Editing Giuseppe Peano

{{short description|Italian mathematician and glottologist (1858–1932)}}
{{Use dmy dates|date=March 2021}}
{{Infobox scientist
| name              = Giuseppe Peano
| caption           = Peano {{c.|1910s}}
| image             = Giuseppe Peano.jpg
| image_size        = 220px
| birth_date        = {{birth date|1858|8|27|df=y}}
| birth_place       = [[Cuneo|Spinetta]], [[Piedmont]], [[Kingdom of Sardinia (1720–1861)|Kingdom of Sardinia]]
| death_date        = {{death date and age|1932|4|20|1858|8|27|df=y}}
| death_place       = [[Turin]], [[Kingdom of Italy|Italy]]
| citizenship       = [[Italy|Italian]]
| field             = [[Mathematics]]<br/>[[Linguistics]]
| work_institutions = [[University of Turin]], [[Accademia dei Lincei]]
| alma_mater        = [[University of Turin]]
| doctoral_advisor  = [[Enrico D'Ovidio]]
| academic_advisors = [[Francesco Faà di Bruno]]
| known_for         = [[Peano axioms]]<br/>[[Peano curve]]<br/>[[Peano existence theorem]]<br />[[Jordan measure|Peano-Jordan measure]]<br/>[[Peano kernel theorem]]<br />[[Peano–Russell notation]]<br />[[Latino sine flexione]]<br/>[[Vector space]]<br/>[[Peano surface]]<br/>[[Logicism]]
| notable_students  = [[Maria Gramegna]]
| prizes            = Knight of the [[Order of Saints Maurizio and Lazzaro]] <br/>Knight of the [[Order of the Crown of Italy|Crown of Italy]] <br/>Commendatore of the Crown of Italy <br/>Correspondent of the [[Accademia dei Lincei]]
}}

'''Giuseppe Peano''' ({{IPAc-en|p|i|ˈ|ɑː|n|oʊ}};<ref>[http://www.dictionary.com/browse/peano "Peano"]. ''[[Random House Webster's Unabridged Dictionary]]''.</ref> {{IPA|it|dʒuˈzɛppe peˈaːno|lang}}; 27 August 1858 – 20 April 1932) was an Italian [[mathematician]] and [[glottologist]]. The author of over 200 books and papers, he was a founder of [[mathematical logic]] and [[set theory]], to which he contributed much [[Mathematical notation|notation]]. The standard [[axiomatization]] of the [[natural number]]s 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]]. He also created an international auxiliary language, [[Latino sine flexione]] ("Latin without inflections"), which is a simplified version of Classical Latin. Most of his books and papers are in Latino sine flexione, while others are in Italian.

==Biography==
[[File:Peano - Aritmetica generale e algebra elementare, 1902 - 3935060.tif |thumb|''Aritmetica generale e algebra elementare'', 1902]]
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 [[calculus]]. Due to Genocchi's poor health, Peano took over the teaching of calculus course within two years. His first major work, a textbook on calculus entitled ''Calcolo differenziale, e principii di calcolo integrale'', was published in 1884 and was credited to Genocchi.<ref>{{cite book|author=Genocchi, Angelo|year=1884|title=Calcolo differenziale, e principii di calcolo integrale|url=https://archive.org/details/calcolodifferen00peangoog/page/n12/mode/2up|publisher=[[Fratelli Bocca]]|postscript=; pubblicato con aggiunte dal Dr. Giuseppe Peano (published with additions by Dr. Giuseppe Peano)}}</ref><ref>{{cite web|author=Gouvêa, Fernando Q.|author-link=Fernando Q. Gouvêa|date=May 11, 2011|url=https://maa.org/press/maa-reviews/giuseppe-peano-between-mathematics-and-logic |title=Review of ''Giuseppe Peano: Between Mathematics and Logic'' edited by Fulvia Skof|website=MAA Reviews, Mathematical Association of America }}</ref> A few years later, Peano published his first book dealing with mathematical logic. Here the modern symbols for the [[union (set theory)|union]] and [[intersection (set theory)|intersection]] of sets appeared for the first time.<ref>{{cite book|author1=Richard N. Aufmann|author2=Joanne Lockwood|title=Intermediate Algebra: An Applied Approach|url=https://books.google.com/books?id=S7mEGD-VC1AC&pg=PA10|date=29 January 2010|publisher=Cengage Learning|isbn=978-1-4390-4690-6|page=10}}</ref>

Peano joined [[Freemasonry]]. It is not known where he was initiated, but on December 24, 1885, he was affiliated as [[Venerable Master|Master]] in the "[[Dante Alighieri]]" Masonic Lodge in Turin.<ref>Vittorio Gnocchini, ''L’Italia dei Liberi Muratori'', Ed.Erasmo, 2005, p.213. As quoted in {{cite web|url=https://www.afsu.it/giuseppe-peano/|title=Giuseppe Peano|website=Accademia di filosofia e delle scienze umane|access-date=December 27, 2024}}</ref><ref>{{cite journal | doi=10.15517/rehmlac.v9i1.28189 | title=Il Grande Oriente d'Italia e l'educazione: l'Azione delle logge nelle grandi città (1868–1925) / The Grand Orient of Italy and Education: The lodges and their deeds in big cities (1868–1925) | date=2017 | last1=Xoccato | first1=Demetrio | journal=Revista de Estudios Históricos de la Masonería Latinoamericana y Caribeña | volume=9 }}</ref> Here he knew the Italian socialist and freemason Giovanni Lerda (1853-1927),<ref>{{cite book|url=https://philarchive.org/archive/PASICF|format=PDF|author=Enrico Pasini|language=it|chapter=Il carteggio Peano-Berneri|access-date=December 27, 2024|title=Giuseppe Peano: matematica, cultura e società|author2=Clara Silvia Roero|location=Cuneo, IT|year=2011|publisher=l'Artistica Savigliano|pages=iii+103|oclc=941880941|archive-url=https://web.archive.org/web/20200806110740/https://philarchive.org/archive/PASICF |archive-date=6 August 2020 }} (here: p. 5)</ref> a close collaborator of [[Cesare Lombroso]].

[[File:Mrmrspeano.jpg|thumb|right|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 (art)|Madonna]]''.<ref>[http://www.schoenstatt.co.uk/news2005/luigicrosio.html The man who painted the MTA. Luigi Crosio 1835–1916] {{webarchive|url=https://web.archive.org/web/20080605062417/http://www.schoenstatt.co.uk/news2005/luigicrosio.html |date=5 June 2008 }}. Schoenstatt webpage</ref> In 1886, he began teaching concurrently at the [[Royal Military Academy (Italy)|Royal Military Academy]], and was promoted to Professor First Class in 1889. In that year he published the [[Peano axioms]], a formal foundation for the collection of [[natural number]]s. The next year, the University of Turin also granted him his full professorship. The [[Peano curve]] was published in 1890 as the first example of a [[space-filling curve]] which demonstrated that the unit interval and the unit square have the same [[cardinality]]. Today it is understood to be an early example of what is known as a [[fractal]].

In 1890 Peano founded the journal ''Rivista di Matematica'', which published its first issue in January 1891.<ref>{{cite journal|author=Ziwet, Alexander|title=A New Italian Mathematical Journal|journal=Bull. Amer. Math. Soc.|year=1891|volume=1|issue=2|pages=42–43|url=https://www.ams.org/journals/bull/1891-01-02/S0002-9904-1891-00023-1/|doi=10.1090/s0002-9904-1891-00023-1|doi-access=free}}</ref> In 1891 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 numeral system|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 struck by Peano's innovative logical symbols and after the conference, he retired to the country "to study quietly every word written by him or his disciples".<ref>Russell B., ''Autobiography'', London, NY: Routledge, 1998, p.148. See {{cite book|url=https://books.google.com/books?id=uIKMAgAAQBAJ&pg=PA135 | title=2019 edition |pages=135–136| isbn=978-1-135-22381-6 | last1=Russell | first1=Bertrand | date=2009 | publisher=Routledge }} [https://books.google.com/books?id=uIKMAgAAQBAJ&pg=PA136 p. 136]</ref>

Peano's students [[Mario Pieri]] and [[Alessandro Padoa]] also had papers presented at the philosophy congress. 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 [[mathematical analysis|analysis]], foundations and logic, made many contributions to the teaching of calculus and also contributed to the fields of [[differential equation]]s 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.<ref>[[Hubert Kennedy]] (1980) ''Peano, Life and Works of Giuseppe Peano'', Chapter 6: The ''Formulario Project'', pages 44&ndash;50, Chapter 17: Completion of the ''Formulario'', page 118&ndash;24, [[D. Reidel]] {{ISBN|90-277-1067-8}}</ref>

In 1903 Peano announced his work on an international auxiliary language called ''[[Latino sine flexione]]'' ("[[Latin]] without inflexion," later called Interlingua, and the precursor of the [[Interlingua]] of the [[International Auxiliary Language Association|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. On 3 January 1908, he read a paper to the ''Academia delle Scienze di Torino'' in which 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.<ref>[[Frederick Bodmer|Bodmer, Frederick]] (1944), ''The Loom of Language'', London: George Allen & Unwin Ltd, p.468</ref>

The year 1908 was important 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 favour 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 [[International auxiliary language|auxiliary language]]s, 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).

During the years 1913–1918, Peano published several papers that dealt with the remainder term for various [[numerical integration|numerical quadrature]] formulas, and introduced the [[Peano kernel]].<ref name=numericalMath>{{Cite book| last1=Hämmerlin | first1 = Günther | last2=Hoffmann | first2= Karl-Heinz|title = Numerical Mathematics | url=https://archive.org/details/numericalmathema00hmme_566 | url-access=limited | publisher = Springer | year = 1991 | pages = [https://archive.org/details/numericalmathema00hmme_566/page/n202 192]–194 | isbn = 9780387974941}}</ref>

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 [[myocardial infarction|heart attack]].

==Milestones and honours received==
[[File:Vinadio-IMG_1153.JPG|thumb|Memorial bust of Peano in [[Vinadio]].]]
* 1881: Published first paper.
* 1884: ''Calcolo Differenziale e Principii di Calcolo Integrale''.<ref>{{Cite book |last=Angelo Genocchi |first=Giuseppe Peano |url=http://archive.org/details/calcolodifferen00peangoog |title=Calcolo differenziale e principii di calcolo integrale |date=1884 |publisher=Fratelli Bocca |others=Harvard University |language=Italian}}</ref>
* 1887: ''Applicazioni Geometriche del Calcolo Infinitesimale''.<ref>{{Cite book |last=Giuseppe Peano |url=http://archive.org/details/applicazionigeo00peangoog |title=Applicazioni geometriche del calcolo infinitesimale |date=1887 |publisher=Fratelli Bocca |others=Harvard University |language=Italian}}</ref>
* 1889: Appointed Professor First Class at the Royal Military Academy.
* 1889: ''Arithmetices principia: nova methodo exposita.''<ref>{{Cite book |last=Giuseppe Peano |url=http://archive.org/details/arithmeticespri00peangoog |title=Arithmetices principia: nova methodo |date=1889 |publisher=Fratres Bocca |others=Harvard University |language=Latin}}</ref>
* 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.<ref>{{Cite book |last=Peano |first=Giuseppe |url=http://archive.org/details/lezionidianalis00peangoog |title=Lezioni di analisi infintesimale |date=1893 |publisher=Torino : G. Candeletti |others=Harvard University}}</ref>
* 1895: Promoted to Ordinary Professor.
* 1901: Made Knight of the [[Order of Saints Maurice and Lazarus|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.

==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.

== See also ==
{{Portal|Biography|Philosophy}}
* ''[[Arithmetices principia, nova methodo exposita]]''
* [[Foundations of geometry]]

==References==
{{Reflist}}

==Further reading==
* 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.
* Segre, Michael, 1994. "Peano's Axioms in their Historical Context," ''Archive for History of Exact Sciences'' 48, pp.&nbsp;201–342.
* Ferreirós, José, 2005. "R. Dedekind, Was Sind und Was Sollen die Zahlen? (1888), G. Peano, Arithmetics Principia, Nova Methodo Exposita (1889)". Pag. 613–626 of ''Landmark Writings in Western Mathematics 1640–1940'', ed. I. Grattan-Guinness. Amsterdam, Elsevier, 2005. {{ISBN|0444508716}}

==External links==
{{Commons category}}
{{Wikiquote}}
* {{Gutenberg author | id=37909| name=Giuseppe Peano}}
* {{Internet Archive author |sname=Giuseppe Peano}}
* {{MacTutor Biography|id=Peano}}
* {{MathGenealogy |id=43284}}
* {{cite web | url = https://hubertkennedy.angelfire.com/TwelveArticles.pdf | title = Twelve articles on Giuseppe Peano | author-link = Hubert Kennedy | first = Hubert | last = Kennedy | year = 2002 | publisher = Peremptory Publications | location = San Francisco | access-date =8 April 2012 }} Collection of articles on life and mathematics of Peano (1960s to 1980s).
* [http://mono.eik.bme.hu/~galantai/LSF/fonte.html Instituto Pro Latino Sine Flexione]

{{Authority control}}

{{DEFAULTSORT:Peano, Giuseppe}}
[[Category:1858 births]]
[[Category:1932 deaths]]
[[Category:People from Cuneo]]
[[Category:People from the Kingdom of Sardinia]]
[[Category:19th-century Italian mathematicians]]
[[Category:20th-century Italian mathematicians]]
[[Category:20th-century Italian philosophers]]
[[Category:Linear algebraists]]
[[Category:Constructed language creators]]
[[Category:Knights of the Order of Saints Maurice and Lazarus]]
[[Category:University of Turin alumni]]
[[Category:Academic staff of the University of Turin]]
[[Category:Textbook writers]]
[[Category:Historical linguists]]
[[Category:Linguists from Italy]]
[[Category:19th-century writers in Latin]]
[[Category:Latin-language writers from Italy]]
[[Category:Italian Freemasons]]