The Last Man Who Knew Everything

by David N. Schwartz

  Sometime during the summer of 1914, as Europe edged toward catastrophic war, Enrico began to meet his father after work and accompanied him on the forty-minute walk from the ministry to their apartment on Via Principe Umberto. Amidei occasionally joined the father and son, and soon Enrico learned that his father’s colleague was an engineer with a strong mathematics and physics background. He summoned up the courage to ask Amidei a particularly abstruse question: “Is it true that there is a branch of geometry in which important geometric properties are found without making use of the notion of measure?”

  Amidei explained to the youth that this branch of mathematics was known as projective geometry. The idea puzzled Fermi, and he asked, “But how can such properties be used in practice—for example, by surveyors or engineers?” Amidei recalled that in Pisa he had studied a book on projective geometry by a German mathematician named Theodor Reye that had an excellent introduction explaining the practical uses of the discipline. He lent Enrico the book. Two months later Enrico revealed he had mastered the material, having worked through all of the theorems and solved all the problems at the back of the book. Amidei was understandably skeptical because the book had been difficult for him as a university student and, as a result, he had never completed the proofs himself. When Fermi gave Amidei the proofs for the theorems, the older man’s doubts vanished.

  Enrico Fermi was thirteen years old.

  This anecdote about Fermi’s grasp of projective geometry is the first example we have of what would become Fermi’s typical style of learning. He studied Reyes’s book by himself (or if it was with someone, it was with Giulio, who had not yet died) and, not satisfied with a cursory reading, worked through the proof of every theorem in the volume until he mastered the entire text. At this young age he displayed independence, thoroughness, and a willingness to grind through difficult material to ensure he mastered it. In this, as in all future work, he was never satisfied with a superficial grasp of a subject.

  Amidei was suitably impressed and later wrote, “I became convinced that Enrico was truly a prodigy, at least with respect to geometry. I expressed this opinion to Enrico’s father, and his reply was: Yes, at school his son was a good student, but none of his professors had realized that the boy was a prodigy.”

  This may not strictly be true. Fermi scholar Roberto Vergara Caffarelli cites a letter to Laura Fermi from Ida’s sister Olga, dated August 27, 1951, in which Olga recounts a chance encounter during this early period of Ida, Olga, the young Enrico, and Enrico’s teacher from his middle school. The teacher shook hands enthusiastically with mother and aunt, proclaiming the young Enrico a “second Galileo.” He may have been the first, but would not be the last, to do so. Of course memories shift and distort through the lens of time, and by 1951 Olga de Gattis’s memory of the event may well have been colored by Enrico’s subsequent development into a master physicist, but somewhere during this period a towering intellect started to make itself known. Amidei may not have been the first to notice it, but he certainly was the first to do anything about it.

  Confronted with this young phenomenon, Amidei took a fateful step. Enrico had mentioned his forays into the bookstalls at Campo de’ Fiori and his efforts to learn physics and mathematics from odd books he picked up. It was just at the time when Fermi and his brother (and later Persico) would try to explain the physics of spinning tops. Responding to this, Amidei decided to impose a certain intellectual structure on Fermi’s education. He would guide the youth through a carefully arranged sequence of textbooks to educate him in undergraduate physics. He explained that a fundamental understanding of the behavior of a top would require a thorough grounding in classical mechanics, which first required a foundation in trigonometry, analytical geometry, algebra, and calculus, including differential equations. Once he had this under his belt, he assured his young friend, Enrico would find the equations of motion for a spinning top easier to understand.

  This disciplined approach appealed to Fermi, although in retrospect it is apparent that he also continued his forays into physics textbooks independently of the informal but highly accelerated plan Amidei outlined. The curriculum does not look that much different from what a young entry-level physics undergraduate would undertake today. Amidei first intended to give Fermi a sufficiently strong foundation in mathematics to begin a serious study of classical mechanics.

  Amidei sequenced the mathematics carefully over the next three years, beginning with trigonometry and moving through analytical geometry to calculus. It helped that Amidei was a proficient mathematician and that Italian mathematicians at that moment stood at the forefront of the field internationally. It also helped that Amidei was teaching a unique genius.

  By 1917—Fermi was fifteen or sixteen—Amidei believed that Fermi was ready for a thorough course in classical mechanics and lent him the classic treatise on the subject by French mathematician Siméon-Denis Poisson, originally published in two volumes, in 1811 and 1833.

  For the study of classical mechanics and the mathematics required to understand it, no better curriculum could be provided, not even today. Not only is the subject matter virtually unchanged since these books were written but also the volumes represent the very best thinking on the subjects they cover.

  Years later Amidei remained astonished by Fermi’s ability to absorb material. Some forty years after the fact, he recalled that by the time Fermi graduated from liceo (in 1918, a year early):

  I had already ascertained that when he read a book, even once, he knew it perfectly and didn’t forget it. For instance, I remember that when he returned the calculus book by [Ulisse] Dini I told him that he could keep it for another year or so in case he needed to refer to it again. I received this surprising reply: “Thank you, but that won’t be necessary because I’m certain to remember it. As a matter of fact, after a few years I’ll see the concepts in it even more clearly than now, and if I need a formula I’ll know how to derive it easily enough.”

  Amidei’s efforts notwithstanding, Fermi could not keep himself from some side reading in physics. At the central public library of Rome, he tackled the magisterial five-volume, four-thousand-page Treatise on Physics by Russian physicist Orest Chwolson. Not for the faint of heart, it covers in depth every aspect of classical physics—mechanics, thermodynamics, statistical mechanics, optics, electromagnetic theory, even acoustics. After discovering that he had already mastered some thousand pages of the text, presumably as a result of his study of Poisson, he spent time every morning in the library poring over the balance of the book, assimilating its material, working out problems. It took him a little over a year, from August 1917 until September 1918, but master it he did.

  According to Persico, he and Fermi also studied a relatively new book by British physicist Owen W. Richardson, The Electron Theory of Matter. Published in 1914, it was a graduate-level text, incorporating British physicist Joseph John (J. J.) Thomson’s 1897 discovery of the electron into the broader framework of electromagnetic theory. By the time they tackled it, the two youths had significant physics and mathematics under their respective belts. (A few years later, Fermi also recommended the book to his university friend Franco Rasetti.)

  For Amidei, the experience of mentoring Fermi was sufficiently profound that he decided to write down statements made by the boy as a record for posterity—hence the reliability of his recollections four decades later.

  For Fermi, as well, the experience was extraordinary. Here was an adult he could talk to about the subjects that mattered most to him, someone who cared enough to tutor him on all things related to mathematics and physics. It may also have been the first time Fermi fully realized his great gifts in these areas. Time and again he discovered that he understood the material Amidei threw at him faster and more comprehensively than Amidei ever could. An experience he would have throughout his subsequent education, it gave him a sense of confidence in his abilities that was only to grow in later years.

  During this last year, Amidei in
quired as to whether the young man, now sixteen years old, wanted to pursue mathematics or physics at university. Fermi’s reply was straightforward: “I studied mathematics with passion because I considered it necessary for the study of physics, to which I want to dedicate myself exclusively.” Mathematics was the means to an end. He would always be proud of his mathematical ability, sometimes to the point of boastfulness, but physics would always be his one true love.

  Amidei understood that Fermi’s decision at such a young age to become a practicing physicist meant that Fermi needed to learn German. The world’s leading physics journals—most notably Annalen der Physik and Zeitschrift für Physik—were published in German. Amidei insisted, and Fermi complied, once again demonstrating his ability to quickly master a new language. When he arrived at university in the fall of 1918, he was, according to friends, reading German as he read Italian.

  ALL OF THIS WAS TAKING PLACE AGAINST THE BACKDROP OF World War I.

  When Italy entered the conflict in mid-1915, on the side of the Allies, neither Amidei nor Fermi’s father was drafted. They were too old and, also, to the extent that the railways were a strategic asset in the war, they both held important positions right where they were.

  It may have been a relief for Amidei to have the distraction of training young Enrico in the intricacies of mathematics and physics. The war effort cost Italy dearly, although not as much as other European combatants: between 460,000 and 610,000 men were lost, fewer than for England, France, or Germany, but an enormous loss nevertheless. Fortunately, the war did not directly affect the Fermi family, but it was a major concern for them. And it did have a direct effect on the intake of students at the Scuola Normale Superiore in Pisa, where Fermi landed in the fall of 1918, just as the war was ending. Nine of his twelve classmates were admitted in 1915 but were deferred for military service until the war ended.

  That said, Enrico’s distance, both psychologically and physically, from the travails of the war is notable. It seems not to have affected him at all. Perhaps the loss of his brother was enough. Perhaps compared to Giulio’s tragic and untimely death, the impersonal statistics of Italian war dead simply did not register. We know that Fermi threw himself into his friendship with Persico and his studies with Amidei with an energy and passion that bespeaks a gritty determination to overcome that loss, a far greater personal loss than anything the war raging around him could deliver.

  BY THE FINAL YEAR OF LICEO, AMIDEI HAD WORKED WITH ENRICO for almost four years and understandably took a proprietary interest in the young prodigy’s future. In Amidei’s view, that future lay in one direction: Pisa’s Scuola Normale Superiore.

  The school was founded by Napoleon in 1810 as an Italian equivalent to the École normale supérieure in Paris. By 1918 it was the most prestigious institution of higher education in Italy. Only a dozen or so students were admitted every year, half of whom would focus on the humanities, half on the sciences. In Fermi’s year it was even more competitive than in previous years, given the deferrals granted because of the war. The competition for the three open spots was intense.

  The University of Rome was another obvious option, but Amidei’s advice to Alberto and Ida was to send Enrico to Pisa. The Scuola Normale had produced towering figures in mathematics and the humanities, and its mathematics faculty was world class. That there were no notable physicists (except perhaps for Vito Volterra, more of a mathematician than a physicist) among its graduates was more a commentary on the state of Italian physics at the time than on the school. Indeed, physics students would be expected to take a parallel set of courses in physics at the University of Pisa, just a short walk away.

  Fermi’s parents objected. They were proud of Enrico and wanted the best for him, but they also wanted him to remain at home. In an age before widespread access to telephones, sending Enrico off some two hundred miles north would mean that they would have no contact with him except for the occasional letter. The devastating loss of Giulio made Enrico’s parents, especially Ida, doubly reluctant to part with their son. The University of Rome was strong and the physics department was close enough to walk to, in an area just to the west of the grand Santa Maria Maggiore church on the Esquiline Hill, on a street called Via Panisperna. A famous physicist, Orso Mario Corbino, had just taken over the physics department, with the intention of making it an elite center for teaching and research. He was also a rising figure in the Italian government, having been named chairman of the Public Works Council (he would soon become a member of the senate, too). Why couldn’t Enrico study with him? That Amidei succeeded in persuading them to allow Enrico to apply to the Scuola Normale and, once accepted, to attend is a testament to Amidei’s persistence and commitment to Enrico’s advancement. It is also clear that Enrico wanted to go, even though doing so would separate him from his parents and from Persico, who had decided to attend the University of Rome.

  The entrance exam paper Fermi submitted for physics remains legendary to this day. The subject was a close analysis of the vibrations of a rod fixed at one end. He brought to bear all that he had learned from Poisson and Chwolson about harmonic waves and their behavior, and the analysis he presented demonstrated a graduate level of sophistication. The examiners were more than impressed. They may have suspected fraud and in any case wanted to meet the youngster who submitted the essay. The examiner, a professor of geometry at the University of Rome named Giuseppe Pittarelli, called Enrico in for an interview, something that rarely if ever occurred. In the course of the interview, the young prodigy satisfied Pittarelli that the work was his own. Pittarelli considered the exam to be at the level of a doctoral thesis and told him so. He also told Fermi that he was destined to become an important scientist. Fermi placed first among those who took the exam and was admitted without reservation. He would, in time, become the fabled institution’s most famous graduate.

  With trepidation and heavy hearts, Alberto and Ida bade farewell to Enrico in October 1918. He was off to Pisa, where the next phase of his life as a physicist would begin.

  CHAPTER TWO

  PISA

  PISA IS A LITTLE OVER TWO HUNDRED MILES NORTH OF ROME, but in 1918 it was, and remains, centuries apart in time. The Rome Fermi left behind was a turbulent, noisy, crowded mess—a beautiful mess, an inspiring mess, but a mess just the same; a nineteenth-century city in full-throated transition to the twentieth century. In sharp contrast, Pisa was a quiet, medieval university town, frozen somewhere in the early to mid-fourteenth century, when it lost out to its great commercial and cultural Tuscan rival, Florence. The university officially dates itself from 1343, but like its counterparts throughout Europe, Pisa was probably home to scholars at least as early as the eleventh century. When Fermi arrived in late 1918, the main academic departments, including physics, were housed in old buildings scattered around the medieval heart of the city; now the only departments that remain there are those relating to humanities, philology, history, and law. The technical and scientific departments, as well as the medical school, have migrated to modern, functional facilities on the city’s outskirts. In Fermi’s time the physics and mathematics departments were in an ochre nineteenth-century edifice in Piazza Torricelli, a short walk from the Scuola Normale Superiore in Piazza dei Cavalieri. They are now about half a mile east, just inside the old city walls. The older building was not architecturally distinguished, but neither is the new one. It is, in fact, a 1974 renovation of a textile factory built in 1939 by the famous Pisan Jewish family, the Pontecorvos.

  However, the building that houses the Scuola Normale Superiore is indeed distinguished and must have seemed magical to the young Fermi. Largely the work of Renaissance architect Giorgio Vasari, it is one of the most beautiful buildings in a city known for the magnificence of its architectural heritage.

  Students who are admitted to the Scuola are also admitted to the university and are required to take classes at the university in addition to the seminars offered at the Scuola Normale. They receive degrees from both in
stitutions, a licenza from the Scuola Normale and a laurea from the university. The laurea entitles the holder to be called dottore, although it is not the equivalent of a PhD, which was officially adopted in Italian education only in 1980. In later years a formal graduate program, called a perfezionamento, was added to the Scuola Normale’s offerings. Today only about sixty undergraduates out of a pool of one thousand applicants are admitted to this most prestigious and competitive academic institution in Italy.

  Students, called normalisti, were housed in small rooms within the palazzo, each equipped with a simple desk and bed. There was no central heat, and the students relied on small coal burners to provide what little comfort they could get during the raw Tuscan winters. The Scuola Normale provided free room and board as well as a small stipend. In this, normalisti had it easier than other less exalted university students, who were on their own when it came to finances and to housing. Unlike Oxford or Cambridge, the University of Pisa was not organized along a residential college system, and to this day students are expected to find their own accommodations within the city, although the education is heavily subsidized.

  And so Enrico Fermi arrived in this quaint ancient college town, intent on mastering his chosen field.

  FERMI’S REPUTATION SURELY PRECEDED HIM, AND PROFESSORS LIKE famed mathematician Luigi Bianchi and Luigi Puccianti, the professor of physics at the university, were probably already aware of the young man and his brilliant entrance exam in physics. Fermi must have sought them out, too, given his training with Amidei and his independent reading. It was clear to everyone that he had already mastered the physics coursework on offer, with the exception of experimental physics. Much of his time would be spent on independent reading and study.