Enrico Fermi

Born: 29 September 1901 in Rome, Italy
Died: 28 November 1954 in Chicago, Illinois, USA

Enrico Fermi's father was Alberto Fermi and his mother was Ida de Gattis. Ida was a remarkable person who was the daughter of an army officer. She trained as a school teacher and taught in elementary schools for most of her life. Highly intelligent, she was the major influence on her children after her marriage to Alberto in 1898. Ida was 27 years old when she married but her husband Alberto was 41. He worked for railway companies in various parts of Italy but had moved to Rome in 1888. He was promoted to inspector in the year he married Ida and by the end of his career he had risen to play a major role in what was by that time the state owned railway company. Enrico was the third of his parents' children having an older sister Maria (born in 1899) and older brother Giulio (born in 1900). In line with the custom of the time, Enrico was brought up by a nurse away from the family until he was about 30 months old. He was then strictly brought up although the family were not religious (something which upset Alberto's family who were all devout Catholics except Alberto).

When he was six years old Enrico began to attend an elementary school which was chosen because it was a secular establishment). He showed great talents, especially in mathematics and by the time he left elementary school at the age of ten he was puzzling out how the equation x2 + y2 = r2 represented a circle. He then spent five years at the ginnasio and then a further three years at the liceo preparing to enter university. He was an outstanding student throughout his education being clearly the most able in his class. He enjoyed science and spent much time building electric motors and mechanical toys with Maria and Giulio. In January 1915, when Enrico was 14, tragedy struck the family when Giulio died undergoing a minor operation for a throat abscess. This, of course, had a deep and lasting affect on Enrico who, already somewhat introverted, became even less outgoing. At this time he became friends with Enrico Persico, who was in the same class as school. Persico, who also went on to become a professor of theoretical physics, later wrote (see for example [4]):-

We formed the habit of taking long walks together, crossing the city of Rome from one side to the other, discussing all kinds of subjects with the brashness characteristic of youth. But in these adolescent talks Enrico brought a precision of ideas, a self-assurance, and an originality which continually surprised me. Furthermore, in mathematics and in physics he showed knowledge of many subjects well beyond what was taught at school. He knew these topics not in a scolastic fashion, but in such a way that he could use them with extreme facility and familiarity. For him, even at this time, to know a theorem or law meant chiefly to know how to use it.
Entry to the Scuola Normale Superiore in Pisa was by competitive examination. Fermi sat the exam on 14 November 1918 and wrote an essay on the given theme of Characteristics of sound. In his essay Fermi derived the system of partial differential equations for a vibrating rod, then used Fourier analysis to solve them. It was written at the level of a doctoral thesis rather than a school examination. When the examiner read Fermi's entry he was so amazed that he set up a meeting with him, telling him that it would undoubtedly win the competition and moreover that Fermi would without doubt become a famous scientist.

In Pisa Fermi was advised by the director of the physics laboratory Luigi Puccianti. Perhaps we should clarify this statement, for although Puccianti nominally had this role he acknowledged that there was little that he could teach Fermi, and frequently he asked Fermi to teach him something. Soon Fermi was publishing papers, his first Sulla dinamica di un sistema rigido di cariche elettriche in moto traslatorio being published in 1921. Another publication in 1921 was followed by the most important of his early papers in the following year, namely Sopra i fenomeni che avvengono in vicinanza di una lina oraria (On the phenomena occurring near a world line). This paper gave an important result about the Euclidean nature of space near a world line in the geometry of general relativity. Fermi submitted his doctoral thesis Un teorema di calcolo delle probabilità ed alcune sue applicazioni to the Scuola Normale Superiore and was examined on 7 July 1922. Laura Fermi writes about this event in [3]:-

The eleven examiners in black togas and square-topped hats were sitting in solemn dignity behind a long table. Fermi, also in a black toga, stood in front of them, and he started talking with cool, deliberate assurance. As he proceeded, some of the examiners repressed yawns, some sent their brows up in wonder, others relaxed and did not try to follow. Clearly Fermi's erudition was above their comprehension. Fermi received his degree magna cum laude. But none of the examiners shook hands with him or congratulated him, and the customary honour of having the thesis published by the university was not conferred upon him.
The thesis was published in his Collected Works in 1962. After the award of his doctorate Fermi returned to Rome and began working with the mathematicians there, particularly Castelnuovo, Levi-Civita and Enriques. He also made contact with the director of the physics laboratory. In October 1922 he was awarded a Government Scholarship which enabled him to work with Max Born in Göttingen in the first half of 1923. He was then appointed to teach mathematics to scientists in Göttingen during the academic year 1923-24. After spending the summer of 1924 hiking in the Dolomites, he went to Leiden to work with Ehrenfest. He returned to Italy for the start of academic year 1924-25 and he spent that academic year and the following one as a temporary Lecturer in Mathematical Physics and Mechanics at the University of Florence. At this point Fermi was trying to maximise his chances of an academic career so he published a large number of papers. He was disappointed to lose out to Giovanni Giorgi in the competition for the chair of mathematical physics at the University of Cagliari in Sardinia. It is worth noting that both Levi-Civita and Volterra supported Fermi. Perhaps it was good that Fermi lost for in 1926 another competition was announced, this time for the chair of theoretical physics at the University of Rome. This time, despite being very young for such a position, Fermi was appointed by the committee which recognised the exceptional quality of his scientific work.

At Rome Fermi began to built up the physics institute, which was surprisingly small when he arrived. Fermi married Laura Capon on 19 July 1928; they had one daughter Nella born 31 January 1931 and one son Giulio born on 16 February 1936. In 1929 he was elected to the Accademia dei Lincei. Well this is not quite accurate since he Mussolini appointed him to the Academy without an election. Certainly he deserved the honour on academic grounds but one should not assume that his appointment by Mussolini meant that Fermi supported fascism. Perhaps it is more likely that because Fermi was pretty non-political, Mussolini felt that at least he was not appointing an political opponent. The Academy appointment provided Fermi with a substantially additional salary. He made his first visit to the United States in 1930 when he visited the University of Michigan at Ann Arbor. He had interesting discussions with George Uhlenbeck, who had moved there from Holland, and Ehrenfest joined them over the summer. Fermi gave lectures on quantum theory.

In 1934 Fermi carried out his most important work on the artificial radioactivity produced by neutrons. He published this in Radioattività indotta dal bombardamento di neutron (1934) and in further papers Artificial radioactivity produced by neutron bombardment (1934, 1935) in the Proceedings of the Royal Society of London and On the absorption and diffusion of slow neutrons (1936). This work led to the discovery of nuclear fission and experimentalists were able to use his results to create new elements. Fermi was awarded the Nobel Prize in Physics in 1938. The citation states that the award is:-

... for his demonstrations of the existence of new radioactive elements produced by neutron irradiation, and for his related discovery of nuclear reactions brought about by slow neutrons.
Another important paper, published by Fermi in 1935, was Sulla quantizzazione del gas perfetto monoatomico. In this paper he presented Fermi statistics, giving a statistical model of the atom and nucleus.

In the summer of 1938 Mussolini suddenly followed Hitler in Germany in starting a campaign against Jews. Fermi was not Jewish but his wife was and, although his two children were Roman Catholics, the family's situation became uncomfortable. Fermi decided to write to universities in the United States looking for a position. He did this with complete secrecy for fear that he would be prevented if the authorities learnt of his intentions. He wrote letters to various universities and posted them all in different towns not to arouse suspicions. He received five offers and accepted the one from Columbia University. The award of the Nobel Prize proved a wonderful opportunity for the family to leave Italy and travel to the presentation ceremony in Stockholm, then go straight on to the United States. Amusingly, Fermi had to pass an arithmetic test before being granted a visa for the United States. He arrived with his family in New York on 2 January 1939.

Fermi's work at Columbia University, in collaboration with other members of his team, soon showed possible applications of his research. George Pegram, professor of physics at Columbia, wrote to Admiral Hooper in the Navy Department on 16 March 1939 (see for example [4]):-

Experiments in the physics laboratories at Columbia University reveal that conditions may be found under which the chemical element uranium may be able to liberate its large excess of atomic energy, and that this might mean the possibility that uranium might be used as an explosive that would liberate a million times as much energy per pound as any known explosive.
It took a while for things to get moving on the uranium project but a decision to make a major effort was taken, by coincidence, the day before Pearl Harbour in December 1941. The project was to be carried out at the University of Chicago with various groups, including Fermi's group at Columbia, being brought together there. This was not greatly to Fermi's liking for a number of reasons. First he was very happy at Columbia University, second it made him more of an administrator and less of a scientist, and thirdly once the United States was at war with Italy, Italians were classed as 'enemy aliens' and severe travel restrictions within America were imposed. However, the difficulties were overcome and by the summer of 1942 Fermi was in Chicago. On 2 December 1942 the team, headed by Fermi, achieved the first controlled release of nuclear energy - it is probably not an understatement to say that a new era had begun. In 1944, Fermi became American citizen and in that year he began to take a full part in the Los Alamos project to build a bomb. He taught various courses at Los Alamos for the scientists taking part in the project.

After the war ended Fermi decided that he wanted to return to university life. He accepted the offer of a professorship at the University of Chicago in 1945. Over the next few years he undertook research, becoming interested in the origin of cosmic rays and he also worked on pion-nucleon interaction trying to make progress on understanding strong interactions. He made many research visits such as Los Alamos, which he visited every year, the University of Washington (1947), the University of California at Berkeley (1948) and the Brookhaven National Laboratory (1952). He attended a high-energy physics conference in Como, Italy, in 1949. This was his first trip back to Europe since he left over ten years before. During this trip he also lectured to the Accademia dei Lincei with Castelnuovo chairing the meeting.

In the summer of 1954 Fermi returned to Italy and gave a series of lectures in the Villa Monastero in Varenna on Lake Como. He then went on to a summer school near Chamonix in France. He tried to follow his usual energetic life style with walks in the mountains and playing sports. However, he was clearly suffering from health problems which doctors had failed to diagnose. Back in Chicago doctors diagnosed stomach cancer and an operation was carried out. He survived the operation and returned home. He had told his friends that he would write up his course on nuclear physics as his last service to science if he was spared long enough. He only managed to write an incomplete page of contents for the course. Eugene Wigner wrote:-

Ten days before Fermi died he told me, 'I hope it won't take long.' He had reconciled himself perfectly to his fate.
E Sergè writes [4]:-
He preserved to the last an almost superhuman courage, strength of character, and clarity of thought.
Fermi was buried in Oak Woods Cemetery in Chicago.

Article by: J J O'Connor and E F Robertson

November 2006
MacTutor History of Mathematics