Giuseppe Peano
Born	(1858-08-27)27 August 1858 Spinetta, Piedmont, Italy
Died	20 April 1932(1932-04-20) (aged 73) Turin, Italy
Residence	Italy
Citizenship	Italian
Fields	Mathematics
Institutions	University of Turin, Accademia dei Lincei
Alma mater	University of Turin
Known for	Peano axioms Peano existence theorem Formulario mathematico Latino Sine Flexione
Influences	Euclid, Angelo Genocchi
Influenced	Bertrand Russell, Giovanni Vailati
Notable awards	Knight of the Order of Saints Maurizio and Lazzaro Knight of the Crown of Italy Commendatore of the Crown of Italy Correspondent of the Accademia dei Lincei

Giuseppe Peano (Italian pronunciation: [dʒuˈzɛppe peˈaːno]; 27 August 1858 – 20 April 1932) was an Italian mathematician, whose work was of 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 the Peano axioms in his honor. As part of this effort, he made key contributions to the modern rigorous and systematic treatment of the method of mathematical induction. He spent most of his career teaching mathematics at the University of Turin.

Biography[link]

Peano was born and raised on a farm at Spinetta, a hamlet now belonging to Cuneo, Piedmont, Italy. He attended the Liceo classico Cavour in Turin, and 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. A few 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.^[1]

Giuseppe Peano and his wife Carola Crosio in 1887

In 1887, Peano married Carola Crosio, the daughter of the Turin-based painter Luigi Crosio, known for painting the Refugium Peccatorum Madonna.^[2] 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 cannot 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, i.e. "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 students Mario Pieri and Alessandro Padoa had a papers presented at the philosophy congress also. For the mathematical congress, Peano did not speak, but Padoa's memorable presentation has been frequently recalled. 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 inflexion," later called Interlingua, but which should not 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.

The year 1908 was big 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[link]

• 1881: Published first paper.
• 1884: Calcolo Differenziale e Principii di Calcolo Integrale.
• 1887: Applicazioni Geometriche del Calcolo Infinitesimale.
• 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.
• 1893: Lezioni di Analisi Infinitesimale, 2 vols.
• 1895: Promoted to Ordinary Professor.
• 1901: Made Knight of the Order of Saints Maurizio and Lazzaro.
• 1903: Announces Latino sine flexione.
• 1905: Made Knight of the Order of the Crown of Italy. Elected a corresponding member of the Accademia dei Lincei in Rome, the highest Italian honour for scientists.
• 1908: Fifth and final edition of the Formulario mathematico.
• 1917: Made an Officer of the Crown of Italy.
• 1921: Promoted to Commendatore of the Crown of Italy.

See also[link]

	Biography portal
	Logic portal

• Peano axioms

Bibliography[link]

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 literature

• 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).

References[link]

External links[link]

• O'Connor, John J.; Robertson, Edmund F., "Giuseppe Peano", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Peano.html .
• Giuseppe Peano at the Mathematics Genealogy Project
• Hubert Kennedy (2002). "Twelve articles on Giuseppe Peano" (PDF). San Francisco: Peremptory Publications. http://hubertkennedy.angelfire.com/TwelveArticles.pdf. Retrieved 8 April 2012.  Collection of articles on life and mathematics of Peano (1960s to 1980s).
• Instituto Pro Latino Sine Flexione

This article is an orphan, as few or no other articles link to it. Please introduce links to this page from related articles; suggestions may be available. (February 2009)

Gabriele Paolini (Milan, 12 October 1974) is a famous Italian television prankster and condom advocate. He calls himself the "prophet of the condom" and "the prophylactic prophet." In Italy he is also referred to as a disturbatore televisivo, which means a television disturber. His antics usually involve exhibiting condoms in the background behind interviews or other unwitting live reporters. He has also been involved with singing contests and sporting events.

Overview[link]

Gabriele Paolini began his career as a "television polluter" when a friend of his died of AIDS at age 22, contracting the disease some years after unprotected sex with a prostitute. Paolini's reaction was to invade TV news reports wearing or waving chains of condoms. Sometimes Paolini also uses a photo of a politician or of the Pope.

The son of a retired general, Paolini is in the Guinness Book of Records for his more than 30'000^[1] very short appearances waving over the shoulders of hundreds of displeased TV journalists.

Over the years, Paolini has angered many in the media. During one interrupted interview, journalist Paolo Frajese began to kick Paolini. Journalists have asked the legal office of RAI TV in Saxa Rubra for a legal injunction to "eliminate the disturber." In response, Gabriele Paolini showed the media a list of interviewers who had in fact requested his presence. However, Italy's Supreme Court upheld a three month suspended sentence against him.^[2] TG5 editor-in-chief Salvo Sottile and communications expert Enrico Mieli launched a petition on Facebook to "abolish" Paolini from the Italian television due to his insensitivity.^[3]

On March 5, 1995, Paolini personally disguised a condom as a request in a paper and gave it to Pope John Paul II at a church in Rome.^{[citation needed]}

In 2008, Paolini was sentenced to a 5-month prison term for offenses against the Pope, stemming from his actions in 2005 when he interrupted a live TV show of RAI TV insulting the Pope and the Italian premier.^[4]

References[link]

External links[link]

• Personal website of Gabriele Paolini
• "The prophylactic prophet". Guardian News & Media. 2002-09-27. http://www.buzzle.com/editorials/9-27-2002-27154.asp. Retrieved 2008-12-16. 

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Piergiorgio Odifreddi (2007)

Piergiorgio Odifreddi taking part in a seminar at Sarzana's "Festival of the Mind". (2006)

Piergiorgio Odifreddi (born July 13, 1950 in Cuneo), is an Italian mathematician, logician and aficionado of the history of science, who is also extremely active as a popular science writer and essayist, especially in a perspective of philosophical atheism as a member of the Italian Union of Rationalist Atheists and Agnostics.

Born in Cuneo (Piedmont), he received his Laurea in mathematics in Turin in 1973. From 1983 to 2002, he taught in both Italy (Turin, Alessandria, Siena, Milan) and in the United States (Cornell University). Since 2001, he has been a professor of mathematical logic in the Department of Mathematics at the University of Turin.

He has written editorials and books reviews for La rivista dei libri (the Italian edition of the New York Review of Books), is a regular contributor to Le Scienze (the Italian edition of Scientific American), and has also written for several newspapers such as La Repubblica, La Stampa and the weekly L'Espresso. The television stations Radio Tre, RAI Due and RAI Tre have hosted many of his discussions on various scientific topics.

Piergiorgio Odifreddi participated in the Stock Exchange of Visions project in 2007.

Honors[link]

• 1998 - Galileo Prize of the Italian Mathematical Union.
• 2002 - Peano Prize of Mathesis
• 2005 - Commander OMRI

Works[link]

Academic writings[link]

• Classical recursion Theory, North Holland - Elsevier, 1988
• Classical recursion Theory. Volume II, North Holland - Elsevier, 1999

Popular writings[link]

• Il Vangelo secondo la Scienza, Einaudi, 1999, ISBN 88-06-14930-X (The Gospel According to Science)
• La matematica del '900, prefazione di Gian-Carlo Rota, Einaudi, 2000, ISBN 88-06-15153-3 (The Mathematics of the 20th Century)
• Il computer di Dio, Cortina, 2000, ISBN 88-7078-663-3 (God's Computer)
• C'era una volta un paradosso, Einaudi, 2001, ISBN 88-06-15090-1 (Once upon a time there was a paradox)
• La repubblica dei numeri, Cortina, 2002, ISBN 88-7078-776-1 (The Republic of Numbers)
• Zichicche, Dedalo, 2003, ISBN 88-220-6260-4
• Il diavolo in cattedra. La logica matematica da Aristotele a Kurt Gödel, Einaudi, 2003, ISBN 88-06-16721-9 (The Devil in the Professor's Chair: Mathematical Logic from Aristotle to Kurt Goedel)
• Divertimento geometrico - Da Euclide ad David Hilbert, Bollati Boringhieri, 2003, ISBN 88-339-5714-4 (Geometric Diversions - From Euclid to Hilbert)
• Le menzogne di Ulisse. L'avventura della logica da Parmenide ad Amartya Sen, Longanesi, 2004, ISBN 88-304-2044-1 (Ulysses' Lies. The Adventure of Logic from Parmenides to Amartya Sen)
• Il matematico impertinente, Longanesi, 2005, ISBN 88-304-2222-3 (The Impertinent Mathematician)
• Penna, pennello, bacchetta: le tre invidie del matematico, Laterza, 2005, ISBN 88-420-7643-0 (Pen, brush, baton: the three envies of the mathematician)
• Idee per diventare matematico, Zanichelli, 2005, ISBN 88-08-07063-8 (Ideas for becoming a mathematician)
• Incontri con menti straordinarie, Longanesi, 2006, ISBN 88-304-2346-7 (Meetings with extraordinary minds)
• Che cos'è la logica?, Luca Sossella editore, 2006, ISBN 88-89829-19-2 (What is logic?)
• La scienza espresso: Note brevi, semibrevi e minime per una biblioteca scientifica universale, Einaudi, 2006, ISBN 978-88-06-18258-8 (Science express)
• Perché non possiamo essere cristiani (e meno che mai cattolici), Longanesi, 2007, ISBN 978-88-304-2427-2 (Why we cannot be Christians (much less Catholics))

See also[link]

Wikimedia Commons has media related to: Piergiorgio Odifreddi

• Antonino Zichichi
• UAAR

External links[link]

• Piergiorgio Odifreddi's Official Site (IT)
• Article by Odifreddi on Recursive Functions in Stanford Encyclopedia of Philosophy