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 variable 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.According to Somigliana (1910, p. 573; 1910a, p. 605): these commemorations include also a list of Morera's published works. According to , his family was a wealthy one, his father being a rich merchant. This occurrence eased him in his studies after the laurea:According to and to Somigliana (1910, p. 573; 1910a, p. 605). however, he was an extraordinarily hard worker and he widely used this ability in his researches.According to and , while not particularly inventive, he nevertheless approached many difficult questions, introducing original views that simplified considerably the theories he worked on. 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 Genoa in 1886, living here for the next 15 years. While in Genoa, he married his fellow-citizen Cesira Faà.See and From 1901 on to his death he worked in Turin:There is a discrepancy between the statement of source and the ones of sources , , : the former one refers that he lived in Genoa 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. he died of pneumonia on 8 February 1909. and refer that he died in few days, notwithstanding his strong constitution.
Education and academic career
He earned in 1878 the laurea in engineering and then, in 1879, the laurea in mathematics, both awarded him from the Polytechnic University of Turin:According to and . According to , the title of his thesis in the mathematical sciences was: "Sul moto di un punto attratto da due centri fissi colla legge di Newton"."On the motion of a point attracted by two fixed centres according to Newton's law". Somigliana (1910, p. 573 and 1910a, p. 605) does not say if it was published as his first paper : however, the title is the same and the dates nearly coincide. In Turin he attended the courses held by Enrico d'Ovidio, Angelo Genocchi and particularly the ones held by Francesco Siacci: later in his life, Morera acknowledged Siacci as his mentor in scientific research and life.According to , who uses precisely the Italian respectful title "maestro". Somigliana (1910, p.574 and 1910a, p. 605) and refer also that it was Francesco Siacci who guided Morera towards the study of rational mechanics. After graduating, he followed several advanced courses: he studied in Pavia from 1881 to 1882According to and . under Eugenio Beltrami, Eugenio Bertini reports "Eugenio Berbini" (see also ) which is obviously a typo. 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.According to reference . Since Adolph Mayer and Felix Klein were teaching in universities outside Leipzig, it is not clear from the reference if the courses Morera attended in Germany were privately held or were advanced university courses. Nevertheless, states precisely these dates, names and places, as does . In 1885 he went in Berlin in order to follow the lessons of Hermann von Helmholtz, Gustav Kirchhoff, Leopold KroneckerOnly cites Kronecker as one of his teachers. 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".According to . The "Scuola di Magistero", literally "Teaching School", was a particular University school aimed to the training of teachers. In 1886, after passing the required competitive examination by a judging commission, 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. he became professor of rational mechanics at the University of Genoa: he lived there for 15 years, serving also as dean and as rector.Precisely, according to he served the University of Genoa as dean for the periods 1891–1892 and 1896–1897, and as rector in the two years following his last dean mandate. In 1901 he was called by the University of Turin to hold the chair of rational mechanics, left vacant by Vito Volterra. In 1908 he passed to the chair of "Meccanica Superiore""Higher Mechanics": the locution identifies an advanced course on rational mechanics. and was elected dean of the Faculty of Sciences..
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)According to the yearbook of the academy, p. 494. and of the Accademia delle Scienze di Torino (elected on 9 February 1902).Cossa (1902, p. 252) also describes briefly his election ceremony to resident member, i.e. "socio residente". 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
In his commemorative papers, Carlo Somigliana describes extensively Morera's personality: states that they were friends for more than twenty years and also colleagues from 1901 onward, talking about their scientific research almost every day. In and he complains about the pain of commemorating him, nevertheless aiming to do this in order to spread the knowledge of his personality and work. according to him, he was a devoted friend and precious colleague,See and . capable of serenely judging men and facts.See , and . Somigliana exactly states that he possessed "Serenità nel giudicare uomini e cose". On the very personal level, he remembers him as a cheerful person and a witty talker.According to Somigliana (1910, p. 580; 1910a, p. 610) and .
His intelligence is described as sharp and penetrating,See , and . his mind as uncommonly lucid, 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"). himself as possessing analytic and critical abilities and being versatile, capable to grasp and appreciate every kind of manifestation of the human intellect.See and . Nevertheless, Somigliana also states that he was not interested in any scientific or other kind of field outside of his own realm of expertise.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. himself, in the inaugural address as the rector of the University of Genoa, after quoting a statement attributed to Peter Guthrie Tait,"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). revealed the reason behind his views: "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".The exact words of 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".
Acknowledged as honest, loyal and conscientious,See , and . good-tempered and with a good intellect,See . his simple manners earned him affection even when performing the duties of dean and rector at the University of Genoa.Again according to . Also 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 being successful in social relations, he did not care for, nor appreciate, 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. He did not make a display of himself, careless of not being acknowledged by everyone for his true value: he also had a serious conception of life and strongly disliked vanity and superficiality.
According to Somigliana, his entire life was devoted to the higher unselfish ideal of scientific research: and also remarks that only his beloved family shared the same attentions and cares he reserved for his lifelong ideal.
Work
Research activity
According to Somigliana, he was not particularly inventive: he did not create any new theory since this was not his main ability.See . Instead, he perfected already developed theories:See . 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, clearly and precisely exposed.See . He had an exquisite sense for the applicability of his work, derived from his engineering studies,According to , his first university studies were in the field of engineering, as briefly detailed in the "Education and academic career" subsection of this entry. and mastered perfectly all known branches of mathematical analysis and their mechanical and physical applications.See and .
He authored more than 60 research works: nearly complete lists of his publications are included in the commemorative papers , and . In particular, classifies Morera's work by assigning each publication to a particular research field: this classification is basically adopted in the following subsections.However, Maggi's terminology is not strictly followed: a modern terminology is used when needed in order to ease the comprehension.
Complex analysis
Morera wrote eight research works on complex analysis:According to 's classification, these works belong to "analytic function theory" i.e. "Teoria delle funzioni analitiche". the style he used for their writing probably inspired Somigliana in the quotation introducing the "Research activity" section.According to 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". Morera's theorem, probably the best known part of his scientific research, was first proved in the paper . gives a short account of the history of the theorem, and refers also to the later paper . There Morera defines holomorphic functions using his theorem, and then derives some interesting consequences. The theorem states that if, in the complex plane , the line integral of a given continuous complex–valued function satisfies the equation
for every closed curve in a given domain , then is holomorphic there.
Differential equations