends and colleagues who were not members (the Accademia recorded and published all presented papers given in sessions).

He was further honoured by the government in 1917, when he was made an "Officer of the Crown of Italy', and again in 1921 with promotion to "Commendatore of the Crown of Italy".

In 1925 Peano swapped Chairs (unofficially) from Infinitesimal Calculus to Complementary Mathematics, a field which better suited his current style of mathematics. This move became official in 1931.

Giuseppe Peano continued teaching at Turin University until the day before he died, April 20, 1932, when he suffered a fatal heart attack.

He [Peano] was a man I greatly admired from the moment I met him for the first time in 1900 at a Congress of Philosophy, which he dominated by the exactness of his mind.

- Bertrand Russell 1932

Reference: "Peano: Life and Works of Giuseppe Peano" Hubert C. Kennedy

See also: Peano axioms

External links

• A picture of Peano http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Peano.html