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# Francesco Faà di Bruno

The Blessed Francesco Faà di Bruno was an Italian priest and advocate of the poor, as well being a leading mathematician of his era and a noted religious musician. In 1988 he was beatified by Pope John Paul II.[1] He is the eponym of Faà di Bruno's formula.

Life

Early life

Francesco Faà di Bruno

Faà di Bruno was born in Alessandria, then part of the Kingdom of Sardinia, on 29 March 1825. He was of noble birth, being the twelfth and youngest child of the Marchese Luigi Faà di Bruno and the Lady Carolina Sappa de' Milanesi. He was raised in a home marked by happiness, the arts and a concern for the poor arising from the parents' strong Catholic faith.[2]

As a young man, he entered the Royal Army and held, at one time, the rank of Staff Officer. He resigned his commission, and went to Paris, where he did doctoral studies in mathematics under Augustin Cauchy, and Urbain Le Verrier, who both shared in the discovery of the planet Neptune. He was in close contact with the Abbé Moigno and Charles Hermite.

On his return to Turin, he took up the post of Professor of Mathematics at the University there. In recognition of his achievements as a mathematician, the degree of Doctor of Science was conferred on him by the Universities of Paris and Turin.

Social reformer

While carrying out his career responsibilities, Faà di Bruno also became actively invovled in the social outreach to the poor being developed by leading figures of the Catholic Church in Turin. He became a close friend of St. John Bosco.[3] He helped establish refuges for the elderly and the poor. He oversaw the construction of a church in Turin, Our Lady of Suffrage, which was dedicated to the memory of Italian soldiers who had lost their lives in the struggle over Italian Unification.[4]

Priest and Founder

Somewhat late in his life, Faà di Bruno came to feel that pursuing Holy Orders would help him in his religious activities, and commenced the necessary studies in theology. What he found, however, was that the Archbishop of Turin at that time would not accept an older man for ordination, Faà di Bruno being in his late 40's at that time. For centuries, the traditional route for this profession began in a boy's mid-teens.

Faà di Bruno appealed to Pope Pius IX and received his support, finally being ordained at age 51. He founded the Minim Sisters of St. Zita in 1881 to provide help for maids and domestic servants, later expanding its outreach to include others, such as unmarried mothers.[5] With their help, he also established another refuge, one dedicated to taking in prostitutes.

Faà di Bruno died in Turin on 27 March 1888.

Research in mathematics

In addition to some ascetical writings, the composition of some sacred melodies, and the invention of some scientific apparatus, Faà di Bruno made numerous and important contributions to mathematics. Today, he is best known for Faà di Bruno's formula on derivatives of composite functions, although it is now certain that the priority in its discovery and use is of Louis François Antoine Arbogast: Faà di Bruno should be only credited for the deteminant form of this formula.[6] However, his work is mainly related to elimination theory and to the theory of elliptic functions.[7]

He was the author of about forty original articles published in the "Journal de Mathématiques" (edited by Joseph Liouville), Crelle's Journal, "American Journal of Mathematics" (Johns Hopkins University), "Annali di Tortolini", "Les Mondes", "Comptes rendus de l'Académie des sciences", etc.; the first half of an exhaustive treatise on the theory and applications of elliptic functions which he planned to complete in three volumes; "Théorie générale de l'élimination" (Paris, 1859); "Calcolo degli errori" (Turin, 1867), translated into French under the title of "Traité élémentaire du calcul des erreurs" (Paris, 1869); and most important of all, "Théorie des formes binaires" (Paris, 1876), translated into German (Leipzig, 1881). For a list of the memoirs of Faà di Bruno, see the "Catalogue of Scientific Papers of the Royal Society: (London, 1868, 1877, 1891), t. II, vii, and ix.

Among his most noted students were the noted mathematicians Corrado Segre and Giuseppe Peano.

Veneration

The cause for the canonization of Faà di Bruno opened in the early 20th century by the Archdiocese of Turin and he was declared a Servant of God. He was declared Venerable by Pope Paul VI in 1971, and beatified by Pope John Paul II on the centennial of his death in 1988.

See also

Elimination theory

Elliptic functions

Faà di Bruno, for other members of the family

Faà di Bruno's formula

List of Roman Catholic scientist-clerics

Notes

^ Vatican New Service Papal Office for Liturgical Celebrations(Italian)

^ Solari, Patrizia (April 2008), "Beato Francesco Faà di Bruno", [http://www.caritas-ticino.ch/media/rivista/archivio/riv_1004/rivistaonline.htm Caritas Insieme XXVI (1): 44–47

^ Solari

^ Saint of the Day

^ Vatican New Service

^ See the paper of Craik (2005, pp. 233–234): this well written and informative paper details also the works of other earlier scientists.

^ See Tricomi (1962) and various papers in the volume edited by Giacardi (2005): particularly in this later reference it is stated that he introduced the Faà di Bruno's formula in order to deal with problems in elimination theory.

Bibliography

Giacardi, Livia, ed. (2004) (in Italian), Francesco Faà di Bruno. Ricerca scientifica insegnamento e divulgazione (Scientific research teaching and popularization), Studi e fonti per la storia dell'Università di Torino, XII, Torino: Deputazione Subalpina di Storia Patria, pp. 671. A detailed exposition of sources and other documents related to Francesco Faà di Bruno's scientific work, including his teaching and engineering activity.

Giacardi, Livia, ed. (2005) (in Italian and English), L'opera matematica di Francesco Faà di Bruno in Cd-Rom (The Mathematical Works of Francesco Faà di Bruno in Cd-Rom), Collana CD-ROM del Dipartimento di Matematica dell'Università di Torino, Dipartimento di Matematica dell'Univertsità di Torino.

Solari, Patrizia (luglio 2007), "Beato Francesco Faà di Bruno (Blessed Francesco Faà di Bruno)" (in Italian), Caritas Insieme XXV (2): 40–44. This reference and the following one (part two) deal with aspects of the biography of Faà di Bruno other than his scientific achievements.

Tricomi, G. F. (1962), Francesco Faà di Bruno, "Matematici italiani del primo secolo dello stato unitario (Italian mathematicians of the first century of the unitary state)" (in Italian), Memorie dell'Accademia delle Scienze di Torino. Classe di Scienze fisiche matematiche e naturali, series IV I: 120, Zbl 0132.24405. Available from the website of the Società Italiana di Storia delle Matematiche.

References

Arbogast, L.F.A. (1800) (in French), Du calcul des derivations, Strasbourg: Levrault, pp. xxiii+404. Entirely freely available from Google books.

Craik, Alex D.D. (February 2005), "Prehistory of Faà di Bruno's Formula", American Mathematical Monthly 112 (2): 217–234, doi:10.2307/30037410, MR 2121322, Zbl 1088.01008.

Faà di Bruno, F. (1855), "Sullo sviluppo delle funzioni" (in Italian), Annali di Scienze Matematiche e Fisiche 6: 479–480. A well-known paper where Francesco Faà di Bruno presents the two versions of the formula that now bears his name, published in the journal founded by Barnaba Tortolini. Entirely freely available from Google books.

Faà di Bruno, F. (1857), "Note sur une nouvelle formule de calcul differentiel" (in French), The Quarterly Journal of Pure and Applied Mathematics 1: 359–360. Entirely freely available from Google books.

Faà di Bruno, Francesco (1859) (in French), Théorie générale de l'élimination, Paris: Leiber et Faraguet, pp. x+224. Entirely freely available from Google books.

Faà de Bruno, F. (1876) (in French), Théorie des formes binaires, Turin: Librairie Brero, pp. XVI+358, JFM 08.0056.02, archived from the original on 2006-06-23. One of Faà di Bruno most important work, highly praised by Paul Gordan (see his letter to Faà di Bruno at page V).

Johnson, Warren P. (March 2002), "The Curious History of Faà di Bruno's Formula", American Mathematical Monthly 109 (3): 217–234, doi:10.2307/2695352, JSTOR 2695352, MR 1903577, Zbl 1024.01010.

External links

Dell'Aglio, L. (2008), "FAÀ DI BRUNO, Francesco" (in Italian), Enciclopedia Treccani: Dizionario Biografico degli Italiani, retrieved February 2, 2011 (in Italian). The (fairly comprehensive) biographical entry about Francesco Faà di Bruno in the "Dizionario Biografico degli Italiani (Biographical Dictionary of Italians)" section of the Enciclopedia Treccani.

Linehan, P. (1909), "Francesco Faa di Bruno" (in English), Catholic Encyclopedia, Vol. 5, New York: Robert Appleton Company, retrieved February 2, 2011. The original article in the Catholic Encyclopedia whose content was originally included in this entry.

O'Connor, John J.; Robertson, Edmund F., "Francesco Faà di Bruno", MacTutor History of Mathematics archive, University of St Andrews.

Roero, C. S. (May 19, 2005) (in Italian), Francesco Faà di Bruno (29/03/1825 – 27/03/1888), retrieved February 2, 2011. A short biographical sketch, available from the website of Torinoscienza.it.

Ufficio delle Celebrazioni Liturgiche del Sommo Pontefice, ed. (June 27, 2002), "Beatificazione 25 settembre 1988: Franciscus Faà Di Bruno" (in Italian), Beati e Santi del Pontificato di Giovanni Paolo II, retrieved February 2, 2011. The date of his beatification as listed in the Vatican web site.

This article incorporates text from a publication now in the public domain: Herbermann, Charles, ed. (1913). Catholic Encyclopedia. Robert Appleton Company.

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