Formulario mathematico

Formulario Mathematico (Latino sine flexione:^[1] Formulation of mathematics) is a book^[2] by Giuseppe Peano which expresses fundamental theorems of mathematics in a symbolic language developed by Peano. The author was assisted by Giovanni Vailati, Mario Pieri, Alessandro Padoa, Giovanni Vacca, Vincenzo Vivanti, Gino Fano and Cesare Burali-Forti.

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 ∈, ⊂, ∩, ∪ 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, 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!^[3]

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, 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.^[4]

Such a dismissal of the oral tradition in lectures at universities was the undoing of Peano's own teaching career, as explained in chapter 14 of Kennedy's book.

Notes

1. ↑ While Latino sine Flexione was sometimes called Interlingua, it should not be confused with modern Interlingua, developed between 1924 and 1951 by the International Auxiliary Language Association.
2. ↑ There are many editions. Here are two:
   • (French) Published 1901 by Gauthier-Villars, Paris. 230p. OpenLibrary OL15255022W, PDF.
   • (Italian) Published 1960 by Edizione cremonese, Roma. 463p. OpenLibrary OL16587658M.
3. ↑ Kennedy (1980) page 45
4. ↑ quoted by Kennedy (1980), page 66

References

• Ivor Grattan-Guinness (2000) The Search for Mathematical Roots 1870-1940. Princeton University Press.
• H.C. 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 .