Giuseppe Peano (; ; 27 August 1858 – 20 April 1932) was an Italian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and glottologist. The author of over 200 books and papers, he was a founder of

mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of forma ...

and

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concern ...

, to which he contributed much notation. The standard

axiomatization In mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contai ...

of the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called '' cardinal ...

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 Mathematical induction is a method for proving that a statement ''P''(''n'') is true for every natural number ''n'', that is, that the infinitely many cases ''P''(0), ''P''(1), ''P''(2), ''P''(3), ... all hold. Informal metaphors help ...

. He spent most of his career teaching mathematics at the

University of Turin The University of Turin (Italian language, Italian: ''Università degli Studi di Torino'', UNITO) is a public university, public research university in the city of Turin, in the Piedmont (Italy), Piedmont region of Italy. It is one of the List ...

. 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, others are in Italian.

Biography

Peano was born and raised on a farm at Spinetta, a hamlet now belonging to

Cuneo Cuneo (; pms, Coni ; oc, Coni/Couni ; french: Coni ) is a city and ''comune'' in Piedmont, Northern Italy, the capital of the province of Cuneo, the fourth largest of Italy’s provinces by area. It is located at 550 metres (1,804 ft) in ...

Piedmont it, Piemontese , population_note = , population_blank1_title = , population_blank1 = , demographics_type1 = , demographics1_footnotes = , demographics1_title1 = , demographics1_info1 = , demographics1_title2 ...

Italy Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical ...

. He attended the Liceo classico Cavour in

Turin Turin ( , Piedmontese language, Piedmontese: ; it, Torino ) is a city and an important business and cultural centre in Northern Italy. It is the capital city of Piedmont and of the Metropolitan City of Turin, and was the first Italian capital ...

, and enrolled at the

in 1876, graduating in 1880 with high honors, after which the University employed him to assist first

Enrico D'Ovidio Enrico D'Ovidio (1842-1933) was an Italian mathematician who is known by his works on geometry. Life and work D'Ovidio, son of a liberal parents involved in the Italian independence movement, studied at the university of Naples The Unive ...

, and then Angelo Genocchi, the Chair of

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...

. 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, 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 In mathematics, the intersection of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously. For example, in Euclidean geometry, when two lines in a plane are not parallel, thei ...

of sets appeared for the first time. Mrmrspeano

In 1887, Peano married Carola Crosio, the daughter of the Turin-based painter

Luigi Crosio Luigi Crosio (1835–1915) was an Italian painter who lived and worked in Turin, Italy. He died in Turin and is recorded as having been born in Alba, but the town of Acqui Terme, a few miles south of Alba, claims Crosio was born there. He attend ...

, known for painting the '' Refugium Peccatorum

Madonna Madonna Louise Ciccone (; ; born August 16, 1958) is an American singer-songwriter and actress. Widely dubbed the " Queen of Pop", Madonna has been noted for her continual reinvention and versatility in music production, songwriting, a ...

''. In 1886, he began teaching concurrently at the 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

s. The next year, the University of Turin also granted him his full professorship. The

Peano curve In geometry, the Peano curve is the first example of a space-filling curve to be discovered, by Giuseppe Peano in 1890. Peano's curve is a surjective, continuous function from the unit interval onto the unit square, however it is not in ...

was published in 1890 as the first example of a

space-filling curve In mathematical analysis, a space-filling curve is a curve whose range contains the entire 2-dimensional unit square (or more generally an ''n''-dimensional unit hypercube). Because Giuseppe Peano (1858–1932) was the first to discover one, ...

which demonstrated that the unit interval and the unit square have the same

cardinality In mathematics, the cardinality of a set is a measure of the number of elements of the set. For example, the set A = \ contains 3 elements, and therefore A has a cardinality of 3. Beginning in the late 19th century, this concept was generalized ...

. Today it is understood to be an early example of what is known as a

fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as ill ...

. 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 The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rena ...

was held in

Zürich , neighboring_municipalities = Adliswil, Dübendorf, Fällanden, Kilchberg, Maur, Oberengstringen, Opfikon, Regensdorf, Rümlang, Schlieren, Stallikon, Uitikon, Urdorf, Wallisellen, Zollikon , twintowns = Kunming, San Francisco Z ...

. 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 Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. Si ...

was the venue for the Second

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 Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, a ...

and gave him a copy of ''Formulario''. Russell was struck by Peano's innovative logical symbols and after the conference he retired in the country "to study quietly every word written by him or his disciples." Peano's students Mario Pieri and

Alessandro Padoa Alessandro Padoa (14 October 1868 – 25 November 1937) was an Italian mathematician and logician, a contributor to the school of Giuseppe Peano. He is remembered for a method for deciding whether, given some formal theory, a new primitive noti ...

had 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 Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...

, foundations and logic, made many contributions to the teaching of calculus and also contributed to the fields of

differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, ...

s and vector analysis. Peano played a key role in the

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 Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...

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.Bodmer, Frederick (1944), ''The Loom of Language'', London: George Allen & Unwin Ltd, p.468 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 Idiom Neutral is an international auxiliary language, published in 1902 by the International Academy of the Universal Language () under the leadership of Waldemar Rosenberger, a St. Petersburg engineer. History The Academy had its origin a ...

, 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 The Accademia dei Lincei (; literally the " Academy of the Lynx-Eyed", but anglicised as the Lincean Academy) is one of the oldest and most prestigious European scientific institutions, located at the Palazzo Corsini on the Via della Lungara in R ...

'' 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 A myocardial infarction (MI), commonly known as a heart attack, occurs when blood flow decreases or stops to the coronary artery of the heart, causing damage to the heart muscle. The most common symptom is chest pain or discomfort which ma ...

Milestones and honors 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 Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of ari ...

at the

. * 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 The Order of the Crown of Italy ( it, Ordine della Corona d'Italia, italic=no or OCI) was founded as a national order in 1868 by King Vittorio Emanuele II, to commemorate the unification of Italy in 1861. It was awarded in five degrees for civi ...

. Elected a corresponding member of the

Rome , established_title = Founded , established_date = 753 BC , founder = King Romulus ( legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption ...

, 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.

References

External links

* * * * * * Collection of articles on life and mathematics of Peano (1960s to 1980s).
Instituto Pro Latino Sine Flexione
{{DEFAULTSORT:Peano, Giuseppe 1858 births 1932 deaths People from Cuneo People from the Kingdom of Sardinia 19th-century Italian mathematicians 20th-century Italian mathematicians 20th-century Italian philosophers Linear algebraists Constructed language creators Knights of the Order of Saints Maurice and Lazarus University of Turin alumni University of Turin faculty Textbook writers Historical linguists Linguists from Italy 19th-century Latin-language writers

Biography

Milestones and honors received

Bibliography

See also

References

Further reading

External links