Giuseppe Peano (/piˈɑːnoʊ/;Italian: [dʒuˈzɛppe peˈaːno]; 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 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. 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.
Giuseppe Peano | |
|---|---|
 Peano c. 1910s | |
| Born | 27 August 1858 Spinetta, Piedmont, Kingdom of Sardinia |
| Died | 20 April 1932 (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 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 |
| 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 |
Biography
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. 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.
Peano joined Freemasonry. It is not known where he was initiated, but on December 24, 1885, he was affiliated as Master in the "Dante Alighieri" Masonic Lodge in Turin. Here he knew the Italian socialist and freemason Giovanni Lerda (1853-1927), a close collaborator of Cesare Lombroso.
In 1887, Peano married Carola Crosio, the daughter of the Turin-based painter Luigi Crosio, known for painting the Refugium Peccatorum Madonna. In 1886, he began teaching concurrently at the , 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 numbers. 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. 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 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".
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 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, and the precursor of the 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. 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.
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 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).
During the years 1913–1918, Peano published several papers that dealt with the remainder term for various numerical quadrature formulas, and introduced the Peano 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 fatal heart attack.
Milestones and honours received
- 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 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.
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
- Arithmetices principia, nova methodo exposita
- Foundations of geometry
References
- "Peano". Random House Webster's Unabridged Dictionary.
- Genocchi, Angelo (1884). Calcolo differenziale, e principii di calcolo integrale. Fratelli Bocca; pubblicato con aggiunte dal Dr. Giuseppe Peano (published with additions by Dr. Giuseppe Peano)
{{cite book}}: CS1 maint: postscript (link) - Gouvêa, Fernando Q. (11 May 2011). "Review of Giuseppe Peano: Between Mathematics and Logic edited by Fulvia Skof". MAA Reviews, Mathematical Association of America.
- Richard N. Aufmann; Joanne Lockwood (29 January 2010). Intermediate Algebra: An Applied Approach. Cengage Learning. p. 10. ISBN 978-1-4390-4690-6.
- Vittorio Gnocchini, L’Italia dei Liberi Muratori, Ed.Erasmo, 2005, p.213. As quoted in "Giuseppe Peano". Accademia di filosofia e delle scienze umane. Retrieved 27 December 2024.
- Xoccato, Demetrio (2017). "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)". Revista de Estudios Históricos de la Masonería Latinoamericana y Caribeña. 9. doi:10.15517/rehmlac.v9i1.28189.
- Enrico Pasini; Clara Silvia Roero (2011). "Il carteggio Peano-Berneri". Giuseppe Peano: matematica, cultura e società (in Italian). Cuneo, IT: l'Artistica Savigliano. pp. iii+103. OCLC 941880941. Archived from the original (PDF) on 6 August 2020. Retrieved 27 December 2024. (here: p. 5)
- The man who painted the MTA. Luigi Crosio 1835–1916 Archived 5 June 2008 at the Wayback Machine. Schoenstatt webpage
- Ziwet, Alexander (1891). "A New Italian Mathematical Journal". Bull. Amer. Math. Soc. 1 (2): 42–43. doi:10.1090/s0002-9904-1891-00023-1.
- Russell B., Autobiography, London, NY: Routledge, 1998, p.148. See Russell, Bertrand (2009). 2019 edition. Routledge. pp. 135–136. ISBN 978-1-135-22381-6. p. 136
- Hubert Kennedy (1980) Peano, Life and Works of Giuseppe Peano, Chapter 6: The Formulario Project, pages 44–50, Chapter 17: Completion of the Formulario, page 118–24, D. Reidel ISBN 90-277-1067-8
- Bodmer, Frederick (1944), The Loom of Language, London: George Allen & Unwin Ltd, p.468
- Hämmerlin, Günther; Hoffmann, Karl-Heinz (1991). Numerical Mathematics. Springer. pp. 192–194. ISBN 9780387974941.
- Angelo Genocchi, Giuseppe Peano (1884). Calcolo differenziale e principii di calcolo integrale (in Italian). Harvard University. Fratelli Bocca.
- Giuseppe Peano (1887). Applicazioni geometriche del calcolo infinitesimale (in Italian). Harvard University. Fratelli Bocca.
- Giuseppe Peano (1889). Arithmetices principia: nova methodo (in Latin). Harvard University. Fratres Bocca.
- Peano, Giuseppe (1893). Lezioni di analisi infintesimale. Harvard University. Torino : G. Candeletti.
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. 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
- Works by Giuseppe Peano at Project Gutenberg
- Works by or about Giuseppe Peano at the Internet Archive
- O'Connor, John J.; Robertson, Edmund F., "Giuseppe Peano", MacTutor History of Mathematics Archive, University of St Andrews
- Giuseppe Peano at the Mathematics Genealogy Project
- Kennedy, Hubert (2002). "Twelve articles on Giuseppe Peano" (PDF). San Francisco: Peremptory Publications. Retrieved 8 April 2012. Collection of articles on life and mathematics of Peano (1960s to 1980s).
- Instituto Pro Latino Sine Flexione
Giuseppe Peano p i ˈ ɑː n oʊ Italian dʒuˈzɛppe peˈaːno 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 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 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 Giuseppe PeanoPeano c 1910sBorn 1858 08 27 27 August 1858 Spinetta Piedmont Kingdom of SardiniaDied20 April 1932 1932 04 20 aged 73 Turin ItalyCitizenshipItalianAlma materUniversity of TurinKnown forPeano axioms Peano curve Peano existence theorem Peano Jordan measure Peano kernel theorem Peano Russell notation Latino sine flexione Vector space Peano surface LogicismAwardsKnight 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 LinceiScientific careerFieldsMathematics LinguisticsInstitutionsUniversity of Turin Accademia dei LinceiDoctoral advisorEnrico D OvidioOther academic advisorsFrancesco Faa di BrunoNotable studentsMaria GramegnaBiographyAritmetica 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 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 Peano joined Freemasonry It is not known where he was initiated but on December 24 1885 he was affiliated as Master in the Dante Alighieri Masonic Lodge in Turin Here he knew the Italian socialist and freemason Giovanni Lerda 1853 1927 a close collaborator of Cesare Lombroso 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 In 1886 he began teaching concurrently at the 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 numbers 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 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 Zurich 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 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 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 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 and the precursor of the 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 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 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 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 During the years 1913 1918 Peano published several papers that dealt with the remainder term for various numerical quadrature formulas and introduced the Peano 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 fatal heart attack Milestones and honours receivedMemorial bust of Peano in Vinadio 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 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 BibliographyPeano s writings in English translation1889 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 amp Unwin See alsoBiography portalPhilosophy portalArithmetices principia nova methodo exposita Foundations of geometryReferences Peano Random House Webster s Unabridged Dictionary Genocchi Angelo 1884 Calcolo differenziale e principii di calcolo integrale Fratelli Bocca pubblicato con aggiunte dal Dr Giuseppe Peano published with additions by Dr Giuseppe Peano a href wiki Template Cite book title Template Cite book cite book a CS1 maint postscript link Gouvea Fernando Q 11 May 2011 Review of Giuseppe Peano Between Mathematics and Logic edited by Fulvia Skof MAA Reviews Mathematical Association of America Richard N Aufmann Joanne Lockwood 29 January 2010 Intermediate Algebra An Applied Approach Cengage Learning p 10 ISBN 978 1 4390 4690 6 Vittorio Gnocchini L Italia dei Liberi Muratori Ed Erasmo 2005 p 213 As quoted in Giuseppe Peano Accademia di filosofia e delle scienze umane Retrieved 27 December 2024 Xoccato Demetrio 2017 Il Grande Oriente d Italia e l educazione l Azione delle logge nelle grandi citta 1868 1925 The Grand Orient of Italy and Education The lodges and their deeds in big cities 1868 1925 Revista de Estudios Historicos de la Masoneria Latinoamericana y Caribena 9 doi 10 15517 rehmlac v9i1 28189 Enrico Pasini Clara Silvia Roero 2011 Il carteggio Peano Berneri Giuseppe Peano matematica cultura e societa in Italian Cuneo IT l Artistica Savigliano pp iii 103 OCLC 941880941 Archived from the original PDF on 6 August 2020 Retrieved 27 December 2024 here p 5 The man who painted the MTA Luigi Crosio 1835 1916 Archived 5 June 2008 at the Wayback Machine Schoenstatt webpage Ziwet Alexander 1891 A New Italian Mathematical Journal Bull Amer Math Soc 1 2 42 43 doi 10 1090 s0002 9904 1891 00023 1 Russell B Autobiography London NY Routledge 1998 p 148 See Russell Bertrand 2009 2019 edition Routledge pp 135 136 ISBN 978 1 135 22381 6 p 136 Hubert Kennedy 1980 Peano Life and Works of Giuseppe Peano Chapter 6 The Formulario Project pages 44 50 Chapter 17 Completion of the Formulario page 118 24 D Reidel ISBN 90 277 1067 8 Bodmer Frederick 1944 The Loom of Language London George Allen amp Unwin Ltd p 468 Hammerlin Gunther Hoffmann Karl Heinz 1991 Numerical Mathematics Springer pp 192 194 ISBN 9780387974941 Angelo Genocchi Giuseppe Peano 1884 Calcolo differenziale e principii di calcolo integrale in Italian Harvard University Fratelli Bocca Giuseppe Peano 1887 Applicazioni geometriche del calcolo infinitesimale in Italian Harvard University Fratelli Bocca Giuseppe Peano 1889 Arithmetices principia nova methodo in Latin Harvard University Fratres Bocca Peano Giuseppe 1893 Lezioni di analisi infintesimale Harvard University Torino G Candeletti Further readingGillies 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 201 342 Ferreiros Jose 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 0444508716External linksWikimedia Commons has media related to Giuseppe Peano Wikiquote has quotations related to Giuseppe Peano Works by Giuseppe Peano at Project Gutenberg Works by or about Giuseppe Peano at the Internet Archive O Connor John J Robertson Edmund F Giuseppe Peano MacTutor History of Mathematics Archive University of St Andrews Giuseppe Peano at the Mathematics Genealogy Project Kennedy Hubert 2002 Twelve articles on Giuseppe Peano PDF San Francisco Peremptory Publications Retrieved 8 April 2012 Collection of articles on life and mathematics of Peano 1960s to 1980s Instituto Pro Latino Sine Flexione
