Abstract
In 1990, after a long break, Ennio De Giorgi returned to Pisa. But he wasn’t the same man as before; something had changed: “Professor Sergio Campanato said he had become more comprehensible when he explained something—remembers Eduardo Pascali.—Maybe, when he was with us, in Lecce, he knew he wasn’t in an environment like that of the Scuola Normale, and he tried harder to make himself understood.” He was certainly more aware that he had to pace his efforts, even though he didn’t stop carrying out his many undertakings: he followed students, battled with tenacity for human rights, and participated in the conferences of the group Science and Faith. “In the latter years,—recalls his sister Rosa, —as if he had the premonition that he would not last long, he never stopped his activities.”
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Notes
- 1.
E. Pascali, Lecce, 4 December 2006.
- 2.
R. De Giorgi Fiocco, commemorative speech, Lecce, September 2007.
- 3.
The Wolf Prize is awarded in Israel by the eponymous foundation created by Ricardo Wolf (1887–1981), a Jewish philanthropist, inventor, and diplomat, born in Germany. Ricardo Wolf emigrated to Cuba before the First World War and supported Fidel Castro’s revolution; later, in 1969, he became Cuba’s ambassador to Israel, where he remained for the rest of his life. The Wolf Prize consists of a diploma and of a cash prize of US$100,000, and is awarded each year for research in several disciplines (agriculture, chemistry, mathematics, physics, medicine, and arts), following a rigorous selection process. “The International Jury in the field selected De Giorgi from among about 30 candidates nominated that year.—says Y. Gruder (email, 19 January 2007), director general of the Wolf Foundation.—The Jury is formed of three members, all of them strong mathematicians, usually one from Europe, one from the USA or Canada, and one from Israel. They receive the nomination files from us, and then they have a meeting and select the winner(s). After the decision, no other body of the Foundation can change it. Every year a new Jury is appointed. This has been our policy since the beginning in 1978, not only in Mathematics, but also in the other fields in which we award the Wolf Prizes.” E. De Giorgi was selected with the following reason: “For his innovating ideas and fundamental achievements in partial differential equations and calculus of variations.”
- 4.
Y. Gruder, email, 19 January 2007.
- 5.
Giuseppe Montalenti (1904–1990), Italian biologist and geneticist. At the time, he was president of the Accademia dei Lincei.
- 6.
Hans Lewy (1904–1990) taught at the University of California and was known for his studies on partial differential equations. He won the Wolf Prize in 1984–1985.
- 7.
A. Fiocco, Lecce, 26 December 2007.
- 8.
“During his stay in Israel at that time, he delivered two lectures, at the Tel Aviv University and at the Technion-Israel Institute of Technology, Haifa,” adds Y. Gruder (email, 19 January 2007).
- 9.
M. Forti, Lecce, 7 December 2007.
- 10.
E. De Giorgi, Sui pregiudizi antislamici (On anti-Islamic prejudices), letter to the editor of Corriere della Sera, December 1990.
- 11.
E. De Giorgi, Osservazioni su diritti umani, tolleranza, comprensione ed amicizia tra vari gruppi umani (Observations on human rights, tolerance, comprehension, and friendship between various human groups), considerations directed towards the members of the Accademia Dei Lincei, 7 July 1993. Published in [2].
- 12.
E. De Giorgi, Riflessioni sulla responsabilità degli uomini di cultura nel momento presente (Reflections on the responsibilities of people of culture in the present time) presumed date, 1991. Published in [2].
- 13.
N. Bobbio, La Stampa, 1 February 1991.
- 14.
E. De Giorgi, “Una lettera aperta a Norberto Bobbio” (an open letter to Norberto Bobbio), La Stampa, 13 February 1991. Published in [2] with a reply from N. Bobbio.
- 15.
Ennio De Giorgi, Boll. Umi, Sez. B (8) 2 (1999). The Lectio Magistralis by De Giorgi was entitled: Il valore sapienziale della matematica (The wisdom value of mathematics).
- 16.
F. Di Stefano, Lecce, 6 December 2006.
- 17.
According to his family, the tumor was diagnosed in September. In the autumn, De Giorgi underwent radiotherapy in Pisa, and then went through additional treatments in Florence. In April 1993, he underwent surgery in Paris, where he went with his sister Rosa. In June 1994, he returned to Paris for a check-up visit, which confirmed the success of the operation. During his time in France, De Giorgi was helped by his friend Giuseppe Geymonat, a mathematician and the son of the Italian philosopher Ludovico Geymonat.
- 18.
Letter to the members of the Pontifical Academy of Sciences (Pisa, 29 October 1992). At the time, De Giorgi was also working on minimizing movements, a subject that was born out of mathematics applied to numerical analysis, and was connected to Gamma-convergence. “The idea emerged in 1992, inspired by a paper by F. Almgren, J. Taylor and L. Wang (Curvature driven flows: a variational approach, Siam J. of Control and Opt. 31, 1993), and it concerned the definition of the evolution of a physical system through a sequence of intermediate equilibrium states (metastable), that are obtained resolving as many minimum problems as possible. This method, known as implicit Euler’s method, is used in numerical analysis; De Giorgi developed it in general terms.” L. Ambrosio, Pisa, 13 February 2007.
- 19.
G. Bellettini, 25 September 2008.
- 20.
This area of research is connected to the one on gradient flows that was born in the 1970s (see Ch. 11) and to the studies by L. Modica and S. Mortola (see Ch. 19). Regarding mean curvature, L. Ambrosio adds (Pisa, 13 February 2007): “The technique for mean curvature motion also tied in with another problem that De Giorgi faced: the evolution of a surface in the presence of a singularity (i.e. a point at which the surface is not well defined from a mathematical standpoint). In these cases, a possible strategy is to immediately stop the evolution before the singularity appears, cutting the surface and restarting the movement.”
- 21.
Named after Gregorio Ricci Curbastro (1835–1925), an Italian mathematician known for inventing absolute differential calculus, on which Einstein based his General Theory of Relativity.
- 22.
Poincaré conjecture was formulated in 1904 and its proof immediately became one of the most desirable goals in mathematics. It was one of the seven millennium problems, the resolution for which the Clay Institute had reserved a million-dollar prize. The Russian Grigori Perelman, who presented the proof in 2003, refused to accept the prize (and the Fields Medal) saying that a mathematician does not need these motivations to carry out his research activities.
- 23.
See, for example, E. De Giorgi’s Congetture riguardanti alcuni problemi di evoluzione (Conjectures regarding a few evolution problems), Duke Math. J. 81 (1996). “Another important contribution by De Giorgi in this field was that he explained how to realize the motion of surfaces in a codimension greater than one—explains G. Bellettini (25 September 2008).—He wrote it in a text for a presentation at a conference in Pavia in 1994, entitled Barriere, frontiere, movimenti di varietà (Barriers, boundaries, motion of manifolds). The text was translated into English and was circulating among us. A large part of that paper was completed and published by L. Ambrosio and H. M. Soner in the article ‘A level set approach for the evolution of surfaces of any codimension,’ J. Differential Geometry 43 (1996).”
- 24.
L. Carbone, 20 December 2007.
- 25.
A. Leaci, Lecce, 18 December 2006.
- 26.
G. Lenzi, Pisa, 8 February 2007.
- 27.
L. Radicati confirms De Giorgi’s interest in looking across disciplines. “We had to recruit someone in the Science faculty; remembering Bernardini’s dream to see biology developing in the Scuola Normale, where such a discipline had never been traditionally taught (until the 1960s, the only scientific discipline taught in the Scuola Normale was mathematics, with the later addition of physics), I proposed to call an illustrious neurobiologist. The proposal was met with a frosty reception, and only De Giorgi’s enthusiastic support allowed this to happen.”—L. Radicati, commemoration held for the board of the Scuola Normale, 8 November 1996.
- 28.
E. De Giorgi, Valore sapienziale della matematica (Wisdom value of mathematics), conference at the Accademia Pontaniana (Naples, 12 February 1992), Atti Accademia Pontificia (1993). Published in [4].
- 29.
E. De Giorgi, La matematica e la Sapienza, conference at Casarano (3 December 1994). Published in [4].
- 30.
The study was carried out to determine how much interest there was in having a better knowledge of the Universal Declaration of Human Rights and was based on a survey form with six questions, to be handed out to students, teachers, and parents.
- 31.
E. De Giorgi, letter to the president of the Accademia dei Lincei G. Salvini (early 1994).
- 32.
Ennio De Giorgi was a member of the following academies (the year he joined is in parentheses): Accademia Nazionale delle Scienze (1977), Accademia delle Scienze di Torino (1978), Accademia dei Lincei (1978), Istituto Lombardo (1980), Pontifical Academy of Sciences (1981), Accademia Ligure di Scienze e Tecniche (1983), Accademia Pontaniana (1988), Académie Internationale de Philosophie des Sciences de Bruxelles (1994), Académie des Sciences (1995), US National Academy of Sciences (1995), Latin America’s Academy of Science.
The Italian Accademia Nazionale delle Scienze (National Academy of Sciences) was founded in Verona in 1780, and is thus the oldest Italian national academic institution. This academy was modelled on the Académie Française, and comprises 40 scientists (in addition to 12 foreign members), who have the task of editing a volume of members’ memoirs, called I Rendiconti. The Academy was originally named Società Italiana and welcomed members such as Alessandro Volta, Benjamin Franklin, and Antoine Lavoisier, thus capturing the interest of Napoleon Bonaparte. Under the more recent name of Società Italiana delle Scienze, it has welcomed scientists such as Guglielmo Marconi, Tullio Levi Civita, and Enrico Fermi. It named itself an Academy in 1949.
- 33.
The Pontifical Academy of Sciences was founded in 1936 by Pope Pius XI, who restarted a previous attempt by Pope Pius IX to reconstitute the ancient Accademia dei Lincei of Cesi. According to its 1976 charter “The Pontifical Academy of Sciences’ objective is to promote progress in physical, natural, and mathematical sciences, and to study the related epistemological issues.”
- 34.
E. De Giorgi, Riflessioni sul ruolo delle accademie, Rome, 24 October 1994.
- 35.
G. Salvini, 2007.
- 36.
M. L. Rosato in [3].
- 37.
Among which a debate on the responsibility of science specifically in the context of chemical warfare, on which he delivered a speech on 31 October 1988.
- 38.
- 39.
Ibid. The text can be found as a footnote in [2].
- 40.
L’Osservatore Romano, 29 October 1994. Published in [2].
- 41.
This was the same expression used by De Giorgi in his presentation.
- 42.
This was the same expression used by De Giorgi in his presentation.
- 43.
A. De Giorgi, Lecce, 23 December 2007.
- 44.
E. De Giorgi, Riflessioni preliminari sulla Carta dei doveri, 6 February 1992. Published in [2].
- 45.
The final text was drafted in Trieste, during a conference that took place from 25 to 27 November 1993.
- 46.
E. De Giorgi, Riflessioni sulla Dichiarazione dei doveri, Lecce, 18 May 1994.
- 47.
L. Carbone, 20 December 2007.
- 48.
L. Carbone, 20 December 2007. Carbone explains that the assessment consisted of the commission’s valuation on teaching and research papers presented by the candidate and not of an oral examination.
- 49.
Phone call, 28 December 2007.
- 50.
R. De Giorgi Fiocco and A. De Giorgi Fiocco, Lecce, 12 December 2007.
- 51.
L. Carbone, 20 December 2007.
- 52.
F. Bassani, Pisa, 8 February 2007.
- 53.
F. Bassani also said: “To avoid having to deal with even the smallest worries, such as phone bills, he didn’t want to have an outside line to abroad in his college room.”
- 54.
L. Carbone, 20 December 2007.
- 55.
De Giorgi’s adversary in these elections was Carlo Pucci (1925–2003), an old friend, but with whom Stampacchia had strong disagreements. Pucci was an important figure for the organization of Italian mathematics. Born in 1925, he graduated in Florence under the direction of Giovanni Sansone, and then became the president of the National Committee for Mathematical Sciences within the Italian National Council for Research (CNR) from 1968 to 1976, and then president of the Italian Mathematical Union (UMI), from 1976 to 1982. “As a young man, he was a rising star in the Action Party, and had joined the liberation war as a volunteer. He was the nephew of Ernesto Rossi, an important figure in the Italian post-war period.” L. Carbone, 20 December 2007.
- 56.
L. Carbone, 20 December 2007.
- 57.
As Carbone stated, E. De Giorgi never took on any institutional responsibilities. However, according to L. Modica, he was keen on his students doing so. L. Modica (12 September 2008) gives an example: “In 1980, for the first time, a law that introduced national research projects was enacted. Therefore, in 1981, the dilemma was to define the group that would be headed by Ennio. He did not want to lead any groups, so I found myself in this role.” In this way, Ennio would still be able to influence indirectly institutional and political university issues. “Among the rules to select people for available university teaching positions, there is one that candidates only have to present their most relevant work. This rule was based on the fact that De Giorgi did not like modern scientific evaluation criteria, based on an ‘impact factor’ index, and he sustained that to evaluate a mathematician ‘all you might need is a single paper.’”
- 58.
Other than De Giorgi, M. Miranda and F. Rosati also sat on the examining commission.
- 59.
“I keep insisting that, with regard to the Moro case, there are no mysteries.” P. Baschieri, email, 19 December 2008.
- 60.
An Italian terrorist group that operated during the 1970s and 1980s (translator’s note).
- 61.
F. Bassani in [7].
- 62.
At the time of writing the first Italian edition of this book, Baschieri was still involved in research at the National Research Council laboratories in Pisa. His friends consider him a peaceful character. P. Baschieri is the son of an illustrious academic, Lidio Baschieri.
- 63.
L. Carbone, 20 December 2017.
- 64.
P. Tilli, Turin, 8 January 2007.
- 65.
Liouville’s Theorem, from the French mathematician Joseph Liouville (1809–1882).
- 66.
In this context, we are talking about spatial dimensions.
- 67.
F. Bassani in [7].
- 68.
This is confirmed by a communication by De Giorgi to the Accademia dei Lincei and dated Pisa, 24 October 1994 (and sent in a fax from E. Magenes to the SNS secretarial office on 4 November 1994), that concerned a note by G. Bellettini and M. Paolini with the title Teoremi di confronto fra diverse nozioni di movimento secondo la curvatura media.
- 69.
E. De Giorgi did not sign his students’ papers (L. Modica, 12 September 2008) and often his name did not appear on papers for which he had provided decisive contributions.
- 70.
G. Letta, Pisa, 6 February 2007.
- 71.
M. Forti, Lecce, 7 December 2007.
- 72.
F. Bassani, Pisa, 8 February 2007.
- 73.
F. Bassani, Pisa, 8 February 2007.
- 74.
F. Flandoli, Pisa, 7 February 2007.
- 75.
F. Honsell, Genova, 31 October 2016.
- 76.
Communication sent on 20 April 1995, and signed by F. Gros.
- 77.
F. Bassani in [7]. F. Bassani adds (Pisa, 8 February 2007): “It was a fantastic ceremony, with drums and uniforms, very solemn, as is usual in France.”
- 78.
R. De Giorgi Fiocco, Lecce, 22 December 2007. Rosa was devoted to the relic, that, according to tradition had been built in 1930 by the novice nun Catherine Labouré, following instructions from the Virgin Mary.
- 79.
De Giorgi received a communication from Giancarlo Rota in Lecce on 25 April 1995 at 3 pm. On the same day, a similar note, signed by S. Rowland, was sent to the Scuola Normale. The note specified that De Giorgi had been elected during the 132nd meeting of the Academy.
- 80.
Giancarlo Rota (1932–1999). Born in Vigevano, he moved to Ecuador to escape fascist persecutions. In 1960, he went to the United States. His most significant contributions were in the field of combinatorics. Rota was the vice-president of the American Mathematical Society from 1995 to 1997.
- 81.
D. Senato, November 2007.
- 82.
E. De Giorgi, letter to the President of the Chamber of Deputies. Pisa, 3 April 1995.
- 83.
- 84.
Candidature for the Nobel Peace Prize, proposed by the Russian academician N. Voronzov, in favour of S. Kovalev, La Pensée Russe, 5–11 January 1995.
- 85.
In particular, the letter referenced more specific rights such as the “right to life, liberty, and security of person” (Article 3 of the UDHR); the definition that the “family is the natural and fundamental group unit of society and is entitled to protection by society and the State” (Article 16); the “right to freedom of thought, conscience, and religion” (Article 18); the right that everyone has to “a standard of living adequate for the health and well-being of himself and of his family, including food, clothing, housing and medical care and necessary social services, and the right to security in the event of unemployment, sickness, disability, widowhood, old age or other lack of livelihood in circumstances beyond his control,” noting also that “motherhood and childhood are entitled to special care and assistance. All children, whether born in or out of wedlock, shall enjoy the same social protection” (Article 25); the right to education that: “shall be directed to the full development of the human personality and to the strengthening of respect for human rights and fundamental freedoms. It shall promote understanding, tolerance and friendship among all nations, racial or religious groups,” and that “parents have a prior right to choose the kind of education that shall be given to their children” (Article 26). E. De Giorgi and S. Mortola, open letter to Italian parliamentarians, 18 March 1995.
- 86.
E. De Giorgi, Costituzione italiana e Dichiarazione universale dei diritti umani, Coscienza, 11 July 1995. Published in [2].
- 87.
The text also reads “The true enemies of the Declaration are not those who, having read it with care, and having compared it with diverse real-world situations, then express reservations or criticism for some of its articles, but rather those who claim they accept it, but do not read it with due care, and do not refer to it when facing important issues such as those of family, education, bioethics, and do not say a word in defense of people, families and populations to whom the most elementary human rights are denied.” E. De Giorgi, S. Mortola, open letter to Italian parliamentarians, 18 March 1995.
- 88.
On that occasion, Nash himself says that he did not have the time to get a personal impression of De Giorgi. J. F. Nash, email, 12 January 2007. The two mathematicians thought highly of each other, and if they had sparse communications, this was probably because of the circumstances and the language barrier.
- 89.
E. De Giorgi, letter to Calogero Vinti, 8 March 1995.
- 90.
A. Fiocco, Lecce, 26 December 2007 and L. Carbone, Naples, October 2006.
- 91.
E. De Giorgi and S. Mortola, letter sent to the editor of the magazine Città Nuova, 25 May 1996.
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Parlangeli, A. (2019). French Drums. In: A Pure Soul. Springer, Cham. https://doi.org/10.1007/978-3-030-05303-1_23
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