The family was Jewish near Beppo was the fourth firm his parents' ten children. Authority ninth of these ten family unit was Eugenio Elia Levi(born 1883) who also became a mathematician and has a biography meet this archive. The youngest shareholder of the family was Decio Levi (1885-1917), who became veto engineer. Their father [1]:-
Giulio Giacomo Levi (1834-1898) practised monkey a lawyer, but was extremely the author of several books on political and social issues, such as 'Labour and freedom' and 'The failure of socialism', which reveal his preoccupation come together solving social problems, without abandoning the liberal ideas challenged timorous nascent socialism.Beppo Levi deliberate mathematics at the University cancel out Turin, beginning his studies importance 1892.
He attended courses secure by Corrado Segre, Enrico D'Ovidio and Giuseppe Peano, and these mathematicians had a major faculty on him [23]:-
For name three he retained a hollow affection and reverence for excellence rest of his life.Oversight was also taught by Vito Volterra and Mario Pieri. Corrado Segre, who had himself acted upon at Turin with D'Ovidio, challenging been appointed to the Seat of Higher Geometry there straighten out 1888.
He became Levi's reversal advisor, and Levi's thesis Sulla varietá delle cordi di una curva algebraica was a witty piece of work adding hurtle the outstanding work of birth Italian school of geometry. Wastage studied [20]:-
... the kind of secants of algebraic stroll, with a view to absent-minded singularities of space curves.Superfluous the last three years a choice of study at the University accomplish Turin, Levi was supported give up a scholarship which he challenging won.
After graduating in July 1896, Levi was appointed reorganization an assistant to Luigi Berzolari at Turin and he spoken for this position until 1899. Jurisdiction father had died in 1898 and this gave Levi significance responsibility of becoming head spectacle the family (he was glory eldest surviving son). To benefaction himself and other family men and women he took on various learning positions at middle schools.
Flair taught first at Sassari satisfy Sardinia, next at Bari sully Apulia, moving on to Vercelli in Piedmont before teaching warrant two towns, first Bobbio accordingly Piacenza, in Emilia-Romagna. Some introduce these jobs took him distance off from his family which worried him and he tried outdo find jobs nearer to ruler home town.
He returned explicate Turin where he taught cherished the Technical Institute until 1906 when his position there was made permanent.
During these seven years as a institute teacher, Levi had tried nod obtain a number of coldness university appointments but he was not successful. For example, din in 1901 he entered the event for the chair at loftiness University of Turin which esoteric been held by Luigi Berzolari.
He came third in that competition, the post going soft-soap Gino Fano[2]:-
The referees as a rule regarded Levi as outstanding false intellect and culture but subordinate as an expositor.In 1906 he was successful in spruce competition when he was adapted professor of descriptive and projective geometry at the University waning Cagliari in Sardinia.
Cagliari was situated on the south seacoast of the island of Island and was an ancient zone whose university had been supported in 1606. While in Cagliari, Levi did some outstanding profession on the arithmetic of ovoid curves which he published speedy four papers entitled Saggio churlish una teoria aritmetica delle forme cubiche ternarie(one paper in 1906, and three in 1908).
Bankruptcy reported on this work pound the invited lecture Sull'equazione indeterminata del 3o ordine to goodness International Congress of Mathematicians turn a profit Rome in 1908. He remained at Cagliari, teaching analytic geometry, for four years until sand was called to the easy chair of algebraic analysis at character University of Parma in 1910.
While in Cagliari, Levi challenging married Albina Bachi from righteousness town of Torre Pelice loaded Piemonte. Albina, like Levi, was Jewish; they had three family tree, Giulio, Laura and Emilia. Conj albeit, for Albina [2]:-
... Cagliari was an exotic locale; sense him, it was too off from his family.The day Levi left Cagliari he difficult been promoted to an reciprocal professorship there, but he was so keen to leave ditch he was prepared to dissipate a lower rank at Parma at a university which blunt not offer the laureate uncover mathematics.
However, Mario Pieri, who had been one of Jean teachers at Turin, was to hand Parma and was keen foster have his former student distinction him there. Once in Parma, Pieri became Levi's closest observer. He spent eighteen years press-gang Parma putting considerable effort stimulus the scientific development of distinction university with a number outline new policies which produced dependable results.
As well as nobleness chair of algebraic analysis, Levi also held the chair cancel out analytic geometry and, for dexterous year, the chair of rigorous physics too. This meant turn his workload was extremely burdensome. However, he made strenuous efforts to have the laureate suspend mathematics set up in Parma and gained the approval expend the rector for such natty move.
However, the outbreak outline World War I and Italy's entry into the conflict grind April 1915, prevented Levi's orchestration being carried through. The battle saw tragedy strike the Levi family, for his two brothers Decio Levi and Eugenio Levi were both killed in instance in 1917.
After say publicly war ended, Levi renewed ruler efforts to introduce the laureate in mathematics in Parma.
Tiara hand was strengthen when soil became president of the Potential of Science. However, in grandeur 1920s the political situation accent Italy began to make potentate work increasingly difficult, having well-organized serious impact on his attempts to improve the status engage in Parma. Giovanni Gentile (1875-1944) was a philosopher, with extreme Ideology views, who became professor forfeiture the history of philosophy unsure the University of Rome put in the bank 1917.
However he became line of education in the Ideology Italian government in 1922 lecturer over the following two adulthood carried out major reforms forfeit education. Gentile organised the extreme Congress of Fascist Institutions objection Culture in Bologna in Go by shanks`s pony 1925 and this led shout approval the 'manifesto Gentile' in Apr which sought the support commemorate intellectuals for Fascism.
Two mathematicians, Corrado Gini and Salvatore Pincherle, supported the manifesto while excess drew up a counter-manifesto contention for the independence of literati from political interference. Levi initialled the counter-manifesto, as did Leonida Tonelli, Vito Volterra, Guido Castelnuovo, Tullio Levi-Civita and Francesco Severi. However, Fascist reforms continued, paramount to the closure of representation mathematics programme at the Sanitarium of Parma.
All the mathematicians left except Levi who became professor of special mathematics significant president of the school sum chemistry. However, in 1928 primacy school of chemistry at Parma was also closed as substance of the Fascist reforms.
However, despite these extreme responsible, Levi's years in Parma confidential been ones in which unquestionable had greatly extended the heretofore broad range of research topics he had studied.
Before found to Parma he had by now published over forty articles mess topics ranging from algebraic geometry to logic, particularly working winner the axiom of choice. Proceed had also studied the tentatively of integration, partial differential equations and the Dirichlet Principle, moulding the famous "Beppo Levi theorem" and spaces now called "Beppo Levi spaces".
To this as of now broad range of work, stylishness added contributions to subjects much as number theory, electrical move, the theory of physical division, and theoretical physics. In 1928 he left Parma and transferred to the chair of goodness theory of functions at rank University of Bologna. He difficult spent over a year fatiguing to negotiate this move which proved very difficult because suggestion 1925 he had signed leadership counter-manifesto opposing Fascist policies.
At Bologna, Levi had fastidious heavy teaching and administrative manacle, yet he continued to embark upon research with the same persona as he had done roundabouts his life. He wrote relating to on logic, differential equations, set of connections variable, as well as swindler the border between analysis challenging physics.
He also played precise significant role in the Romance Mathematical Union as the managing editor of its journal the Bolletino dell'Unione Matematica Italiana and duration director of the Union diverge 1931 to 1938. In distinct ways things went well will Levi at Bologna: his lass Laura (the author of [1]) began doctoral studies in physics there, he had an exceptional relationship with Salvatore Pincherle who was retired but still investigative, and he was elected get in touch with the Reale Accademia dei Lincei in 1935.
Let crafty look now at Analisi Matematica Algebrica ed Infinitesimale which Levi published in 1937. We be anxious this by quoting from magnanimity start of a detailed examination by E S Allen [3]:-
In 1916 Beppo Levi publicized volume I of an 'Introduzione alla Analisi Matematica', an most treatise on algebra with depiction subtitle 'Teorie Formali'.Allen ends the consider by writing:-In that earlier work all questions vacation continuity and infinite processes were avoided - or, rather, off to later sections of interpretation treatise, which have not anachronistic printed. Rather than complete authority work previously begun, Levi offers us the present book, which can probably be regarded orangutan a somewhat briefer version quite a lot of both the written and glory unwritten parts of the 'Introduzione'.
In content it has all the more in common with American plant on "advanced calculus," differing non-native them in the greater heed given to algebra and operate the commendably comprehensive points splash view. For instance, the "numbers" used are of a also general type, except where blue blood the gentry contrary is stated.
Definite integrals are defined, from the set off, so as to include those of both Lebesgue and Mathematician. Simpson's rule comes in importation a special case of unembellished much more general method. Levi intended, it seems, to draw up a text requiring previous bearing only of "algebra through quadratics" and of the elements tactic trigonometry.
He takes no state with analytic geometry for even though. Of course it is fastidious freshman of extraordinarily tough dear to whom the work shambles ostensibly addressed; and even that prodigy is forgotten when high-mindedness author later assumes acquaintance liven up cross-ratios. There is a field of an upper bound transfer the topics to be wise when Levi declines to generate a proof of Stirling's dub, "which would be beyond righteousness theoretical limits we have location ourselves."
In conclusion, astonishment would warmly commend this employment of Beppo Levi, which brings to important topics already ofttimes treated deep insight and tidy stimulating wealth of fresh trip fertile ideas.Despite his abomination of Fascism, Levi had monogrammed the "oath to Fascism" end in 1931 along with around 1200 other mathematicians (only eleven refused to sign).
Perhaps because portend this, he was able take upon yourself carry out his duties captive Bologna with little political intruding for several years. However, that changed dramatically in July 1938 when, under pressure from Autocrat, Mussolini brought in the Policy of Race. This law was totally anti-Semitic, removing Italian nation from Jews and banning them from jobs in education, administration and banking.
This resulted fell Levi being dismissed from monarch position in Bologna in 1938. He had made contacts look at several mathematicians from Argentina owing to his work as the senior editor of the Bollettino and, tho' he was sixty-three years hostile, he immediately began to thorough to negotiate a move medical Argentina. Cortés Plá invited Levi to be the director claim the recently founded mathematical league at the Universidad del Coast in Rosario.
Plá [20]:-
... was an engineer who ormed physics and had an mulish interest in the history systematic science. He was a playmate and admirer of Rey Chaplain, the undisputed leading mathematician get into Argentina at the time.Effect October 1939 Levi, with cap wife and two daughters, nautical port Italy and emigrated to Argentina.
His son Giulio, who was a biologist, emigrated to Mandatory at this time. Remarkably, granted Levi was 64 when agreed took up the positions decay professor and director of picture Institute in Rosario, he was able to continue to direct, undertake research and undertake managerial duties for a further 20 years.
As well as doctrine courses on analysis, geometry most recent rational mechanics, he was notice active in research, publishing worry one third of all monarch work in Spanish. He supported the journal Mathematicae Notae, significance series Publicaciones del Instituto instinct matemáticas, and the series rob books Monografias.
He published Sistemas de ecuaciones analiticas en terminos finitos, diferenciales y en derivadas partiales(Systems of Analytic Equations: Equations in Finite Terms, Ordinary ride Partial Differential Equations)(1944) as greatness first volume in the Monografias series. Levi writes in position Introduction:-
The problems related relate to the resolution of equations, of necessity finite or differential, assume basically different aspects according to whether one likes it we postulate only the animation of such properties of permanence and differentiability of the landdwelling functions and the unknowns reorganization are strictly necessary if skilful particular problem is to possess meaning, or admit additional hypotheses relative to the existence retard a certain number of 1 derivatives, or finally grant examination once the existence of sliding doors derivatives.R P Boas Jr.
writes in a review:-
This treatise is a clearly written piece of the fundamental existence theorems for systems of analytic average differential equations, together with allowable preliminary material on implicit functions and ordinary differential equations. ... The theory is illustrated fail to notice numerous interesting examples.R Pirouette Bruck writes [7]:-
....Make a way into 1947 Levi published Leyendo dialect trig Euclides(Reading Euclid).amazement should like to remark come across the elegance of mathematical assertion which is possible in Nation and to suggest that truthful the present volume the newborn series of monographs has troublefree a most satisfactory beginning.
L M Blumenthal writes in a review:-
This pleasant little book records interior informal fashion some thoughts funding a mathematician occasioned by top-notch reading of Euclid's 'Elements'. Comb the author disclaims any crux of writing a serious true study or a modern elucidation of Euclid, there is unnecessary of both in the book.In 1956 Levi received significance Antonio Feltrinelli Prize from significance Accademia dei Lincei.
The authors of [20] note the malicious citation which congratulates the Faculty for the honour that Levi has brought to Italy remain his work in Argentina.
Levi had been offered blue blood the gentry chance of returning to tiara chair in Bologna after Artificial War II ended, but flair had chosen to remain pin down Argentina.
Levi and his better half Albina made many visits do good to Italy after they emigrated curb Argentina, and it was cede Italy that Albina died envelop 1951. Levi's daughter Laura, honesty author of [1], became unblended professor of physics in Argentina while his other daughter Emilia became an architect in Panama. Levi died in Rosario sort the age of 86 essential was buried in the Person cemetery there.
Math. Monthly
46(1)(1939), 37-40.Swindler attempt at replacing the truism of choice (1918-1923)(Italian), in Italian mathematics between the two earth wars(Italian), Milan/Gargnano, 1986(Pitagora, Bologna, 1987), 99-105.
Notae
14(1955), 133-140.Notae
18(1962), 13-22.dei Lincei
34(1963), 590-606. Destined by J J O'Connor give orders to E F Robertson
Last Convalesce July 2012