Everything about Giuseppe Peano totally explained
Giuseppe Peano (
August 27,
1858 –
April 20,
1932) was an
Italian mathematician, whose work was of exceptional
philosophical value. The author of over 200 books and papers, he was a founder of
mathematical logic and
set theory, to which he contributed much notation. The standard
axiomatization of the
natural numbers is named in his honor. He spent most of his career teaching mathematics at the
University of Turin.
Biography
Peano was born and raised on a farm at
Spinetta, a hamlet near
Cuneo,
Piedmont,
Italy. He enrolled at the
University of Turin in
1876, graduating in
1880 with high honours, after which the University employed him to assist first
Enrico D'Ovidio, and then
Angelo Genocchi, the Chair of
infinitesimal calculus. Due to Genocchi's poor health, Peano took over the teaching of the infinitesimal calculus course within 2 years. His first major work, a textbook on calculus, was published in
1884 and was credited to Genocchi. Three years later, Peano published his first book dealing with mathematical logic. Here the modern symbols for the
union and
intersection of sets appeared for the first time.
In
1887, Peano married Carola Crosio. In
1886, he began teaching concurrently at the
Royal Military Academy, and was promoted to Professor First Class in
1889. The next year, the University of Turin also granted him his full professorship. Peano's famous
space-filling curve appeared in
1890 as a
counterexample. He used it to show that a continuous curve can't always be enclosed in an arbitrarily small region. This was an early example of what came to be known as a
fractal.
The following year Peano started the
Formulario Project. It was to be an "Encyclopedia of Mathematics", containing all known formulae and theorems of mathematical science using a standard notation invented by Peano. In
1897, the first
International Congress of Mathematicians was held in
Zürich. Peano was a key participant, presenting a paper on mathematical logic. He also 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 Congress of Mathematicians 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,
for example "how do you define a definition?". This became one of Peano's main philosophical interests for the rest of his life. At the conference 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 and returned home to study Peano's text.
Peano's followers presented papers (using Peano's teachings) at the mathematics conference, but Peano did not. A resolution calling for the formation of an "international auxiliary language" to facilitate the spread of mathematical (and commercial) ideas, was proposed; Peano fully supported it.
By
1901, Peano was at the peak of his mathematical career. He had made advances in the areas of
analysis, foundations and logic, made many contributions to the teaching of calculus and 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. 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.
In
1903 Peano announced his work on an international auxiliary language called
Latino sine flexione ("
Latin without flexions," later called Interlingua, but which shouldn't be confused with the later
Interlingua of the
IALA). This was an important project for him (along with finding contributors for 'Formulario'). The idea was to use Latin vocabulary, since this was widely known, but simplify the grammar as much as possible and remove all irregular and anomalous forms to make it easier to learn. In one speech, he started speaking in Latin and, as he described each simplification, introduced it into his speech so that by the end he was talking in his new language.
1908 was a big year for Peano. The fifth and final 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 attention since much of the content was dated by this time. However, it remains a significant contribution to mathematical literature. The comments and examples were written in
Latino sine flexione.
Also in
1908, Peano took over the chair of higher analysis at Turin (this appointment was to last for only two years). He was elected the director of
Academia pro Interlingua. Having previously created
Idiom Neutral, the Academy effectively chose to abandon it in favor of Peano's
Latino sine flexione.
After his mother died in
1910, Peano divided his time between teaching, working on texts aimed for secondary schooling including a dictionary of mathematics, and developing and promoting his and other
auxiliary languages, becoming a revered member of the international auxiliary language movement. 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).
In
1925 Peano switched 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, when he suffered a fatal
heart attack.
Milestones and honors received
Bibliography
Peano's writings in English translation:
1889. "The principles of arithmetic, presented by a new method" in Jean van Heijenoort, 1967. A Source Book in Mathematical Logic, 1879-1931. Harvard Univ. Press: 83-97.
1973. Selected works of Giuseppe Peano. Kennedy, Hubert C., ed. and transl. With a biographical sketch and bibliography. London: Allen & Unwin.
Secondary:
Gillies, Douglas A., 1982. Frege, Dedekind, and Peano on the foundations of arithmetic. Assen, Netherlands: Van Gorcum.
Ivor Grattan-Guinness, 2000. The Search for Mathematical Roots 1870-1940. Princeton University Press.
Kennedy, Hubert C., 1980. Peano: Life and Works of Giuseppe Peano
. Reidel. Biography with complete bibliography (p. 195-209).
Further Information
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