Abstract
When De Giorgi reached Rome in 1946, the city was on its knees. First of all, it was hard to reach, as the railway lines were so badly damaged. Then there was political instability and poverty; the entire infrastructure had been destroyed and public transport was almost non-existent. It was difficult to move from one end of the city to the other. All this notwithstanding, Ennio was happy because he had found a stimulating atmosphere in the capital, on account of Mussolini attempting to gather there the best university professors in Italy.
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Notes
- 1.
L. Carlino, one of Ennio’s childhood friends, also studying in Rome at the time, remembers [3]: “Train journeys were long and disastrous; at times, you had to try and jump in through the windows, as there were so many people travelling.”
- 2.
Mussolini’s objectives were more nationalistic than academic, as the race laws of 1938 demonstrated, with regard to which, in a letter on the political climate in 1974, Ennio De Giorgi wrote, “my antifascist beliefs have strong roots. They are the fruit of a long reflection that began when I was a boy and read with disbelief and disgust the texts of the race laws and continued with my painful war experience.” E. De Giorgi in Una lettera sul clima politico, nella imminenza del referendum sul divorzio, May 1974. Published in [2].
- 3.
R. De Giorgi Fiocco, Lecce, 2007.
- 4.
A. Greco, letter (2007).
- 5.
R. De Giorgi Fiocco, Lecce, 2007.
- 6.
A. Greco, letter, 2007.
- 7.
At the time, almost 4000 students were enrolled in the classes of mathematical, physical and natural sciences, in addition to 2500 engineering students, who followed the same first 2-year courses. Only 171 graduated with Ennio in 1950 (data taken from the annals of the Sapienza University of Rome).
- 8.
R. De Giorgi Fiocco, Lecce, 2007.
- 9.
C. Bernardini, 2007. E. Majorana was born in Catania in 1906, and disappeared mysteriously in March 1938.
- 10.
Unlike the course in physics, the one in analysis was split in two distinct exams: algebraic analysis, in the first year, and infinitesimal analysis, in the second.
- 11.
Ugo Amaldi (1975–1957) was an Italian mathematician.
- 12.
M. Rosati 2007.
- 13.
P. Villaggio says that he heard the story from M. Picone. P. Villaggio, Pisa, February 2007. There was also a rumor that De Giorgi had brought Picone a notebook with his work on the “rediscovered” Lebesgue Theory (L. Modica, email, 30 January 2009). Or maybe Picone heard it from Ugo Amaldi and was impressed by it enough to speak about it to others. In any case, the news finally reached Alessandro Faedo (1913–2001), the man who 15 years later would be the instrument of the rebirth of Italian mathematics (see Ch. 8). A. Faedo remembered (Annali Sns Cl. Sc. (4) 25, 1997): “I was working at the Mathematics Institute of Rome University. Later on, a colleague spoke to me of an exceptional student, Ennio De Giorgi, who, after learning during his first year the concept integrals of a continuous function, during his holidays had filled a writing pad with notes that he brought to his professor’s attention, who was amazed. Ennio had rediscovered on his own Lebesgue’s integral, discovered in 1902.”
- 14.
R. De Giorgi Fiocco, in a private communication.
- 15.
M. Rosati, 2007.
- 16.
M. G. Garroni Platone, 2007.
- 17.
E. De Giorgi, Nuovo Quotidiano di Puglia, 6 January 1996.
- 18.
C. Bernardini, Fisica Vissuta, Codice, 2006.
- 19.
R. De Giorgi Fiocco, 2007.
- 20.
Francesco Severi (1879–1961) was an Italian mathematician. He was a believer in the Fascist ideology, and was a proponent of the INDAM (National Institute for Advanced Mathematics), which was created in 1939.
- 21.
M. G. Garroni Platone, 2007.
- 22.
G. Salvini, 22 January 2009, compared the mathematical intuition of Francesco Severi with that of Ennio De Giorgi: both were able to predict results that would require much work to prove.
- 23.
C. Bernardini, Fisica Vissuta, Codice (2006).
- 24.
G. Fichera, D. Caligo, F. Bertolini, etc.
- 25.
G. Fichera, L’opera scientifica di M. Picone, Rend. Mat. vol. 11 (1978).
- 26.
More precisely, analysis is the study of the properties of mathematical functions. In general, a function is an operator that associates every element of a set (called a domain) with an element of another set (called a co-domain).
- 27.
“During the war, as a very capable mathematician, Picone corrected the old firing charts of our artillery and developed new ones that allowed for larger calibres and enabled shooting from high Alpine elevations. He received various awards as well as two promotions, and retired with the grade of Captain.” G. Fichera, L’opera scientifica di M. Picone, Rend. Mat. vol. 11 (1978).
- 28.
See La matematica italiana dopo l’Unità, edited by S. Di Sieno, A. Guerraggio, and P. Nastasi, Marcos y Marcos (1998).
- 29.
INAC eventually became the Mauro Picone IAC (Institute for Computation Applications), and as of today it is the largest research centre for mathematics outside a university.
- 30.
The computer was called FINAC and was built in the UK. It was inaugurated on 14 December 1955, by the Italian President G. Gronchi, and V. De Ferranti, the president of the manufacturing company. It was Italy’s second computer, after the one purchased in 1954 by the General Electronics Institute of Milan Polytechnic (a CRC102A). “Picone had wanted it quite strongly, to enable calculations of numerical processes, some of which had been devised by him, and that could not be resolved using table top calculators”. G. Fichera, Ricordo di A. Ghizzetti, Rend. Mat. series 7, vol. 14 (Rome, 1994).
- 31.
F. Bertolini, email, 10 January 2008.
- 32.
E. De Giorgi, Su alcuni indirizzi di ricerca nel calcolo delle variazioni, conference l. Tonelli’s and M. Picone’s centenary, Rome, 6–9 May 1985.
- 33.
F. Bertolini, Gorzano, 18 February 2007.
- 34.
The title of the thesis is taken from the submission De Giorgi made to the University Director, dated 20 May 1950.
- 35.
Sapienza Archives, Rome, 2007.
- 36.
A. Greco (2007) and R. De Giorgi Fiocco (2007). The construction of the electron accelerator was approved in February 1953.
- 37.
R. De Giorgi Fiocco, 2007.
- 38.
Even after obtaining his scholarship, Ennio continued occasionally visiting INDAM throughout the 1950s.
- 39.
E. Vesentini, Pisa, 7 February 2007.
- 40.
L. Radicati, Barbaricina, 9 February 2007.
- 41.
F. Severi, commemoration to L. Fantappié, at INDAM, 11 April 1957.
- 42.
F. Bertolini, email, 10 January 2008.
- 43.
L. Radicati, Barbaricina, 9 February 2007.
- 44.
M. Miranda, La riforma universitaria e gli studi scientifici. La matematica e la fisica nel biennio propedeutico, speech held on 5 June 2005, in the Ducale Palace in Venice.
- 45.
G. Capriz, email, 15 January 2008.
- 46.
P. Villaggio and L. Radicati, Pisa, 9 February 2007.
- 47.
E. De Giorgi said he started to appreciate calculus of variations after listening to Krall’s lectures.—P. Villaggio Pisa, 9 February 2007. The calculus of variations has this name because it consists of the search for functions that solve a specific problem, by starting from a presumed solution and making small changes to prove it.
- 48.
With some exceptions, such as Pappus, who confronted the problem in the fourth century BC, in the fifth volume of his books on mathematics and physics. The rigorous proof that a circle encloses the greatest area for a given perimeter was only achieved in 1838 by the Swiss mathematician Jakob Steiner (1796–1863). The proof was then extended by other mathematicians to the sphere and hyperspheres in any dimension.
- 49.
Leonhard Euler (1707–1783) was the most prolific mathematician of all time; his work extends to around 80 volumes. He was born in Basel (Switzerland) and studied analysis, number theory, geometry and algebra. He also contributed to the birth of new disciplines such as topology. Euler was a friend of the Bernoulli brothers and of Joseph Louis Lagrange (1736–1813), a mathematician born in Turin (Italy).
- 50.
The solution to the variational problem coincides with the solution to the corresponding Euler–Lagrange equation.
- 51.
M. Miranda, Calcolo delle Variazioni, Storia della Scienza, Enciclopedia Italiana Treccani (2004).
- 52.
Known as the Fermat principle, as it was discovered by the French mathematician Pierre De Fermat (1601–1665).
- 53.
L. Radicati, Barbaricina, 9 February 2007. Confirmed by L. Carbone, 20 December 2007.
- 54.
G. Capriz, February 2007.
- 55.
M. Emmer, Intervista con Ennio De Giorgi, Pisa, July 1996.
- 56.
F. Bertolini, Gorzano, 18 February 2007.
- 57.
M. De Giorgi in [1].
- 58.
L. Bassotti Rizza, (2007).
- 59.
E. De Giorgi, Costruzione di un elemento di compattezza per una successione di un certo spazio metrico, Atti Acc. Naz. Lincei Rendiconti Cl. Sci. Fis. Mat. Natur. (8), 8 (1950) and E. De Giorgi, Un criterio generale di compattezza per lo spazio delle successioni,” Atti Acc. Naz. Lincei Rendiconti Cl. Sci. Fis. Mat. Natur. (8) 9 (1950).
- 60.
Functional analysis is a branch of mathematics that concerns function spaces. It is quite close to the calculus of variations, in which functionals (functions of functions) are studied.
- 61.
E. De Giorgi, Ricerca dell’estremo di un cosiddetto funzionale quadratico, Atti Acc. Naz. Lincei Rendiconti Cl. Sci. Fis. Mat. Natur. (8) 12 (1952).
- 62.
E. De Giorgi, Un teorema sulle serie di polinomi omogenei, Atti Acc. Sci. Torino Cl. Sci. Fis. Mat. Nat. 87 (1953).
- 63.
These types of problem were first studied by the German mathematician Karl Weierstrass in the nineteenth century.
References
Carlino, L.: Ennio De Giorgi. Lions Club Lecce, Lecce (1997)
Bassani, F., Marino, A., Sbordone, C. (eds.): Ennio De Giorgi (Anche la scienza ha bisogno di sognare). Edizioni Plus, Pisa (2001)
Pallara, D., Spedicato, M. (eds.): Ennio De Giorgi—tra scienza e fede. Ed. Panico, Galatina (2007)
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Parlangeli, A. (2019). Roman Halls. In: A Pure Soul. Springer, Cham. https://doi.org/10.1007/978-3-030-05303-1_2
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