Giuseppe Peano

Giuseppe Peano (August 27, 1858 – April 20, 1932) was an Italian mathematician and philosopher best known for his contributions to set theory. Peano published over two hundred minor books and papers, most of them on mathematics. He spent most of his life teaching in Turin. This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... August 27 is the 239th day of the year in the Gregorian Calendar (240th in leap years), with 126 days remaining. ... Jump to: navigation, search 1858 is a common year starting on Friday. ... Jump to: navigation, search April 20 is the 110th day of the year in the Gregorian calendar (111th in leap years). ... Jump to: navigation, search 1932 is a leap year starting on a Friday. ... A mathematician is a person whose area of study and research is mathematics. ... A philosopher is a person devoted to studying and producing results in philosophy. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... Jump to: navigation, search Turin (Italian Torino) is a major industrial city in north-western Italy, capital of the Piedmont region, located mainly on the west bank of the Po River. ...

Personal life

Born on a farm near the village of Spinetta in Piedmont, Italy, Peano enrolled at the nearby University of Turin in 1876. He graduated in 1880 with high honours and began his teaching career. Jump to: navigation, search Piedmont is a region of northwestern Italy. ... The University of Turin (Università degli Studi di Torino, UNITO) is the university of Turin in the Piedmont region of north-western Italy. ... 1876 is a leap year starting on Saturday. ... Jump to: navigation, search 1880 was a leap year starting on Thursday (see link for calendar). ...

On July 27, 1887 he married Carola Crosio. He died in Turin, Italy of heart failure on April 20, 1932. Jump to: navigation, search July 27 is the 208th day (209th in leap years) of the year in the Gregorian Calendar, with 157 days remaining. ... Jump to: navigation, search 1887 is a common year starting on Saturday (click on link for calendar). ... Jump to: navigation, search April 20 is the 110th day of the year in the Gregorian calendar (111th in leap years). ... Jump to: navigation, search 1932 is a leap year starting on a Friday. ...

Milestones and honors received

• 1881: first paper published
• 1884: Calcolo Differenziale e Principii di Calcolo Integrale published
• 1887: Applicazioni Geometriche del Calcolo Infinitesimale published
• 1889: appointed Professor First Class at the Royal Military Academy
• 1890: Extraordinary Professor of Infinitesimal Calculus at Turin University
• 1891: became a member of The Academy of Science in Turin
• 1893: Lezioni di Analisi Infinitesimale (2 volumes) published
• 1895: promoted to Ordinary Professor at Turin University
• 1901: became a knight of the Order of Saints Maurizio and Lazzaro.
• 1903: Latino sine flexione announced
• 1905: became a Knight of the Crown of Italy, elected a corresponding member of the Accademia dei Lincei in Rome, the highest honour for an Italian scientist;
• 1908: Formulario mathematico published (fifth and final edition of the Formulario project)
• 1917: became an Officer of the Crown of Italy
• 1921: promoted from Officer to Commendatore of the Crown of Italy

Jump to: navigation, search 1881 was a common year starting on Saturday (see link for calendar). ... 1884 is a leap year starting on Tuesday (click on link to calendar). ... Jump to: navigation, search 1887 is a common year starting on Saturday (click on link for calendar). ... Jump to: navigation, search 1889 was a common year starting on Tuesday (see link for calendar). ... 1890 was a common year starting on Wednesday (see link for calendar). ... Jump to: navigation, search 1891 was a common year starting on Thursday (see link for calendar). ... Jump to: navigation, search 1893 was a common year starting on Sunday (see link for calendar). ... 1895 was a common year starting on Tuesday (see link for calendar). ... Jump to: navigation, search 1901 was a common year starting on Tuesday (see link for calendar). ... Jump to: navigation, search 1903 has the latest occurring solstices and equinoxes for 400 years, because the Gregorian calendar hasnt had a leap year for seven years or a century leap year since 1600. ... Jump to: navigation, search 1905 was a common year starting on Sunday (see link for calendar). ... The Accademia dei Lincei, (literally the Academy of the Lynxes, but also known as the Lincean Academy), is located at the Palazzo Corsini on the Via della Lungara in Rome, Italy. ... Jump to: navigation, search City motto: Senatus Populusque Romanus – SPQR (The Senate and the People of Rome) Founded 21 April 753 BC mythical, 1st millennium BC Region Latium Mayor Walter Veltroni (Left-Wing Democrats) Area  - City Proper  1290 km² Population  - City (2004)  - Metropolitan  - Density (city proper) 2,546,807 almost... Jump to: navigation, search 1908 is a leap year starting on Wednesday (link will take you to calendar). ... Formulario Mathematico (interlingua: Formulation of mathematics) is a book by Giuseppe Peano which expresses fundamental theorems of mathematics in a symbolic language developed by Peano. ... Jump to: navigation, search 1917 was a common year starting on Monday of the Gregorian calendar (see link for calendar) or a common year starting on Tuesday of the Julian calendar. ... Jump to: navigation, search 1921 was a common year starting on Saturday (see link for calendar). ...

Career

Peano started his career as a university assistant at the University of Turin in 1880. He first assisted Enrico D'Ovidio and then Angelo Genocchi, the chair of infinitesimal calculus. Due to Genochii's poor health, Peano took over the teaching of the infinitesimal calculus course within 2 years. Jump to: navigation, search 1880 was a leap year starting on Thursday (see link for calendar). ... For other uses of the term calculus see calculus (disambiguation) Calculus is a central branch of mathematics, developed from algebra and geometry, and built on two major complementary ideas. ...

His first major work, a textbook on calculus, was credited to Genocchi and published in 1884. Three years later, Peano published his first book dealing with mathematical logic. This book was the first to use the modern symbols for the union and intersection of sets. 1884 is a leap year starting on Tuesday (click on link to calendar). ... In set theory and other branches of mathematics, the union of a collection of sets is the set that contains everything that belongs to any of the sets, but nothing else. ... In mathematics, the intersection of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements. ...

In 1886, Peano starting 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. Jump to: navigation, search 1886 is a common year starting on Friday (click on link to calendar) // Events January 18 - Modern field hockey is born with the formation of The Hockey Association in England. ... Jump to: navigation, search 1889 was a common year starting on Tuesday (see link for calendar). ...

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. Space-filling curves or Peano curves are curves, first described by Giuseppe Peano, whose ranges contain the entire 2-dimensional unit square (or the 3-dimensional unit cube). ... 1890 was a common year starting on Wednesday (see link for calendar). ... In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule, i. ... The Mandelbrot set, named after its discoverer, is a famous example of 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. Jump to: navigation, search Formulario Mathematico (interlingua: Formulation of mathematics) is a book by Giuseppe Peano which expresses fundamental theorems of mathematics in a symbolic language developed 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. Jump to: navigation, search 1897 was a common year starting on Friday (see link for calendar). ... The International Congress of Mathematicians (ICM) is the biggest congress in mathematics. ... Jump to: navigation, search Location within Switzerland Zürich [â–¶] (German pronunciation IPA: ; usually spelled Zurich in English) is the largest city in Switzerland (population: 366,145 in 2004; population of urban area: 1,091,732) and capital of the canton of Zürich. ...

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. Jump to: navigation, search 1898 was a common year starting on Saturday (see link for calendar). ... Jump to: navigation, search The binary numeral system represents numeric values using two symbols, typically 0 and 1. ...

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 followers presented papers (using Peano's teachings) at the mathematics conference, but Peano didn't. A resolution was raised on the formation of an "international auxiliary language" that would make the spread of new mathematical (and commercial) ideas easier; Peano fully supported this idea. Jump to: navigation, search The Eiffel Tower has become a symbol of Paris throughout the world. ... The International Congress of Mathematicians (ICM) is the biggest congress in mathematics. ... 1900 is a common year starting on Monday. ... Jump to: navigation, search The International congress of philosophy is a large, international congress of philosophers. ... Jump to: navigation, search Bertrand Russell The Right Honourable Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970), was an influential British logician, philosopher, and mathematician, working mostly in the 20th century. ...

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. Jump to: navigation, search 1901 was a common year starting on Tuesday (see link for calendar). ... Jump to: navigation, search Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. ... In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ... In mathematics, and in particular in vectorial analysis a vector is an arrow pointing from one point to another. ... In mathematics, axiomatization is the process of defining the basic axiomatic systems from which mathematical theories can be derived. ...

In 1903 Peano announced his work on an international auxiliary language called Latino sine flexione ("Latin without flexions," later called Interlingua). 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 a brilliant 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. Jump to: navigation, search 1903 has the latest occurring solstices and equinoxes for 400 years, because the Gregorian calendar hasnt had a leap year for seven years or a century leap year since 1600. ... Latino sine flexione (Latin without inflections) is an auxiliary language invented by Giuseppe Peano, a mathematician in 1903. ... Jump to: navigation, search Latin is an Indo-European language originally spoken in the region around Rome called Latium. ... This article describes the international auxiliary language created by the IALA. For other usages of the term interlingua, see Interlingua (disambiguation). ...

1908 was a big year for Peano. The final, fifth 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. The comments and examples were written in Latino sine flexione which detracted from its appeal to most mathematicians; however, it remains a significant contribution to mathematical literature. Jump to: navigation, search 1908 is a leap year starting on Wednesday (link will take you to calendar). ...

Also in 1908, Peano took over the chair of higher analysis at Turin (this appointment was to last for only two years). He was also 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. Jump to: navigation, search 1908 is a leap year starting on Wednesday (link will take you to calendar). ... The Academia pro Interlingua was an organization dedicated to the promotion of international auxiliary languages, and is associated in particular with Prof. ... Idiom Neutral is an international auxiliary language, published in 1902 by the International Academy of the Universal Language (Akademi Internasional de Lingu Universal) under the leadership of Waldemar Rosenberger, a St. ... Latino sine flexione (Latin without inflections) is an auxiliary language invented by Giuseppe Peano, a mathematician in 1903. ...

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 artificial 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). Jump to: navigation, search 1910 was a common year starting on Saturday (see link for calendar). ... An artificial or constructed language (known colloquially as a conlang among aficionados), is a language whose vocabulary and grammar were specifically devised by an individual or small group, rather than having naturally evolved as part of a culture as with natural languages. ...

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, April 20, 1932, when he suffered a fatal heart attack. Jump to: navigation, search 1925 was a common year starting on Thursday (link will take you to calendar). ... Jump to: navigation, search 1931 is a common year starting on Thursday. ... Jump to: navigation, search April 20 is the 110th day of the year in the Gregorian calendar (111th in leap years). ... Jump to: navigation, search 1932 is a leap year starting on a Friday. ... A myocardial infarction occurs when an atherosclerotic plaque slowly builds up in the inner lining of a coronary artery and then suddenly ruptures, totally occluding the artery and preventing blood flow downstream. ...

"He [Peano] was a man I greatly admired from the moment I met him for the first time in 1900 at a Congress of Philosophy, which he dominated by the exactness of his mind." — Bertrand Russell, 1932

Jump to: navigation, search 1932 is a leap year starting on a Friday. ...

References

• "Peano: Life and Works of Giuseppe Peano" Hubert C. Kennedy

See also

• Peano axioms

In mathematics, the Peano axioms (or Peano postulates) are a set of first-order axioms proposed by Giuseppe Peano which determine the theory of Peano arithmetic (also known as first-order arithmetic). ...

External links

• Biography at the MacTutor archive