# Giuseppe Peano

**Giuseppe Peano**(1858 - 1932) was an Italian mathematician.

Giuseppe Peano was born on August 27, 1858 at a farm near the village of Spinetta in northeastern 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 first uses the symbols for Union and Intersection of sets as are now used today.

In 1889 Peano is appointed 'Professor first class' at the Royal Military Academy in Turin where he also teaches. Peano's famous space-filling curve appears in a publication of his as a counter-example 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 is also appointed 'Extraordinary Professor of Infinitesimal Calculus' at Turin University.

The following year he becomes a member of 'The Academy of Science' in Turin. This year (1891) sees 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 formulas and theorems of mathematical science using a standard notation invented by Peano.

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

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

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

Paris is the venue for the Second International Conference of Mathematics in 1900. The conference is preceded by the First International Conference of Philosophy where Peano is a member of the Patronage Committee. He presents a paper which poses the question of correctly formed definitions in mathematics (ie How do you define a definition?). This becomes one of Peano's main philosophical interests for the rest of his life. Peano meets Bertrand Russell and gives him a copy of 'Formulario'. Russell is so struck by Peano's innovative logical symbols that he leaves the conference for home where he studies Peano's text. Peano's followers present papers (using Peano's teachings) at the mathematics conference but Peano does not. A resolution is raised on the formation of an International Auxiliary Language that will make the spread of new mathematical (and commercial) ideas easier. Peano is in full support.

By 1901 Peano is at the peak of his mathematical career. He has made advances in the areas of analysis, foundation and logic. Peano has 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 is made a "Knight of the Order of Saints Maurizio and Lazzaro". Peano has by this stage become heavily involved with the 'Formulario' project and his teaching begins to suffer. In fact he becomes so determined to teach his new mathematical symbols that the calculus in his course is neglected. As a result he is dismissed from the Royal Military Academy but retains his post at Turin University.

1903 sees Peano announce his work on an international auxiliary language called "Latino sine flexione" (Latin without flexions). This now becomes an important project (along with finding contributants for 'Formulario').

In 1905 Peano is made a "Knight of the Crown of Italy" and is 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 is the year in which the final (5th) edition of 'Formulario Project', titled "Formulario Mathematico", is published. It contains 4200 formulas 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 flexions" which put most mathematicians off using the book. However, it was (is) a significant piece of mathematical literature. Also in this year Peano takes over the Chair of Higher Analysis at Turin. This lasts for only two years.

In 1910, Peano's mother dies.

For the next twenty-four years, Peano divides (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, on April 20, 1932, aged 73.

*"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