A Pure Soul: Ennio De Giorgi, A Mathematical Genius

This is a remarkable work. Among the mathematical biographies I have read, it is easily the best at conveying the character of the subject of the book in detail. A Pure Soul succeeds on this count by relying on firsthand accounts of episodes in De Giorgi’s life, up-close descriptions, and evaluations of his character by relatives, friends, associates and students. We are presented with a mosaic from which a picture of the man emerges. The narrative is excellent and is amply supplemented by a plethora of footnotes (it’s a many-to-one mapping, footnotes to pages), often containing autonomous anecdotes of great interest. Andrea Parlangeli has done a wonderful job in presenting a readable book overflowing with irresistible information: the detailed story of a brilliant and unusual mathematician, his own man, a practicing Catholic who lived his faith — indeed a pure soul: the book is perfectly titled.

De Giorgi is famous for his work on minimal surfaces and his groundbreaking and revolutionary work in the notoriously difficult area of Partial Differential Equations, including the Nash-De Giorgi Theorem and his solution of the Bernstein problem. He was also heavily involved in mathematical logic and questions of the foundations of mathematics, and was deeply devoted to research in all these areas, in fact starting his own school(s) for their pursuit and the education of suitable acolytes.

It is apposite to draw a parallel of sorts with one of the great prototypes of all teachers: on p. 118 of the book under review, Parlangeli states that

Like Socrates, De Giorgi preferred conversations. He wrote very little given the vastness of his research, he did not read much, and even his most important articles were limited to the essentials. “Written words fly, spoken words stay,” he loved telling his friends, at times mimicking the flight action, with his hands toward the window, of the reams of paper haphazardly placed on his desk. And, like Socrates, he had a school.

Then, on p. 119 we read:

Ennio De Giorgi’s school had a very particular structure and had five distinct movements: student courses, the Tuesday and Wednesday seminars, the meetings with the students in his office, the meetings by the seaside or in the mountains, and the never-ending dinner evenings.

The cores of Ennio’s school were the advanced courses held on Tuesdays and Wednesdays: “They were always held from 11 a.m. to 1 p.m.,” remembers Giuseppe Buttazzo. “Tuesday was reserved for mathematical analysis and Wednesday for logic” — But “the most popular course was analysis.”

But it should be stressed that this book’s greatest charm consists in presenting facets of De Giorgi’s character and personality that add up to a complete picture of, in my opinion, a very engaging, fascinating, and charming human being. To wit, here are a few more excerpts from the book presented in evidence:

De Giorgi’s lifestyle was the perfect stereotype of a scientist: eccentric and immersed in his world - “When he was thinking about mathematics he was oblivious to anything else,” remembers Gianfranco Capriz, one of his friends at the time. … If an insight, an idea, came to him, no matter where he was, any scrap of paper was good enough for him to take notes on. (p. 37)

On being discovered:

In January 1957, Paul Garabedian [from] Stanford came to Italy to recruit new mathematical talent … [Says Garabedian:] “Nobody mentioned De Giorgi.” But then in Naples someone did and Garabedian tracked him down … [Garabedian] communicated to America that this young mathematician had found the proof of one of the most important theorems of the last century. It was De Giorgi’s masterpiece. (p. 39)

Regarding De Giorgi’s attack on Hilbert’s 19th Problem:

Stampacchia did not expect De Giorgi [27 at the time] to take on the problem immediately. … “it was a stroke of genius that … led him to the solution. It was literally like pulling a rabbit out of a hat” [says Livio Clemente Piccinini]. Even Guido Stampacchia couldn’t believe how far his friend had arrived, and went around asking: “Where on Earth did he get those ideas?”

There is, of course, a lot more available in the roughly 200 pages of the book, including accounts of De Giorgi’s work on behalf of human rights causes he believed in and his philanthropic work which he sought to keep secret, as the Lord instructs. Here are two passages from the last two pages of the book proper, preceding the epilogue, dealing with De Giorgi’s death in October 1996.

On Thursday, 24 October, De Georgi was given the Last Rites. Don Sergio moves close and De Georgi whispers: “If I die tomorrow, tell people I die as a good Christian” … Tears crowd at the sight of that room full of books and clutter, now no longer occupied, inanimate, full of reflections of life, but devoid of the life that caused those reflections … dominated by an absence. … “When I saw the room where De Giorgi lived for over 20 years, my heart sank,” remembers Bassani. “It was as small as a convent’s cell, with papers and books strewn everywhere. I thought of St. Francis.”

And:

from his hospital bed, he managed to dictate his last letter. It was for the Pope [St. John Paul ll]: “Your Holiness, I am a mathematician, and a pontifical academician — My failing health only allows me to dictate a few lines — I have always sustained what the Universal Declaration of Human Rights of 1948 calls human dignity and value, and I do not believe that dignity and value are solely definable with the scientific method. Therefore I have much admired what you said on 23 October 1996, and I believe that the speech will be remembered in the history of Church, science, culture, and civilization.” Two hours later, Ennio De Giorgi passed away.

I recommend this book most enthusiastically.

Michael Berg is Professor of Mathematics at Loyola Marymount University in Los Angeles, CA.