Giuseppe Peano

Giuseppe Peano
Peanoc. 1910s
Born	(1858-08-27)27 August 1858 Spinetta,Piedmont,Kingdom of Sardinia
Died	20 April 1932(1932-04-20)(aged 73) Turin,Italy
Citizenship	Italian
Alma mater	University of Turin
Known for	Peano axioms Peano curve Peano existence theorem Peano-Jordan measure Peano kernel theorem Peano–Russell notation Latino sine flexione Vector space Peano surface Logicism
Awards	Knight of theOrder of Saints Maurizio and Lazzaro Knight of theCrown of Italy Commendatore of the Crown of Italy Correspondent of theAccademia dei Lincei
Scientific career
Fields	Mathematics Linguistics
Institutions	University of Turin,Accademia dei Lincei
Doctoral advisor	Enrico D'Ovidio
Other academic advisors	Francesco Faà di Bruno
Notable students	Maria Gramegna

Giuseppe Peano(/piˈɑːnoʊ/;Italian:[dʒuˈzɛppepeˈaːno];27 August 1858 – 20 April 1932) was an Italianmathematicianandglottologist.The author of over 200 books and papers, he was a founder ofmathematical logicandset theory,to which he contributed muchnotation.The standardaxiomatizationof thenatural numbersis named thePeano axiomsin his honor. As part of this effort, he made key contributions to the modern rigorous and systematic treatment of the method ofmathematical induction.He spent most of his career teaching mathematics at theUniversity of Turin.He also wrote 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

Aritmetica generale e algebra elementare,1902

Peano was born and raised on a farm at Spinetta, a hamlet now belonging toCuneo,Piedmont,Italy.He attended theLiceo classico CavourinTurin,and enrolled at theUniversity of Turinin 1876, graduating in 1880 with high honours, after which the University employed him to assist firstEnrico D'Ovidio,and thenAngelo Genocchi,the Chair ofcalculus.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 entitledCalcolo differenziale, e principii di calcolo integrale,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 theunionandintersectionof sets appeared for the first time.

Giuseppe Peano and his wife Carola Crosio in 1887

In 1887, Peano married Carola Crosio, the daughter of the Turin-based painterLuigi Crosio,known for painting theRefugium PeccatorumMadonna.In 1886, he began teaching concurrently at theRoyal Military Academy,and was promoted to Professor First Class in 1889. In that year he published thePeano axioms,a formal foundation for the collection ofnatural numbers.The next year, the University of Turin also granted him his full professorship. ThePeano curvewas published in 1890 as the first example of aspace-filling curvewhich demonstrated that the unit interval and the unit square have the samecardinality.Today it is understood to be an early example of what is known as afractal.

In 1890 Peano founded the journalRivista di Matematica,which published its first issue in January 1891.In 1891 Peano started theFormulario 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 firstInternational Congress of Mathematicianswas held inZürich.Peano was a key participant, presenting a paper on mathematical logic. He also started to become increasingly occupied withFormularioto the detriment of his other work.

In 1898 he presented a note to the Academy aboutbinary numerationand 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.

Pariswas the venue for the SecondInternational Congress of Mathematiciansin 1900. The conference was preceded by the FirstInternational Conference of Philosophywhere 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 metBertrand Russelland gave him a copy ofFormulario.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".

Peano's studentsMario PieriandAlessandro Padoaalso 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 ofanalysis,foundations and logic, made many contributions to the teaching of calculus and also contributed to the fields ofdifferential equationsandvector analysis.Peano played a key role in theaxiomatizationof mathematics and was a leading pioneer in the development of mathematical logic. Peano had by this stage become heavily involved with theFormularioproject 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 calledLatino sine flexione( "Latinwithout inflexion, "later called Interlingua, and the precursor of theInterlinguaof theIALA). 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 theAcademia delle Scienze di Torinoin 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.

The year 1908 was important for Peano. The fifth and final edition of theFormularioproject, titledFormulario 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 inLatino 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 ofAcademia pro Interlingua.Having previously createdIdiom Neutral,the Academy effectively chose to abandon it in favour of Peano'sLatino 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 otherauxiliary languages,becoming a revered member of the international auxiliary language movement. He used his membership of theAccademia dei Linceito 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 variousnumerical quadratureformulas, and introduced thePeano kernel.

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 fatalheart attack.

Milestones and honours received

Memorial bust of Peano inVinadio.

• 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.
• 1889:Arithmetices principia: nova methodo exposita.
• 1890: Appointed Extraordinary Professor ofinfinitesimal calculusat theUniversity 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 theOrder of Saints Maurizio and Lazzaro.
• 1903: AnnouncesLatino sine flexione.
• 1905: Made Knight of theOrder of the Crown of Italy.Elected a corresponding member of theAccademia dei LinceiinRome,the highest Italian honour for scientists.
• 1908: Fifth and final edition of theFormulario 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" inJean 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

• Arithmetices principia, nova methodo exposita
• Foundations of geometry

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 Sciences48, pp. 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 ofLandmark Writings in Western Mathematics 1640–1940,ed. I. Grattan-Guinness. Amsterdam, Elsevier, 2005.ISBN0444508716

External links

• Works by Giuseppe PeanoatProject Gutenberg
• Works by or about Giuseppe Peanoat theInternet Archive
• O'Connor, John J.;Robertson, Edmund F.,"Giuseppe Peano",MacTutor History of Mathematics Archive,University of St Andrews
• Giuseppe Peanoat theMathematics Genealogy Project
• Kennedy, Hubert(2002)."Twelve articles on Giuseppe Peano"(PDF).San Francisco: Peremptory Publications.Retrieved8 April2012.Collection of articles on life and mathematics of Peano (1960s to 1980s).
• Instituto Pro Latino Sine Flexione