Formulario Mathematico is a book by Giuseppe Peano

Giuseppe Peano

Giuseppe Peano was an Italian mathematician, whose work was of philosophical value. 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...

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

Giovanni Vailati

Giovanni Vailati 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 lecture in the history of mechanics there from 1896 to 1899, after working as assistant...

, Mario Pieri

Mario Pieri

Mario Pieri was an Italian mathematician who is known for his work on foundations of geometry.Pieri was born in Lucca, Italy, the son of Pellegrino Pieri and Ermina Luporini. Pellegrino was a lawyer. Pieri began his higher education at University of Bologna where he drew the attention of Salvatore...

, Alessandro Padoa

Alessandro Padoa

Alessandro Padoa 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 notion is truly independent of the other primitive notions...

, Giovanni Vacca

Giovanni Vacca

Giovanni Enrico Eugenio Vacca was an Italian mathematician, Sinologist and historian of science.Vacca studied mathematics and graduated from the University of Genoa in 1897 under the guidance of G. B. Negri. He was a politically active student and was banished for that from Genoa in 1897. He moved...

, Vincenzo Vivanti, Gino Fano

Gino Fano

Gino Fano was an Italian mathematician. He was born in Mantua, Italy and died in Verona, Italy.Fano worked on projective and algebraic geometry; the Fano plane, Fano fibration, Fano surface, and Fano varieties are named for him....

 and Cesare Burali-Forti

Cesare Burali-Forti

Cesare Burali-Forti was an Italian mathematician.He was born in Arezzo, and was an assistant of Giuseppe Peano in Turin from 1894 to 1896, during which time he discovered what came to be called the Burali-Forti paradox of Cantorian set theory. He died in Turin.-Books by C. Burali-Forti:* with R....

.

The Formulario was first published in 1895. The fifth and last edition was published in 1908. Many of the symbols and abbreviations introduced in the book are in common use today. Examples include ∈, ⊂

Subset

In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment...

, ∩

Intersection (set theory)

In mathematics, the intersection of two sets A and B is the set that contains all elements of A that also belong to B , but no other elements....

, ∪

Union (set theory)

In set theory, the union of a collection of sets is the set of all distinct elements in the collection. The union of a collection of sets S_1, S_2, S_3, \dots , S_n\,\! gives a set S_1 \cup S_2 \cup S_3 \cup \dots \cup S_n.- Definition :...

 and A−B.

Kennedy (1980) wrote "the development and use of mathematical logic 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 [are not] editions 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 Latino sine flexione

Latino sine Flexione

Latino sine flexione , or Peano’s Interlingua , is an international auxiliary language invented by the Italian mathematician Giuseppe Peano in 1903. It is a simplified version of Latin, and retains its vocabulary...

, 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

Textbook

A textbook or coursebook is a manual of instruction in any branch of study. Textbooks are produced according to the demands of educational institutions...

, 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

Oral tradition and oral lore is cultural material and traditions transmitted orally from one generation to another. The messages or testimony are verbally transmitted in speech or song and may take the form, for example, of folktales, sayings, ballads, songs, or chants...

 in lecture

Lecture

thumb|A lecture on [[linear algebra]] at the [[Helsinki University of Technology]]A lecture is an oral presentation intended to present information or teach people about a particular subject, for example by a university or college teacher. Lectures are used to convey critical information, history,...

s at universities was the undoing of Peano's own teaching career, as explained in chapter 14 of Kennedy's book.