1. Childhood and adolescence.

I was born in Palermo on 2 May 1885, to Alfonso and Anna Bongiovanni, both from Lercara Friddi, a town in the province of Palermo, where, at the time of my birth, the sulphur mining industry flourished.

My father was an engineer and he lavished his wealth, that had been given to him as a dowry by my mother, in the construction and application of a device, of his own invention, which was to replace the primitive calcarone furnace for the extraction of sulphur from sulphur-bearing minerals dangerously excavated from the mines, avoiding, with this device, the propagation into the atmosphere of sulphur dioxide, deadly for agricultural production and harmful to people.

However, the discovery of rich sulphur mines in America, which had taken place in the meantime, put the Sicilian sulphur industry into crisis, reducing my father's invention inoperative, so, with his wife and three children, he was reduced to poverty. He then competed for teaching positions in construction at Technical Institutes. Having come first in the competition, he chose the chair in this subject at the Technical Institute of Arezzo and from there began his teaching career which he continued until his retirement. In a short time, my sisters and I became perfect Aretines there, even in our speaking.

I was then just five years old, but I was immediately fascinated by the works of art of which Arezzo is rich and my father, realising this, one day when he saw me ecstatic in admiration of paintings by Piero della Francesca, in the church of San Francesco, made me attend, simultaneously with elementary school, the art studio of the unforgettable master Pini, under whose guidance I made some drawings, one of which was awarded, in an exhibition, with an honourable mention from the Petrarca Academy of Arezzo.

I began, therefore, with art, and, later becoming a mathematician. I remained in art, however, since mathematics can be called such only if it has the harmony of the arts and if, like the most refined among these, it satisfies a high aesthetic sense.

However, I did badly at school and very badly at arithmetic. I remember that one day, when I was in the fourth grade, my teacher, who was called Cosimo Citernesi, shouted at me at an answer that I gave him to solve an arithmetic question: "If I had a hat on my head I would hit you with a hat."

When my father came to inquire about my progress at school, my teachers unanimously told him that I was an idiot.

My father, who did not share this opinion, entrusted me to a teacher, the gentle and good teacher Piccioni, whose first name, unfortunately, I do not remember, so that she could give me some lessons. But even from these I did not benefit. Suffice it to recall, in this regard, that one day, when teacher Piccioni had to interrupt the lesson to go to her bedroom, adjacent to the small room where the lesson was held, to see the dressmaker who had come to try on a dress for her, I, left alone, seeing the key to that room in the lock of the door, found nothing better to do than lock the room and go for a walk through the streets of Arezzo. The two ladies, who remained prisoners in the room, were then freed in the evening by the teacher's husband who, when he returned home for dinner, did not find it ready, which must have also happened to the dressmaker's husband!

After obtaining my elementary school diploma, I went to the Technical School, where I received mathematics lessons that were far from attracting me to study this subject, while I began to enjoy Italian and geography, becoming one of the most appreciated students for the drawing of geographical maps, portraying the orographic and water aspects of the regions to which they referred. In the third year of that school, I occasionally had, for a temporary assignment entrusted to him, my father as my mathematics teacher, who taught the subject as a rigorous deductive system.

So I began to enjoy this subject, especially its geometric part. My father made me repeat the year, as it did not seem to him that I had reached the maturity necessary to undertake the studies planned in the next year at the technical institute. He put in my hands the wonderful books of arithmetic, algebra and geometry by the German mathematician Riccardo Baltzer, translated into Italian by our great Luigi Cremona, founder of the unsurpassed Italian geometric school, the collection of geometry problems by the Danish geometer Julius Petersen in the Italian translation by Vincenzo Mollame and that inexhaustible mine of "Exercices de Géometrie" by F.I.C., published in 1882 in Paris by the Poussielgue brothers.

I became passionate about studying these books and, since then, I have intensely loved mathematics, this queen of the sciences.

I was then fortunate to have, in the third and fourth year of the Technical Institute, as a teacher of mathematics, the great geometer Michele de Franchis, who directed me in the study of algebra and analytical geometry, then the subject of the teaching programmes of mathematics in the first two years of university studies for the degree in mathematics, physics and engineering. He made me study the Lessons of Analytical Geometry, dictated by the great mathematician Guido Castelnuovo, at the University of Rome. With Castelnuovo then, separated from de Franchis since he transferred to a university chair, I began, with great pride, an epistolary correspondence for the resolution of some problems of analytical geometry, proposed in those Lessons of his.

From that time on, I was also very attracted by the studies of physics and chemistry, where I saw the application of mathematics, which I undertook in the books of Antonio Roiti, of the Frenchmen Éleuthère Mascart and Charles Joubert, and of the Dutchman Arnold Holleman.

I was subjected to teasing by my classmates at the Technical Institute of Parma, my father having moved there, a truly reprehensible thing. They did not like me because I was from the South, but teasing soon turned into demonstrations of sympathy and even friendship, after the first lessons of mathematics and physics, in which I solved the assigned problems, as soon as the dictation of their statements was finished. I obtained my diploma from that Institute.

As a teacher of Italian there I had the scholar Abd-el-Kader Salza, a gentle and wise man, who took a liking to me. Once I had obtained my diploma from the Technical Institute, he advised me to compete for a place as an internal student at the Scuola Normale Superiore of Pisa, which he called the Alma Mater of Normalists, of which he himself had been a student.

2. Youth.

I followed this advice and, in October 1903, I took part in that competition, coming in first, with 36 out of 40 marks, while the second - who was my unforgettable dear friend Luigi Amoroso, who later became, over time, a great economist of world fame - got 30 out of 40 marks.

My victory in this competition was however embittered by typhoid fever, which struck me right at the end of it, which forced my parents to rush to Pisa to look after me in a small room in a very modest guesthouse. I recovered in three months and entered the Scuola Normale and the University of Pisa in late January 1904.

I enrolled at the University of Pisa to obtain a degree in Physics, following, as was mandatory, the internal courses at the Scuola Normale, in Mathematics and Foreign Languages.

However, at the Institute of Physics, some serious inconveniences arose in the preparation of the experiments on which the research assigned to me for the compilation of the thesis in physics was to be based, so following the advice of my great beloved master Luigi Bianchi, in the third year of studies I abandoned the project of graduating in physics and took up that of graduating in mathematics. Carrying out a thesis assigned to me by Bianchi himself, I graduated in mathematics, at the University of Pisa, obtaining the highest marks, receiving honours and the declaration that the thesis presented was worthy of printing. Awarded, in the following year, the Lavagna Prize of the University of Pisa, I remained there until 1913, as assistant to the chair of infinitesimal analysis held by the great Ulisse Dini.

I must mention the beneficial influence of the daily conversations that I had - in the period 1904-1908 - with the great mathematician and my dear friend Eugenio Elia Levi, on my training as an analyst. He was also a student at the Normale, my predecessor in the assistantship to Ulisse Dini, and rose to the chair of Mathematical Analysis at the University of Genoa in 1908, but died heroically fighting during our defeat at Caporetto, in the 1915-18 war against the Central Powers.

On 30 October 1913, I was married to Miss Maria Jole Agonigi of Pisa, daughter of a wealthy family of honest merchants. My wife had a great beneficial influence on my life as a scholar. With constant joyful renunciation of the superfluous, with incessant material, moral and spiritual assistance, she gave me the opportunity throughout my life, to think of nothing but study and to find in a well-run house the environment most suited to meditation and recreation.

On the same date we moved to Turin, where I held the assistantship for the chairs of Rational Mechanics and Infinitesimal Analysis, both at the Polytechnic and at the University and in 1915 I obtained the docent university teaching qualification in the latter subject.

The outbreak of the First World War 1914-1918, upset our quiet and industrious life.

Called to arms, with my year (of 1885), in April 1916, I was assigned to the 6th Regiment of Fortress Artillery, whose Depot was in Turin, with the rank of second lieutenant of the territorial army without having ever previously performed military service and having never seen, up close, a cannon. In July 1916, after having wasted precious time doing training on foot, I was sent to the combat front and assigned to the First Army, operating in the mountains of Trentino. In this case, by pure chance, I was fortunate, since it was enough that the Command of the Turin Depot, rather than to the First Army, had sent me to one of those operating in the plains, on the Isonzo, because, as will be seen shortly, if my qualities as a mathematician had not had the opportunity to immediately reveal themselves useful, I would have remained, perhaps forever, working with the purely speculative concepts of mathematics.

When I presented myself to the Artillery Command of the First Army, I was greeted with a cold speech, like this:

The depots continue to send us officer after officer, whom we have no need of. We do not know, for the moment, what to do with you. Report back in eight days. What did you do as a civilian?

I replied that I was a lecturer in infinitesimal calculus at the University of Turin and I left dejected and disappointed. At the end of the eighth day I presented myself to the said Command and was informed that Colonel Federico Baistrocchi, commander of the 21st Siege Group, operating between Vallarsa and Vallagra, at the foot of Pasubio, had shown interest in having an officer with expertise in calculus under his command, and that therefore I had been assigned to that Group which, with makeshift means, I had to reach that day.

After a very eventful journey, I arrived, late at night, at the Command to which I had been assigned and was immediately received by the Commander, Colonel Baistrocchi, who was waiting for me. He immediately began to show me, on a military map of scale 1:25000, the deployment of our dependent siege artillery, consisting of large and medium calibres, located along the Vallarsa and Vallagra, at an altitude that varied from 400 to 1000 meters above sea level, which had been assigned the task of hitting the Pasubio and the Alpe di Cosmagnon and their rear, strongholds of the enemy defence, at an altitude of over 2000 meters, behind which our assault troops, composed of Bersaglieri and Alpine troops, and ..., no less, had long been stationed and entrenched. You can well imagine how amazed I was! I was thinking: but how come our artillerymen who have been fighting for almost two years, who should possess the most up-to-date theoretical and practical notions of tactics, learned at the War School, need, in carrying out their current war tasks, the opinion of a territorial lieutenant, who has never seen a cannon, fresh out of the university classrooms?

I replied to Colonel Baistrocchi, perhaps not even managing to hide my astonishment, that I had no knowledge whatsoever of artillery and, even less, of its tactical use. But he, and with this he demonstrated that he was up to the task, said to me:

It is a matter of solving a calculus problem and you must be able to do it, it is a matter of calculating the data to be supplied to our assault artillery, for firing against targets for which the regulation firing tables, which they possess, are not sufficient.

But, I added, I have no knowledge of ballistics, on which, I suppose, those calculations must be based. Then the Colonel took out a yellowed bulky book from an ordinance box and said to me:

Here is the treatise on ballistics by Francesco Siacci. I give you the order to study it and to derive from it, within a month from today, the calculation of the firing data for our siege artillery, against the strongholds of the enemy deployment.

And he dismissed me.

I set to work feverishly, even spending the night there, by the uncertain light of a candle, and soon recognised the correctness of Colonel Baistrocchi's opinions, even coming to explain to me the difficulties, in the calculation of the firing data, encountered by our artillerymen, which could not be overcome by them.

This is how things stood. For artillery fire in the mountains, in the previous peace period, the use of cannons of the smallest calibre, called mountain cannons, transportable on the back of a mule to the highest mountain crests, cannons that fired without calculation, with direct aiming, were used. But due to the recent possibility of rapidly building solid roads, even in the impervious mountain terrain, and of using powerful tractors that could tow, even on steep roads, artillery pieces of any calibre and weight, it was thought - by us and by the enemy - to avail themselves, even in the high mountains, of the assistance of the fire of medium and large calibre cannons and to destroy the enemy's very resistant fortifications and also, with a strong and precise fire, to precede, in the offensive, our own advancing assault troops or to block, in the defensive, the path of the enemy's troops in front of our lines.

However, the regulation firing tables, supplied to medium and large calibre artillery, provided firing data for targets placed on the same horizontal plane as the battery, allowing slight corrections to the data themselves, if differences in level between battery and target occurred, which however must not exceed certain limits. Now in the ravines of Trentino, these limits were usually exceeded, and often exceeded to the point that the difference in level between battery and target was of the same order of magnitude as their mutual horizontal distance. Having ascertained this, I was easily able to determine the causes of the disasters caused by the firing of our artillery, which was often, due to fatal and inevitable errors in calculation, focused on our defences, rather than those of the adversary. It was necessary, without delay, to redo, with completely different criteria, the firing tables for the said artillery, basing them on certain non-immediate improvements of classical rational ballistics, something that could only be achieved by a mathematician.

I obtained them in the month prescribed for me and starting from the following month of September 1916 all the artillery of the 21st Siege Group fired correctly with data calculated by me.

On 9 October 1916, the 44th Division, under the command of General Andrea Graziani, successfully launched its offensive against the enemy strongholds of Pasubio and Alpe di Cosmagnon, conquering them with effective, precise fire from our artillery, destroying enemy fortifications and accompanying our brave advancing troops. For the first time, the elders of the Artillery Command told me, the wounded who returned from the front line during the battle, passing in front of our Command, shouted "Long live the artillery" instead of "Down with the shirkers".

You can imagine, after this success of mathematics, in what a different light it appeared to me. I thought: so, mathematics is not only beautiful, it can also be useful.

During the winter break in the high mountain operations, between the last months of 1916 and the first of 1917, work was carried out at the battle front to compile new firing tables, suitable for the use of medium and large calibre artillery in the mountains, to distribute the tables themselves to the batteries in the various sectors of the mountain front and for the necessary exercises with the new firing methods. In these tables, coefficients were also introduced - at a later time - the necessity of which was noted, during the war, for the correction of firing data in relation to the variations in the physical and dynamic conditions of the atmosphere, as well as those of the ammunition and material, solving mathematical problems for this difficult task as well. Naturally, the need for these last corrections was also imposed on the artillery operating in the plains and in all belligerent exercises. In France, for example, to satisfy this need, an Institute was founded in Paris where famous mathematicians worked, among whom were, no less than the immortal Emile Borel and Jacques Hadamard of the French Academy. At the end of the war, it was possible, nevertheless, to demonstrate that, for the calculation of the corrections to be made to the firing data, regarding the disturbance caused by the wind on the projectile's motion, the method followed by us had a rationality not possessed by the one adopted by the French. The two methods agree when the wind remains constant, in intensity and direction, at various altitudes, and therefore the French could not be easily informed of the irrationality of their method, since in their firings, mainly on the plain, they almost always had to consider almost constant winds at various altitudes. This was not the case for us, however.

For example, a projectile launched from the bottom of Val Brenta, most often encounters, in the narrow valley, during the first 900 meters of ascent, a certain wind in the direction of the valley itself, while then, having exited it, it finds a completely different state of motion of the atmosphere, as was well demonstrated, even then, by the determinations of the aerological stations set up at the very front of the battle.

The new methods of firing spread rapidly, during the war I am speaking of, among all our fighting artillery.

And it is right, I think, to remember one of the great decisive successes achieved by the artillery of the VI Army, under the command of General Roberto Segre, after the complete renewal. When the Austro-Hungarian offensive was launched in mid-June 1918, that Army broke it, on its own front and on part of that of the IV Army, almost exclusively with (night) artillery fire, also managing to paralyse, by counter-attacking it, the enemy artillery.

I am pleased to fulfil the obligation to remember the precious, often decisive, collaboration that the unforgettable deceased friends Alessandro Terracini and Antonio Signorini gave me, in the fulfilment of the difficult tasks indicated above.

In 1916, I achieved promotion to the rank of Lieutenant for exceptional merit, in 1917, promotion to the rank of Captain for war merit, in 1918 the War Merit Cross and the French War Cross with Silver Star. I was recently awarded the title of Cavaliere di Vittorio Veneto.

There is an opinion on my war work by the Marshal of Victory Armando Diaz expressed in the following letter from the Ministry of War.

While I thank you for the pamphlet you sent me on "Italian artillery in the world war", I am deeply pleased with the interest that your excellency retains in military technical studies, to which already during the war, and with such profit for the Army, you dedicated all your intellect and your noble enthusiasm.

After the war, having returned to the university classrooms, although I was immediately seized by the need to regain the position I had lost, during the three years of war, in the purely scientific arena, I never stopped thinking of mathematics as a powerful aid to experimental sciences and technology, and of an organisation of things that would allow the mathematician to intervene promptly in problems, of a purely mathematical nature, that had prevented the progress of research in those sciences and their applications, including industrial ones.

From those first years of regained peace (alas, how temporary!) the idea of ​​creating an Institute, in which mathematicians, equipped with the most powerful numerical calculation tools, could collaborate with scholars of experimental sciences and technicians, to obtain the concrete resolution of their numerical evaluation problems, flashed through my mind.

I thought that mathematical imagination, provided it rests on solid analytical foundations, can be capable of the greatest conquests in the fascinating problems that Natural Science poses to our reasoning, but if we did not want everything to be finished, as Leonardo says "in words" it was essential to provide the mathematician with a powerful organisation giving the means to arrive at the numerical evaluation of the quantities considered in the problems under study. Hence the use of calculating machines, even by the mathematician, hence the conception of laboratories also for the mathematician, who could no longer be depicted as the abstract isolated thinker who only needs paper and pencil for his work. The mathematician had to leave the confines of his study room and descend among the crowd of those who seek to reveal the mysteries of Nature and conquer its hidden treasures.

Since those years, I have been advocating, with inexhaustible tenacity, these ideas of mine among my friends and in my teaching, in scientific and industrial environments. But they progressed extremely slowly! Today more than ever, the opposition to their advancement that came from almost all mathematicians is inexplicable.

But remembering the maxim of Prince William of Orange, according to which "It is not necessary to hope in order to act, nor to succeed in order to persevere" I did not give up, not even after a vote against the creation of the planned Institute of Calculus, issued by the Italian Mathematical Union, also because I had verbal incitements, extremely stimulating, to implement my project, from the illustrious Masters who have passed away:

Luigi Bianchi,
Guido Castelnuovo,
Ludwig Prandtl,
Arnold Sommerfeld,
Vito Volterra.

In 1927, with funds provided by the Bank of Naples, I set up, near my Chair of Infinitesimal Analysis at the University of Naples, an embryonic Institute for Calculus Applications, equipped with calculating machines, of modest power, but sufficient to begin the experiment.

The most unexpected success smiled upon it!

Research in nuclear physics was usefully undertaken along the purely theoretical path followed by Enrico Fermi between 1925 and 1937, in electromagnetism, proposed by the physicist Luigi Puccianti, in the elasticity of solids, proposed by the engineer Luigi Ricci, in thermodynamics, proposed by the chemist Francesco Giordani, in mechanics applied to machines, proposed by the engineer Enrico Brunelli, etc. It was immediately noted that a circumstance had occurred that was easily foreseeable, namely this: Mathematics, put to the test for its application to problems posed by the study of Nature, which, as Laplace said, "is not concerned with analytical difficulties", encountering completely new and unexpected problems, with the condition of arriving at accurate numerical evaluations of the solutions, had to develop in directions that were completely unexplored or to advance greatly in some already followed.

The pure mathematician creating his theories, solely attracted to them, is in some respects a good thing - from the philosophical and aesthetic side of mathematics, sometimes trusting, as Emile Picard says "in a kind of pre-established harmony between its logical and aesthetic satisfactions and the needs of future applications", but the physicist or engineer, in vain, very often, will search, among the results of those theories, for what is right for him. The theory has thoroughly studied a certain class of problems, in a finite interval of variability of the independent variable, and behold, for a problem of the same class, the physicist needs that interval to be infinite; the theory has considered the linear case, and behold, a certain non-linear case presents itself to the physicist; the theory has considered the case that the assigned functions are everywhere finite and continuous, and behold, those same functions present themselves to the physicist, in a certain particular way, as infinite or discontinuous!

Unfortunately, the pure mathematician who enters the field of applications to experimental sciences or technology finds, in his turn, the most bitter and stinging disappointments about the power of what he has created.

The good results obtained, in a short time, by the small Institute of Calculus of the University of Naples, in the new mission that I had entrusted to it, induced, in 1932, the National Research Council, then presided over by Guglielmo Marconi, to take the Institute itself among its own, transferring it to Rome, to whose University I had in the meantime moved, elevating it, under my direction, to the rank of National Institute, with the title of National Institute for the Applications of Calculus.

The original Institute of Naples, which from now on I will designate with the acronym INAC, was able, after that, to greatly expand its sphere of action, penetrating also into numerous industrial or merely technical environments, both Italian and foreign, among which were the technical offices of our Ministries of Defence, Public Works, Transport, Post and Telecommunications, Industry and Commerce.

Collaboration with scholars of physical and natural sciences became more intense and, in particular, with Enrico Fermi, who was also resident in Rome at the time, in his research in nuclear physics, with calculations being carried out at INAC for the spectra of ions and the self-solutions of the Schrödinger equation, fundamental for that research, in correspondence with various values ​​of the atomic number.

Collaboration with the Ministries of the Air Force, the Army and the Navy became a project, governed by a special agreement. For example, INAC is responsible for compiling the computations for aerial bombing, which gave our Air Force considerable offensive power from 1935 onwards; for calculating the critical speeds of aircraft, that is, those speeds of flight of the aircraft, in which a persistent deformation of the wing is possible, which would certainly lead to catastrophe, speeds that must be prohibited; for calculating the critical speeds for drive shafts that cannot exceed that speed without endangering the stability of the shaft, etc.

If we think of the innumerable applications of drive shafts in all the needs of modern life, from the motion of ships, automobiles, airplanes, to that of machines in factories of all kinds, we can then, not without emotion, ask ourselves whether, with a prior, sure knowledge of the critical speeds of drive shafts, in their various uses, we could perhaps avoid many of the disasters that, with painful losses of human life and with huge damages, blight civil progress.

With the industries producing electricity, INAC entered into fruitful collaboration in the projects of large dams to block mountain waters, which must be based on a precise knowledge of the tensions that will arise inside the dam, due to the pressure exerted on one of its walls by the enormous mass of water that will have to be retained at a predetermined height and due to the high thermal gradient to which the dam will be subjected, due to the notable difference in temperature between the wall in contact with the water and the opposite wall, heated by the sun. The terrifying cataclysms caused by the collapse of dams on artificial lakes are well known and one can therefore well imagine the commitment with which INAC tried to do its best in carrying out the difficult calculations that were to lead to that knowledge, at the design stage.

INAC has collaborated with the civil construction industries for building constructions, for the construction of roads, bridges, towers, cranes, etc.

In these constructions, a difficult problem of mathematical analysis arises, concerning the preventive calculation of the frequencies of the oscillations proper to the designed structures, those oscillations, that is, that the structure can acquire, maintaining them for a long time, as a result of a blow. If a structure is subjected to a repeated blow, with a frequency close to that of its own oscillation, it certainly breaks, and then there is a disaster. The said structures must therefore be built in such a way that the frequencies of their own oscillations remain very far away - hence the need for their precise calculation, at the design stage, from those, if it is a question, for example, of a bridge, of repeated blows, inflicted on them by a vehicle, which must cross it.

In leaving the management of INAC in 1960, having reached the age limit, I asked myself whether it was not my precise duty to try to demonstrate to my successors in that management the value of what I was leaving in their hands, so that they would be incessantly encouraged to dedicate the best of their energies to preserving it and, as was certainly possible, to increasing it. It seemed to me that the most effective way to achieve this aim was to gather together in a volume the opinions on the work of INAC, now more than thirty years old, expressed by those who had used it or merely considered using it.

I published such a volume in 1959. It makes known the aforementioned judgments expressed in writings from almost 300 people including world-famous scientists, engineers, industrialists, Italian or foreign ministers, heads of technical services of the Italian and Spanish Ministries of War, Industry, Communications, Public Works, Air, Naval and Army Defence.

It is worth noting the international nature of these judgments that come from the following countries:

Argentina, Austria, Belgium, Brazil, Bulgaria, Canada, Czechoslovakia, China, France, Germany, Japan, India, England, Italy, Yugoslavia, Holland, Peru, Poland, Portugal, Romania, Spain, Sweden, Switzerland, Turkey, Hungary, U.S.S.R., Uruguay and U.S.A.

3. Maturity and old age.

In 1955 I managed to obtain, from the Ministry of the Treasury and Administration of the National Research Council, the funds necessary to equip INAC with an electronic computer. With this it multiplied its numerical calculation capabilities a hundredfold and was able to quickly arrive at the expected resolution of many problems, important for the economic and scientific progress of our country, in which, for the first time, such computers were used.

In 1919 I was called to Catania as a lecturer for the teaching of Infinitesimal Analysis and Higher Analysis.

Having come first in the 1920 competition for Infinitesimal Analysis for the University of Cagliari, I was appointed, starting from October 1920, Professor of that subject.

I was called, in 1921, again to Catania for the teaching of Infinitesimal and Higher Analysis, in 1924 to Pisa to the Chair of Higher Analysis which had been that of my master Ulisse Dini, in 1925 to Naples, for the teaching of Infinitesimal Analysis and Higher Analysis, in 1932 to Rome for the teaching of Higher Analysis, from 1941 as a lecturer, having in that year, transferred to the Chair of Mathematical Analysis in the same University. In 1955 I was removed from my Chair having reached the age of 70 and in 1960 I was retired having reached the age of 75 and at the same time I was awarded the title of Professor Emeritus of the University of Rome.

My work as a lecturer has been one of the most fortunate. The following mathematicians have professed or profess to be my disciples, whom I name in chronological order.

1) Gabriele Mammana (deceased, was Professor at the University of Naples)
2) Renato Caccioppoli (deceased, was Professor at the University of Naples)
3) Antonio Colucci (deceased, was Professor at the Air Force Academy of Caserta)
4) Fabio Conforto (deceased, was Professor at the University of Rome)
5) Giuseppe Scorza Dragoni (Professor at the University of Bologna)
6) Gianfranco Cimmino (Professor at the University of Bologna)
7) Carlo Miranda (Professor at the University of Naples)
8) Demetrio Mangeron (Professor at the University of Iasi)
9) Carlo Tolotti (Professor at the University of Naples)
10) Wolfango Gröbner (Professor at the University of Innsbruck)
11) Lamberto Cesari (Professor at the University of Michigan)
12) Tullio Viola (Professor at the University of Turin)
13) Mario Salvadori (Professor at Columbia University)
14) Luigi Amerio (Professor at the Polytechnic University of Milan)
15) Gaetano Fichera (Professor at the University of Rome)
16) Wolf Gross (Professor at the University of Rome).
17) Giuseppe Grioli (Professor at the University of Padua)
18) Sandro Faedo (Professor at the University of Pisa)
19) Domenico Caligo (Professor at the University of Pisa)
20) Giovanni Aquaro (Professor at the University of Bari)
21) Aldo Ghizzetti (Professor at the University of Rome)
22) Walter Gautschi (Professor at the University of Lafayette)
23) Benedetto Pettineo (Professor at the University of Palermo)
24) Ferdinando Bertolini (Professor at the University of Pittsburgh)
25) Carlo Pucci (Professor at the University of Florence)
26) Ennio De Giorgi (Professor at the University of Pisa)
27) Paolo Tortorici (deceased, was Professor at the University of Aquila).

All these disciples of mine, as I have always desired, have surpassed me in research, invention and teaching, many of them gaining world-wide fame.

I have more than 360 publications concerning ordinary or partial differential equations, integral equations, the calculus of variations, functional analysis, series expansions, approximation of functions, numerical calculus, the theory of functions, differential geometry, mechanics (especially ballistics and shooting technique), the mathematical theory of elasticity, automation of calculation.

The following are my main works.

1) Introductory theory of ordinary differential equations and calculus of variations (Catania, 1922);
2) Lessons in infinitesimal analysis (Catania, 1923);
3) Lessons on differential equations and total differential equations (Rome, 1939);
4) Notes on higher analysis (Naples, first edition 1940, second edition 1946);
5) Foundations of linear functional analysis (Rome, 1943);
6) Modern theory of integration of functions (Pisa, 1946);
7) Lessons in functional analysis (Rome, 1946);
8) Lessons in calculus for engineering students (first edition, Naples, 1925; second edition Rome, 1946);
9) Lectures on Algebra for Engineering Students (Rome, first edition 1942, second edition 1946); .
10) Lectures on Series for Engineering Students (Rome, 1945);
11) Exercises on Mathematical Analysis (in collaboration with C Miranda) (Rome, first edition 1942, second edition 1946);
12) Treatise on General Mathematics (in collaboration with P Tortorici) (Rome, 1947);
13) Introduction to the Calculus of Variations (Rome, 1951);
14) Lectures on Mathematical Analysis for Engineering Students (Rome, first edition 1949, second edition 1951);
15) Lectures on the Modern Theory of Integration (in collaboration with T Viola) (Turin, 1952);
16) Treatise on Mathematical Analysis (in collaboration with G Fichera) (Rome, vol. I, 1954, vol. II, 1955);
17) Lessons on a theory of linear integral equations and their applications, according to the guidance of Jordan-Hilbert (in collaboration with Ennio De Giorgi) (Sao Paulo, 1945);
18) Necessary criteria for an extremum of some functionals (Rome, 1959).

I have been awarded the following prizes and titles.

Royal Prize of the Accademia dei Lincei for Mathematics, Tenore Prize of the Royal Society of Naples, Severi Prize of the National Institute of Higher Mathematics, Gold Medal of the Meritorious Persons of Culture and Art, Gold Medal of the Faculty of Science of the University of Rome, Gold Medal of the National Research Council, Gold Medal of the French Society of Encouragement for Research and Invention. Professor Emeritus of the University of Rome.

Knight Grand Cross of the Order of Merit of the Italian Republic.

Knight of the Civil Order of Savoy.

Academician of the Pontifical Academy of Sciences, of the Accademia Nazionale dei Lincei, of the Accademia Nazionale dei XL, of the National Society of Sciences, Letters and Arts and of the Pontaniana of Naples, of the Academy of Sciences of Turin, of the Academy of Sciences of Palermo, of the Accademia Gioenia di Catania, Honorary member of the Academy of Sciences, Letters and Arts of Modena, Emeritus member of the Institute of Encouragement of Naples.

Corresponding member of the Lombard Institute of Sciences, Letters and Arts, of the Accademia Petrarca di Arezzo, of the Academy of Sciences of the Institute of Bologna.

Member of the Society of Sciences and Letters of Warsaw, of the Polish Academy of Sciences, of the Royal Academy of Exact Sciences of Madrid, of the Academy of Sciences of the Socialist Republic of Romania. Doctor of Mathematics, honoris causa of the University of Sao Paolo (Brazil) and of the University of Bucharest.

Administrator, since 1950, of the Accademia Nazionale dei Lincei. Honorary Director of the National Institute for Applications of Calculus. Honorary member of the Italian Institute of Actuaries and of the Institute of Methodological Studies of Turin. Honorary citizen of the city of Lercara Friddi.

I will end my long speech by reading a judgment by Jacques Hadamard on my work, in science and in proselytism, expressed in a letter addressed to the President of the Committee promoting the honours that were paid to me at the University of Rome on 15 January 1956, upon my seventieth birthday, when, by law, I stepped down from my chair [see the pamphlet "Honours to Mauro Picone", Rome (1956), 45-46].

Mr President and dear Colleagues,

Mathematicians all over the world are unanimous in their admiration for the work of Professor Mauro Picone. A magnificent work in its double aspect.

On the one hand, in fact, Mauro Picone has directly given to Science the most beautiful results, the resolution of numerous and difficult problems at the same time as a profound significance for the progress of our knowledge.

But no less magnificent is the role of animator that assigns him a special place in our scientific generation. His tireless activity has constituted over the past years a galaxy of young researchers who have also obtained, in the field of both theoretical and applied analysis, a number of results that have deserved all our attention.

I believe I agree with all the mathematicians of our time in ardently associating myself with the feelings of admiration and gratitude that will be expressed in the ceremony of15 January 1956.

Please accept, Mr President and dear Colleagues, the assurance of my highest consideration.

Jacques Hadamard

By 1938 Picone's and Severi's visits to Warsaw and Kraków were no longer scientific trips but missions of science and Italianness. For example, during his visit in Poland Picone gave four purely mathematical talks and a political lecture, Gli apporti del Consiglio Nazionale delle Ricerche italiano al progresso dell'Economia e della potenza militare della nazione, delivered in Kraków on 22 April 1939 and replicated in Warsaw on 7 May. Some passages of Picone's correspondence are even more impressive. In a letter to Sierpiński and Banachiewicz, we read for example:

You certainly know the anti-Jewish measures taken by our government for universities and academies and it is therefore urgent that scientists of Aryan race collaborate as actively as possible to show how science can equally advance even without Jewish intervention, and this will be all the more effective if such collaboration be international. I therefore ask you to send me your own unpublished works or papers by your followers as soon as possible for publication in the periodicals edited by the Academy of Lincei and the Royal Society of Naples. In particular, works from Arians are needed for the Accademia dei Lincei, in which the number of members of the Jewish race has reached a very high percentage. Sure that you will certainly want to promote a great increase in Aryan-Polish scientific collaboration with the Italian Academies, waiting for your positive response, I send you ... my best wishes.

The epilogue is tragic. Picone's last letter to Banachiewicz is dated 10 October 1940. Italy had entered the war exactly four months before. A long break in relationships followed. Picone rallied for the release of Wilkosz, Gołąb and Stanisław Turski (1906-1986), who were arrested in the Aktion Gegen Universitat Professoren, but he received no evidence that his appeals were welcomed. Relations were re-established in the autumn of 1945. Both the Polish and the Italian mathematical schools had been terribly affected by war and persecution. Warsaw University had been burned down. Lwów University was no longer in Poland. More than 60% of Polish mathematicians had been killed (by Germans or Soviets) or died in the years 1939-1945. Before and after the war, many excellent mathematicians emigrated (Eilenberg, Ulam, Zygmund, Kac, Nikodym). The Italian School of mathematics no longer existed: Fano, Fubini, Segre, Terracini, and Levi had emigrated; Fubini, Volterra and Levi-Civita had passed away. The Turin University had burned down in 1943, but miraculously, part of its heritage was saved by some willing students and young professors like Tricomi who transferred it to cellars and shelters in the city by night. Picone and Severi themselves failed to conceive so much brutality in a people that gave birth to Goethe and Schiller and to a profusion of scientists whom they loved and with whom they had lived in spiritual communion throughout their intellectual lives.

The last act in this history is again an episode of solidarity. In the name of the scientific exchanges that had united Italian and Polish mathematicians since 1891, the surviving members of the Schools of Peano and Segre organised a sort of rescue mission. Picone wrote to Ugo Amaldi in a letter dated 24 December 1945:

... we badly need to make friends abroad, and Poland is certainly very fertile ground for the renewal of friendships with Italy. Much of the misfortunes that occurred to Europe and in particular in Poland are due to fascisms, and also for this reason it is a duty that Italy try to make amends in those sectors in which it is possible to do so.

The action was coordinated by Picone, who, with a heart full of horror in front of the evidence of Nazi crimes, organised the donation to the Mathematical Seminar in Warsaw of the entire collections of mathematical journals published by Italian scientific academies and societies.