''Formulario Mathematico'' (

Latino sine flexione Latino sine flexione ("Latin without inflections"), Interlingua de Academia pro Interlingua (IL de ApI) or Peano's Interlingua (abbreviated as IL) is an international auxiliary language compiled by the Academia pro Interlingua under the chairmansh ...

: ''Formulary for Mathematics'') is a book by

Giuseppe Peano Giuseppe Peano (; ; 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 notati ...

which expresses fundamental theorems of mathematics in a symbolic language developed by Peano. The author was assisted by

Giovanni Vailati Giovanni Vailati (24 April 1863 – 14 May 1909) was an Italian proto-analytic philosopher, historian of science, and mathematician. Life Vailati was born in Crema, Lombardy, and studied engineering at the University of Turin. He went on to ...

Mario Pieri Mario Pieri (22 June 1860 – 1 March 1913) was an Italian mathematician who is known for his work on foundations of geometry. Biography Pieri was born in Lucca, Italy, the son of Pellegrino Pieri and Ermina Luporini. Pellegrino was a lawyer. Pie ...

, Alessandro Padoa, Giovanni Vacca,

Vincenzo Vivanti Vincenzo is an Italian male given name, derived from the Latin name Vincentius (the verb ''vincere'' means to win or to conquer). Notable people with the name include: Art * Vincenzo Amato (born 1966), Italian actor and sculptor * Vincenzo Bel ...

Gino Fano Gino Fano (5 January 18718 November 1952) was an Italians, Italian mathematician, best known as the founder of finite geometry. He was born to a wealthy Jewish family in Mantua, in Italy and died in Verona, also in Italy. Fano made various contr ...

and

Cesare Burali-Forti Cesare Burali-Forti (13 August 1861 – 21 January 1931) was an Italian mathematician, after whom the Burali-Forti paradox is named. He was a prolific writer, with 180 publications. Biography Burali-Forti was born in Arezzo, and he obtained hi ...

. The ''Formulario'' was first published in 1894. The fifth and last edition was published in 1908.

Nicolas Bourbaki Nicolas Bourbaki () is the collective pseudonym of a group of mathematicians, predominantly French alumni of the École normale supérieure (Paris), École normale supérieure (ENS). Founded in 1934–1935, the Bourbaki group originally intende ...

described Peano's notation in the ''Formulario'' as "following current mathematical usage, and introducing many well-chosen abbreviating symbols, his language succeeded moreover in being fairly readable, ..."

(1968) ''Elements of Mathematics – Theory of Sets'', page 306, Addison-Wesley

Hubert Kennedy Hubert Collings Kennedy (born March 6, 1931) is an American author and mathematician. Career Kennedy was born March 6, 1931, in Polk County, Florida, and studied mathematics at several universities. From 1961 he was a professor of mathematics, w ...

(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 wrote "the development and use of

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

is the guiding motif of the project". He also explains the variety of Peano's publication under the title: :the five editions of the ''Formulario'' re noteditions in the usual sense of the word. Each is essentially a new elaboration, although much material is repeated. Moreover, the title and language varied: the first three, titled ''Formulaire de Mathématiques'', and the fourth, titled, ''Formulaire Mathématique'', were written in French, while

, Peano's own invention, was used for the fifth edition, titled ''Formulario Mathematico''. ... Ugo Cassina lists no less than twenty separately published items as being parts of the 'complete' ''Formulario''! Peano believed that students needed only precise statement of their lessons. He wrote: :Each professor will be able to adopt this ''Formulario'' as a

textbook A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions, but also of learners ( ...

, for it ought to contain all theorems and all methods. His teaching will be reduced to showing how to read the formulas, and to indicating to the students the theorems that he wishes to explain in his course. Such a dismissal of the

oral tradition Oral tradition, or oral lore, is a form of human communication in which knowledge, art, ideas and culture are received, preserved, and transmitted orally from one generation to another.Jan Vansina, Vansina, Jan: ''Oral Tradition as History'' (19 ...

in lectures at universities was the undoing of Peano's own teaching career.

Notes

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References

Ivor Grattan-Guinness Ivor Owen Grattan-Guinness (23 June 1941 – 12 December 2014) was a historian of mathematics and logic. Life Grattan-Guinness was born in Bakewell, England; his father was a mathematics teacher and educational administrator. He gained his ...

(2000) ''The Search for Mathematical Roots 1870-1940''.

Princeton University Press Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial ...

. 1895 non-fiction books 1908 non-fiction books Mathematics books Mathematical terminology Mathematical logic Mathematical symbols