Giacinto Morera

Giacinto Morera

Born 18 July 1856(1856-07-18)
Novara
Died 8 February 1909(1909-02-08) (aged 52)
Turin
Nationality Italian
Fields Complex analysis, Linear elasticity.
Institutions University of Genova, Politecnico di Torino
Alma mater University of Turin (1878) (Engineering degree), (1879) (Mathematics degree)
Known for Morera's theorem, Morera stress function
Influenced Complex analysis, theory of elasticity
Notable awards 1896 Corresponding member of the Accademia Nazionale dei Lincei, 1902 resident member of the Accademia delle Scienze di Torino, 1907 national member of the Accademia Nazionale dei Lincei, 1909 corresponding member of the Kharkov Mathematical Society[1]

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

Contents

Biography

Life

He was born in Novara on 18 July 1856, the son of Giacomo Morera and Vittoria Unico.[2] His family was a wealthy one: his father was a rich merchant. Tricomi (1962) states that this occurrence eased him in his studies after the laurea:[3] however, he was an extraordinary hard worker and he widely used this professional skill in his researches.[4] After studying in Turin he went to Pavia, Pisa and Leipzig: after studying in Leipzig he went back to Pavia for a brief period in 1885, and finally in 1886 he went to Genova, living here for the next 15 years. Somigliana (1910, p. 574) writes that in Genova he also married his fellow-citizen Cesira Faà.[5] From 1901[6] to his death he was in Turin: he died of pneumonia on 8 February 1909.[7]

Education and academic career

He earned his laurea in engineering in 1878, and his laurea in mathematics in 1879, both from the Politecnico di Torino:[8] Somgliana (1910a, p. 605) refers that 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 to the courses of Enrico d'Ovidio, Angelo Genocchi and Francesco Siacci: in particular he acknowledged this last one as his master, both in science and in 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 also 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 a 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 a dean and as a rector.[17] In 1901 he was invited to the chair of rational mechanics at University of Turin, a position left open by Vito Volterra.[6] In 1908 he passed to the chair of "Meccanica Superiore" and was elected dean of the Faculty of Sciences, according to Somigliana (1909, p. 191).

Honours

He was member of the Accademia Nazionale dei Lincei (corresponding member in 1896, then national member in 1907[18]) and of the Accademia delle Scienze di Torino (elected on 9 February 1902).[19] Maggi (1910, p. 317) refers also that the Kharkov Mathematical Society elected him corresponding member in the meeting of the society held on 31 October 1909 (Old Calendar), being not aware of his death.

Tracts of his personality and attitudes

Carlo Somigliana was his friend for more than twenty years and colleague from 1901 onward, discussing with him scientific matters almost every day:[20] he describes him as a devoted friend and a precious colleague.[21]

Described as a cheerful hearted man, he was also a witty incisive talker, according to (Somigliana 1910, p. 580), (Somigliana 1910a, p. 610) and (Maggi 1910, p. 319).

Gifted by a sharp and penetrating intelligence,[22] owning an uncommonly clean mind jointly with analytic and critical capabilities,[23] he is also described as being not interested in sciences and other fields outside is own expertise,[24] however being capable and versatile, with the ability to grasp and appreciate every kind of disclosure produced by the human mind.[25] Morera himself, in the inaugural address (Morera 1889, p. 15), after quoting a statement attributed to Peter Guthrie Tait,[26] discloses the reason behind his views:-[25]"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".[27]

According to Somigliana, he was also acknowledged as an honest, loyal and conscientious man,[28] gifted with exquisite qualities of temperament and intellect,[29] whose simple manners earned him affection even when performing the duties of dean and rector at the University of Genoa:[30] Maggi (1910, p. 319) describes him as a man of great moral value, being this the reason of his success in social relationships and in performing his duties as a civil servant. Somigliana[31] remarks also that he had the ability of serenely judging men and facts.[32]

Despite being successful in social relations, he did not cured nor appreciated much appearances, and was not interested in activities other than the teaching and research ones: consequently, he was not well known outside his the circle of his family and relatives and the circle of his colleagues.[29] He did not make a display of himself, careless of being not known by everyone for his true value: his conception of life was a serious one, and he strongly disliked vanity and superficiality.[21]

Again according to Somigliana,[25] his entire life was devoted to a higher unselfish ideal, i.e. scientific research: and Maggi (1910, p. 319) remarks that only his beloved family shared the same attentions and care he reserved to his 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.[33]

—Carlo Somigliana in Somigliana 1909, p. 192

As Somigliana remarks,[29] he was not gifted by a strong inventiveness, meaning also that he never created new theories: this ability was not his main one.[34] He perfected already developed theories:[35] nearly each of his works appear as the natural result of a deep analysis work on theories that have already reached a high degree of perfection,[34] clearly and precisely exposed.[36] He also had an exquisite sense for the applicability of his work, due to his engineering knowledges:[37] he mastered perfectly all known branches of mathematical analysis and their mechanical and physical applications.[38]

He was the author of more than 60 works: fairly complete lists appear in references (Somigliana 1910, pp. 581–583), (Somigliana 1910a, pp. 610–612) and (Maggi 1910, pp. 320–324). This last reference is particularly useful as Maggi classifies Morera's works according to the topics dealt: his classification is basically followed in the following subsections, however using modern terminology.

Complex analysis

Maggi (1910, p. 321) classifies his works on this topics as pertaining to "analytic function theory".[39] His contributions to complex analysis, notably Morera's theorem, first proved in the paper (Morera 1886b),[40] are still the best known part of his scientific research. He wrote eight research papers on this topic: these papers probably inspired the quotation by Carlo Somigliana reported at the beginning of this section.[41]

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.[42] He wrote twelve papers on this topic: the results he obtained in this 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".[43]

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"[44] and "Attrazione dell'elissoide e funzioni armoniche ellissoidali".[45] 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:[46] 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[47] and his unique paper on differential geometry:[48] 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[49] describes once his teaching ability as incisive. However, his teaching activity 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.[50]

See also

Notes

  1. ^ For more precise information about the awarding or this honor, see the "Honours section".
  2. ^ According to the ample commemorative paper (Somigliana 1910, p. 573) and to the shorter one (Somigliana 1910a, p. 605): these papers include also a list of his publications.
  3. ^ Also Somigliana (1910, p. 573) (Somigliana 1910a, p. 605) underlines this fact.
  4. ^ According to Fichera (1979, p. 14) and Somigliana (1909, p. 192), while not gifted by a strong inventiveness, he nevertheless approached many difficult questions, giving original views that simplified considerably the theories he studied.
  5. ^ The same detail is also cited by Somigliana (1910a, p. 605).
  6. ^ a b Note that there is a discrepancy between the content of the source (Somigliana 1909) and of the sources (Somigliana 1910), (Somigliana 1910a), (Tricomi 1962): the first one states that he lived in Genova for 14 years, while the second ones quantify the duration of the same period in 15 years. Considering also that Vito Volterra went to Rome in 1901, the version of the second group of references has been followed.
  7. ^ Tricomi (1962) and also 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 (1910a, p. 605) (see also Somigliana 1910, p. 573) does not say explicitly that he published his work as his first paper (Morera 1880): however, the titles are the same and the dates nearly coincide.
  10. ^ According to Somigliana (1909, p. 191): Somigliana (1910, p. 574) (see also Somigliana 1910a, p. 605) writes also that Francesco Siacci was the one who directed him towards the study of rational mechanics. This fact is also referred by Maggi (1910, p. 317).
  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 couses. However, Somigliana (1910, p. 574) states precisely these dates, names and places, and Maggi (1910, p. 318) states the same names.
  14. ^ Maggi (1910, p. 318) is the only source citing this name.
  15. ^ According to (Somigliana 1910a, p. 605): the "Scuola di Magistero" is a particular University school aimed to the training of teachers.
  16. ^ Maggi (1910, p. 317) writes exactly "Onorevolmente vinto (Won in honorable way)", possibly alluding to a honorable mention awarded to him by the judging commission.
  17. ^ Precisely, he served the University of Genova as a dean for the periods 1891–1892 and 1896–1897, and as rector in the two years following his last three years as a dean, according to (Somigliana 1910, p. 574).
  18. ^ According to the Comitato Nazionale per il IV Centenario della Fondazione dell'Accademia dei Lincei (1603–2003) (2002).
  19. ^ In reference (Cossa & et al. 1902, p. 252) there is a brief description of his election as a resident member, i.e. "socio residente").
  20. ^ According to Somigliana (1909, p. 194). He also complains about the pain of commemorating his dear friend in (Somigliana 1910) and (Somigliana 1910a), however motivated by his aim to make the personality and work of Morera better known.
  21. ^ a b See (Somigliana 1910, p. 573) and (Somigliana 1910a, p. 604).
  22. ^ See (Somigliana 1909, p. 191), (Somigliana 1910, p. 575) and (Maggi 1910, p. 319).
  23. ^ Somigliana (1910, p. 575) states also that in is his mind, confused and incomplete ideas did not find any place: "... nella quale non trovavano mai posto idee vaghe o incomplete."
  24. ^ According to Somigliana (1910, p. 580) (see also Somigliana 1910a, p. 610), this was a consequence of his particular views, and he excluded, almost feared, everything not being complete strictly scientific knowledge.
  25. ^ a b c See (Somigliana 1910, p. 580) and (Somigliana 1910a, p. 610).
  26. ^ "Schivate la scienza popolare, essa è tanto più perniciosa, quanto più pretenziosi sono quelli che la diffondono", as Carlo Somigliana also reports in (Somigliana 1910, p. 580) and (Somigliana 1910a, p. 610). An English translation reads as:-"Beware of popular science, it is as much as pernicious, as pretentious are the ones who spread it".
  27. ^ The exact quote by Morera (1889, p. 15) is:-"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".
  28. ^ See (Somigliana 1909, p. 191), (Somigliana 1910, p. 580) and (Somigliana 1910a, p. 610).
  29. ^ a b c See (Somigliana 1909, p. 194).
  30. ^ Again according to Somigliana (1910, p. 574).
  31. ^ See (Somigliana 1909, p. 194), (Somigliana 1910, p. 580) and (Somigliana 1910a, p. 610).
  32. ^ "Serenità nel giudicare uomini e cose", as Somigliana exactly states.
  33. ^ An English translation reads more or less as follows:-"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 meticolous particulars, but to the 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".
  34. ^ a b See (Somigliana 1910, p. 575).
  35. ^ See (Somigliana 1909, p. 192).
  36. ^ See (Somigliana 1910, p. 577).
  37. ^ According to (Somigliana 1909, p. 194): it is important to recall that his first university studies were in the engineering field, as briefly described in the "Education and academic career" subsection of this entry.
  38. ^ See (Somigliana 1910, p. 579) and (Somigliana 1910a, p. 609).
  39. ^ He precisely names this section "Teoria delle funzioni analitiche".
  40. ^ See also his later paper (Morera 1902), where he defines holomorphic functions using his theorem as a definition, and then derives some interesting consequences.
  41. ^ (Somigliana 1910, p. 578) states:-"Tipiche fra quelle sue numerose note, brevi e concettose, sono alcune che riguardano la definizione di variabile complessa (Typical examples within his numerous brief and pregnant notes, are some of them dealing with the definition of a complex variable)".
  42. ^ He precisely names this section "Equazioni della Dinamica, equazioni alle derivate parziali del primo ordine ed equazioni ai differenziali totali".
  43. ^ An English translation reads as:-"Various topics in mathematical analysis".
  44. ^ Literally, "fundamentals of the theory of the potential function" (Maggi 1910, p. 321).
  45. ^ "Attraction by an ellipsoid and ellipsoidal harmonics" Maggi (1910, p. 322).
  46. ^ 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).
  47. ^ According to Maggi (1910, pp. 321).
  48. ^ According to Maggi (1910, pp. 324).
  49. ^ See (Somigliana 1909, p. 191).
  50. ^ This first edition is the one which (Maggi 1910, p. 324), (Somigliana 1910, p. 612) and (Somigliana 1910a, p. 583) refer to.

Bibliography

References

External links