# Giacinto Morera

Giacinto Morera
Born 18 July 1856
Novara
Died 8 February 1909 (aged 52)
Turin
Nationality Italian
Fields Complex analysis
Linear elasticity.
Institutions University of Genova
Politecnico di Torino
Alma mater University of Turin (Engineering degree, 1878)
(Mathematics degree, 1879)
Known for Morera's theorem
Morera stress function
Notable awards Corresponding member of the Accademia Nazionale dei Lincei (1896)
Resident member of the Accademia delle Scienze di Torino (1902)
National member of the Accademia Nazionale dei Lincei (1907)
Corresponding member of the Kharkov Mathematical Society (1909)[1]

Giacinto Morera (18 July 1856 – 8 February 1909), was an Italian engineer and mathematician. He is known for Morera's theorem in the theory of functions of a complex variables and for his work in the theory of linear elasticity.

## Biography

### Life

He was born in Novara on 18 July 1856, the son of Giacomo Morera and Vittoria Unico.[2] According to Tricomi (1962), his family was a wealthy one, his father being a rich merchant. This occurrence eased him in his studies after the laurea:[3] however, he was an extraordinarily hard worker and he widely used this ability in his researches.[4] After studying in Turin he went to Pavia, Pisa and Leipzig: then he went back to Pavia for a brief period in 1885, and finally he went to Genova in 1886, living here for the next 15 years. While being in Genova he married his fellow-citizen Cesira Faà.[5] From 1901 on to his death he worked in Turin:[6] he died of pneumonia on 8 February 1909.[7]

### Education and academic career

Francesco Siacci, who tutored Giacinto Morera in the early stage of his career.

He earned in 1878 the laurea in engineering and then, in 1879, the laurea in mathematics, both awarded him from the Politecnico di Torino:[8] According to Somigliana (1910a, p. 605), the title of his thesis in the mathematical sciences was: "Sul moto di un punto attratto da due centri fissi colla legge di Newton".[9] In Turin he attended the courses of Enrico d'Ovidio, Angelo Genocchi and especially the ones of Francesco Siacci, who was acknowledged by him as his mentor in science and life.[10] After graduating, he followed several advanced courses: he studied in Pavia from 1881 to 1882[11] under Eugenio Beltrami, Eugenio Bertini[12] and Felice Casorati. In 1883 he was in Pisa under Enrico Betti, Riccardo de Paolis and Ulisse Dini: a year later, he was in Leipzig under Felix Klein, Adolph Mayer and Carl Neumann.[13] In 1885 he went in Berlin in order to follow the lessons of Hermann von Helmholtz, Gustav Kirchhoff, Leopold Kronecker[14] and Karl Weierstrass at the local university: later in the same year, he went back to Italy, briefly working at the University of Pavia as a professor in the then newly established "Scuola di Magistero".[15] In 1886, after passing the required competitive examination by a judging commission,[16] he became professor of rational mechanics at the University of Genova: he lived there for 15 years, serving also as dean and as rector.[17] In 1901 he was called by the University of Turin to hold the chair of rational mechanics, left vacant by Vito Volterra.[6] In 1908 he passed to the chair of "Meccanica Superiore"[18] and was elected dean of the Faculty of Sciences.[19]

### Honours

He was member of the Accademia Nazionale dei Lincei (first elected corresponding member on 18 July 1896, then elected national member on 26 August 1907)[20] and of the Accademia delle Scienze di Torino (elected on 9 February 1902).[21] Maggi (1910, p. 317) refers that also the Kharkov Mathematical Society elected him corresponding member during the meeting of the society held on 31 October 1909 (Old Calendar), being apparently not aware of his death.

### Tracts of his personality and attitudes

Carlo Somigliana, close friend and biographer of Giacinto Morera.

In his commemorative papers, Carlo Somigliana describes extensively Morera's personality:[22] according to him, he was a devoted friend and precious colleague,[23] capable of serenely judging men and facts.[24] On the very personal level, he remembers him s a cheerful person and a witty talker.[25]

His intelligence is described as sharp and penetrating,[26] his mind as uncommonly lucid,[27] himself as possessing analytic and critical abilities and being versatile, capable to grasp and appreciate every kind of manifestation of the human intellect.[28] Nevertheless, Somigliana also states that he was not interested in any scientific or other kind of field outside of his own realm of expertise.[29] Morera (1889, p. 15) himself, in the inaugural address as the rector of the University of Genova, after quoting a statement attributed to Peter Guthrie Tait,[30] revealed the reason behind his views:[28] "In science, the one who has a sound and solid knowledge, even in a narrow field, holds a true strength and he can use it whenever he needs: the one who has only a superficial knowledge, however wide and striking, holds nothing, and indeed he often holds a weakness pushing him towards vanity".[31]

Acknowledged as honest, loyal and conscientious,[32] good-tempered and with a good intellect,[33] his simple manners earned him affection even when performing the duties of dean and rector at the University of Genoa.[34] Also Maggi (1910, p. 319) describes him as a man of high moral value, and ascribes to such qualities the reason of his success in social relations and in performing his duties as a civil servant.

However, despite of being successful in social relations, he did not cured nor appreciated much appearances and was not interested in activities other than teaching and doing research: consequently, he was not well known outside the circle of his family and relatives and the circle of his colleagues.[33] He did not make a display of himself, careless of being not acknowledged by everyone for his true value: he also had a serious conception of life and strongly disliked vanity and superficiality.[23]

According to Somigliana,[28] his entire life was devoted to the higher unselfish ideal of scientific research: and Maggi (1910, p. 319) also remarks that only his beloved family shared the same attentions and cares he reserved to his life–long ideal.

## Work

### Research activity

Una quantità di quistioni egli chiarì, semplificò o perfezionò, portando quasi sempre il contributo di vedute ingegnose ed originali. Talchè la sua produzione scientifica può dirsi critica nel senso più largo e fecondo, cioè non dedicata allo studio di minuziosi particolari, ma alla penetrazione e soluzione delle quistioni più difficili e complicate. Questa tendenza del suo ingegno si rivelò anche in un carattere esteriore di molte sue pubblicazioni, che egli presentò in forma di lavori brevi e concettosi; dei quali poi particolarmente si compiaceva, ed in conformità del suo carattere sincero, la sua compiacenza non si tratteneva dal manifestare apertamente.[35]

According to Somigliana,[33] he was not particularly inventive: he did not create any new theory since this was not his main ability.[36] Instead, he perfected already developed theories:[37] nearly all of his researches appear as the natural result of a deep analysis work on theories that have already reached a high degree of perfection,[36] clearly and precisely exposed.[38] He had an exquisite sense for the applicability of his work, derived from his engineering studies,[39] and mastered perfectly all known branches of mathematical analysis and their mechanical and physical applications.[40]

He authored more than 60 research works: nearly complete lists of his publications are included in the commemorative papers (Somigliana 1910, pp. 581–583), (Somigliana 1910a, pp. 610–612) and (Maggi 1910, pp. 320–324). In particular Maggi (1910, pp. 320–324) classifies Morera's work by assigning each publication to particular research field: this classification is basically adopted in the following subsections.[41]

#### Complex analysis

A curve C in a domain D, as required by the statement of Morera's theorem.

Morera wrote eight research works on complex analysis:[42] the style he used for their writing probably inspired Somigliana the quotation introducing the "Research activity" section.[43] Morera's theorem, probably the best known part of his scientific research, was first proved in the paper (Morera 1886b).[44] The theorem states that if, in the complex plane ℂ, the line integral of a given complex–valued function f satisfies the equation

$\oint_C f(z)\,\mathrm{d}z = 0$

for every closed curve C in a given domain D, then f is holomorphic there.

#### Differential equations

This section includes all his works on the theory of differential equations, ordinary or partial ones: Maggi (1910, p. 320) classifies this contributions as works in the theory of the equations of dynamics, in the theory of first-order partial differential equations and in the theory of exact differential equations.[45] He wrote twelve papers on this topic: the results he obtained in these works are well described by Somigliana (1910, pp. 575–574). In the paper (Morera 1882a) he gives a very brief proof of a transformation formula for the Poisson brackets first proved by Émile Léonard Mathieu, while in the paper (Morera 1882b) he simplifies the proof of a theorem of Francesco Siacci which is substantially equivalent to Lie's third theorem: the paper (Morera 1883b) is concerned with the Pfaff problem, proving a theorem on the minimum number of integrations to be performed in order to solve the problem.

#### Equilibrium of continuous bodies in elasticity theory

Maggi (1910, p. 322) classifies four of his works within the realm of elasticity theory: his contribution are well described by Truesdell & Toupin (1960) and by Ericksen (1960) in their known monographs. The works within this section are perhaps the second best known part of his research, after his contributions to complex analysis.

#### Mathematical analysis

Maggi (1910, p. 322) classifies four of his works under the locution "Questioni varie di Analisi".[46]

#### Potential theory of harmonic functions

His contribution of this topics are classified by Maggi (1910, pp. 321–322) under two sections, named respectively "Fondamenti della teoria della funzione potenziale"[47] and "Attrazione dell'elissoide e funzioni armoniche ellissoidali".[48] The work Morera (1906) deals with the definition and properties of ellipsoidal harmonics and the related Lamé functions.

#### Rational mechanics and mathematical physics

Maggi (1910, pp. 322) includes in this class twelve works:[49] his first published work (Morera 1880) is included among them.

#### Varia: algebraic analysis and differential geometry

This section includes the only two papers of Morera on the subject of algebraic analysis[50] and his unique paper on differential geometry:[51] they are, respectively, the papers (Morera 1883a), (Morera 1886c) and (Morera 1886a).

### Teaching activity

References (Somigliana 1910), (Somigliana 1910a) and (Maggi 1910) do not say much about the teaching activity of Giacinto Morera: Somigliana[52] describes once his teaching ability as incisive. However, his teaching is also testified by the litographed lecture notes (Morera 1903–1904): according to the OPAC, this book had two editions, the first one being in 1901–1902.[53]

## Notes

1. ^ For more precise information about the awarding or this honor, see the "Honours section".
2. ^ According to Somigliana (1910, p. 573; 1910a, p. 605): these commemorations include also a list of Morera's published works.
3. ^ According to Tricomi (1962) and to Somigliana (1910, p. 573; 1910a, p. 605).
4. ^ According to Fichera (1979, p. 14) and Somigliana (1909, p. 192), while not particularly inventive, he nevertheless approached many difficult questions, introducing original views that simplified considerably the theories he worked on.
5. ^ See (Somigliana 1910, p. 574) and (Somigliana 1910a, p. 605)
6. ^ a b There is a discrepancy between the statement of source (Somigliana 1909) and the ones of sources (Somigliana 1910), (Somigliana 1910a), (Tricomi 1962): the former one refers that he lived in Genova for 14 years, while the others quantify the duration of the same period as 15 years. The version of the second group of references has been adopted, also on considering that Vito Volterra went to Rome in 1901.
7. ^ Tricomi (1962) and Somigliana (1910a, pp. 605–606) refer that he died in few days, notwithstanding his strong constitution.
8. ^ According to Tricomi (1962) and Somigliana (1910a, p. 605).
9. ^ "On the motion of a point attracted by two fixed centers according to Newton's law". Somigliana (1910, p. 573 and 1910a, p. 605) does not say if it was published as his first paper (Morera 1880): however, the title is the same and the dates nearly coincide.
10. ^ According to Somigliana (1909, p. 191), who uses precisely the Italian respectful title "maestro". Somigliana (1910, p.574 and 1910a, p. 605) and Maggi (1910, p. 317) refer also that it was Francesco Siacci who guided Morera towards the study of rational mechanics.
11. ^ According to (Somigliana 1910, p. 573) and (Somigliana 1910a, p. 605).
12. ^ Somigliana (1910, p. 574) reports "Eugenio Berbini" (see also Somigliana 1910a, p. 605) which is obviously a typo.
13. ^ According to reference (Somigliana 1909, p. 191). Since Adolph Mayer and Felix Klein were teaching in universities outside Leipzig, it is not clear from the reference if the courses Morera attended to in Germany were privately held or were advanced university courses. Nevertheless, Somigliana (1910, p. 574) states precisely these dates, names and places, as does Maggi (1910, p. 318).
14. ^ Only Maggi (1910, p. 318) cites Kronecker as one of his teachers.
15. ^ According to Somigliana (1910a, p. 605). The "Scuola di Magistero", literally "Teaching School", was a particular University school aimed to the training of teachers.
16. ^ Maggi (1910, p. 317) states that the examination was "onorevolmente vinto" which literally means "won in honorable way", perhaps alluding to a honorable mention awarded to him by the examining commission.
17. ^ Precisely, according to (Somigliana 1910, p. 574) he served the University of Genova as dean for the periods 1891–1892 and 1896–1897, and as rector in the two years following his last dean mandate.
18. ^ "Higher Mechanics": the locution identifies an advanced course on rational mechanics.
19. ^ (Somigliana 1909, p. 191).
20. ^ According to the yearbook of the academy, p. 494.
21. ^ Cossa (1902, p. 252) also describes briefly his election ceremony to resident member, i.e. "socio residente".
22. ^ Somigliana (1909, p. 194) states that they were friends for more than twenty years and also colleagues from 1901 onward, talking about their scientific researches almost every day. In (Somigliana 1910) and (Somigliana 1910a) he complains about the pain of commemorating him, nevertheless aiming to do this in order to widespread the knowledge of his personality and work.
23. ^ a b See (Somigliana 1910, p. 573) and (Somigliana 1910a, p. 604).
24. ^ See (Somigliana 1909, p. 194), (Somigliana 1910, p. 580) and (Somigliana 1910a, p. 610). Somigliana exactly states that he possessed "Serenità nel giudicare uomini e cose".
25. ^ According to Somigliana (1910, p. 580; 1910a, p. 610) and Maggi (1910, p. 319).
26. ^ See (Somigliana 1909, p. 191), (Somigliana 1910, p. 575) and (Maggi 1910, p. 319).
27. ^ Somigliana (1910, p. 575) goes further stating also that "(nella sua mente) non trovavano mai posto idee vaghe o incomplete" (English translation: "(in is his mind) confused and incomplete ideas did not find any place").
28. ^ a b c See (Somigliana 1910, p. 580) and (Somigliana 1910a, p. 610).
29. ^ This was a consequence of his particular opinions, again according to Somigliana (1910, p.580; 1910a, p. 610): he excluded, and almost feared, everything not being classifiable as complete strictly scientific knowledge.
30. ^ "Schivate la scienza popolare, essa è tanto più perniciosa, quanto più pretenziosi sono quelli che la diffondono" (English translation: "Beware of popular science, it is as much as pernicious, as pretentious are the ones who spread it"), as also reported by Somigliana (1910, p. 580; 1910a, p. 610).
31. ^ The exact words of Morera (1889, p. 15) are:-"Nella scienza chi ha cognizioni salde e profonde, in un campo anche ristretto, possiede una vera forza e all'uopo sa giovarsene; chi invece ha solo cognizioni superficiali, anche molto estese ed appariscenti, possiede nulla, anzi spesso ha in sè un elemento di debolezza, che lo sospinge alla vanità".
32. ^ See (Somigliana 1909, p. 191), (Somigliana 1910, p. 580) and (Somigliana 1910a, p. 610).
33. ^ a b c See (Somigliana 1909, p. 194).
34. ^ Again according to Somigliana (1910, p. 574).
35. ^ (English translation) "He cleared, simplified or perfected, a number of questions, bringing almost always the (personal) contribution of ingenious and original views. Therefore his scientific production can be defined a critical review in the wider, prolific sense, not aimed to the study of minutious particulars, but to the deep understanding and solution of the most difficult and complex questions. This tendency of his skill revealed itself in the formal character of many of his publications, that he presented in the form of brief, pregnant works; he was particularly satisfied of them, and according to his sincere nature, he did not refrain to manifest his satisfaction frankly".
36. ^ a b See (Somigliana 1910, p. 575).
37. ^ See (Somigliana 1909, p. 192).
38. ^ See (Somigliana 1910, p. 577).
39. ^ According to Somigliana (1909, p. 194), his first university studies were in the field of engineering, as briefly detailed in the "Education and academic career" subsection of this entry.
40. ^ See (Somigliana 1910, p. 579) and (Somigliana 1910a, p. 609).
41. ^ However, Maggi's terminology is not strictly followed: a modern terminology is used when needed in order to ease the comprehension.
42. ^ According to Maggi (1910, p. 321)'s classification, these works belong to "analytic function theory" i.e. "Teoria delle funzioni analitiche".
43. ^ According to Somigliana (1910, p. 578) himself, "Tipiche fra quelle sue numerose note, brevi e concettose, sono alcune che riguardano la definizione di variabile complessa", i.e. (English translation) "Typical examples of his numerous brief and pregnant notes, are some dealing with the definition of a complex variable".
44. ^ Burckel (1979, p. 188) gives a short account of the history of the theorem, and refers also to the later paper (Morera 1902). There Morera defines holomorphic functions using his theorem, and then derives some interesting consequences.
45. ^ He precisely names this section "Equazioni della Dinamica, equazioni alle derivate parziali del primo ordine ed equazioni ai differenziali totali".
46. ^ An English translation reads as:-"Various topics in mathematical analysis".
47. ^ Literally, "fundamentals of the theory of the potential function" (Maggi 1910, p. 321).
48. ^ "Attraction by an ellipsoid and ellipsoidal harmonics" Maggi (1910, p. 322).
49. ^ He classifies those works exactly as "Questioni varie di Meccanica e di Fisica matematica (Various topics in Mechanics and Mathematical Physics)" (Maggi 1910, p. 321).
50. ^ According to Maggi (1910, pp. 321).
51. ^ According to Maggi (1910, pp. 324).
52. ^ See (Somigliana 1909, p. 191).
53. ^ This first edition is the one which (Maggi 1910, p. 324), (Somigliana 1910, p. 612) and (Somigliana 1910a, p. 583) refer to.