The Life of Kurt Otto FrierdrichsBy Constance ReidWritten in 1983 for a mathematical journal and later published as an introduction to the two volume selected works of K.O. Friedrichs |

I knew K. O. Friedrichs only during the last dozen years of his life when, for a long period, we worked very closely on a book about

Richard Courant. Since his life and Courant’s were intimately connected, he told me a great deal about himself in the course of telling me

about Courant. I have drawn also on the recollections of his family and a few colleagues — especially Hans Lewy — and on the account

of his scientific work which he himself wrote for McGraw-Hill’s Modern Scientists and Engineers.

Friedrichs was born on September 28, 1901, in Kiel, a Baltic port and the capital of the German state of Schleswig-Holstein. He was

christened Kurt Otto, but in later years he objected to the sharp, abrupt sound of “Kurt,” which he felt didn’t suit him, and preferred to be

called “Frieder”.

He was the second of three children. (An older sister became a teacher of English and a brother, a distinguished English translator and

interpreter.) The mother, Elisabeth Entel Friedrichs, was from Silesia. She was an exceptionally lovely woman whom the boy Friedrichs

adored and for whom he was to name his only daughter. The father, Karl Friedrichs, was a lawyer and legal writer, an expert on laws

affecting the Civil Service. He could be maddeningly fussy in small matters — “quite impossible” — but superb and very wise in the big

things, so Friedrichs described him. It was a description which his own sons would later feel could be even more appropriately applied to

him.

The Friedrichs family had long been established and politically active in Schleswig and Holstein — the great-grandfather having fought for

their independence from Denmark — but the family left Kiel shortly after Friedrichs’s birth and by the time he was ready for school had

settled in Dusseldorf. There the elder Friedrichs became acquainted with another lawyer, the brother of the mathematician Felix Klein, the

powerful director of mathematics at the University of Gottingen — commonly known, even beyond the borders of Germany, as “the

mecca of mathematics”.

Throughout his youth, Friedrichs was plagued by asthma and rarely able to participate in the activities of the other young people. He

remembered himself as very timid; however, after he had made the Abitur at the Realgymnasium in Dusseldorf, he moved — following

the custom of the day — from university to university: to Greifswald for a term, to Freiburg for a year, and to the Austrian university of

Graz for a term.

“Then I said to myself, ‘Now I must go to the mecca of mathematics!”’

In the fall of 1922 he arrived in G6ttingen with a letter of introduction from Felix Klein’s lawyer brother. Richard Courant had just

recently succeeded Klein as director of mathematics and was now attempting in his own way to recreate the scientifically stimulating

environment which he had known at the university during his student days.

The times had become much harder since the war of 1914—1918. Inflation had reached staggering proportions. A university mess hail

had replaced glamorous dining clubs; and, as unappetizing soups and stews were ladled from a long trough, students flirted with serving

girls in the most often unfulfilled hope of getting larger portions. Constantly thinking about food, they found it impossible to concentrate

on their books. Friedrichs, like many others, lived in a former prisoner-of-war camp.

“[Yet] in spite of a high degree of enforced frugality,” Courant later recalled, “the general intellectual life in the university was intense,

idealistic, permeated by profound desires to find a firm position in the struggle with the problems of the times, political, philosophical,

religious, humanistic, artistic, and literary, not to speak of the challenges which came from the new emerging scientific fields of relativity,

quantum mechanics, genetics, aerodynamics, etc.”

Friedrichs did not come unprepared for such an intellectual life. In Freiburg he had been “infected,” as he put it, by the philosophy of

Husseri and Heidegger. His original scientific interest had been mathematical physics; and his mathematical hero was Hermann Weyl, who

was making contributions to the foundations of mathematics as well as to relativity theory in the early 1920’s.

Another student who arrived in Gottingen the same year as Friedrichs was Hans Lewy, with whom he later collaborated on several

important papers. Lewy, two years younger, was impressed by Friedrichs’s “vast and well organized” knowledge; but Friedrichs himself

was overwhelmed by the superior knowledge of the young lecturers and assistants in Gdttingen. These included such future luminaries as

Carl Ludwig Siegel and Emil Artin — “such a bunch of people who knew everything about everything!”

He was also captivated by the informal and scientifically exciting atmosphere which existed around Courant and by Courant’s approach to

mathematics (although it would always be quite different from his own). Reading the Hurwitz-Courant book on function theory, which

appeared in 1922, he found the two sections by Hurwitz “very neat, very clear, to the point, you could learn from them,” but the third

section by Courant on geometric function theory— “I started reading one morning, I read morning and night without stopping. It was the

most breathtaking book I have ever read in mathematics.” Inaccuracies which would bother other mathematicians did not faze him —

“because, in spite of them, the essence came through so marvelously!”

On his side, Courant quickly recognized Friedriclis’s gifts in spite of the first impression which the young man made (“as if he could not

‘his drei zahien”’). Only a few years later, in 1929, he noted that even as a student Friedrichs had stood out because of the independence

and originality of his observations and the seriousness of his scientific aspirations.

It is the opinion of Lewy that a less keen observer of human abilities and human nature than Courant would not have put much stock in

Friedrichs at that time.

“He was a very retiring person, not much at ease with himself or the rest of the world. I guess on most people he would have made a

negative impression as to his abilities. Oh yes, I was impressed by him; but I was, you see, a student and on the same level with him. But

thinking how he would have appeared to a teacher. I think it took keen observation as well as a really intense human interest on Courant’s

part to see what was there.”

(However, when Courant was asked a year before his death who of all hismany students had most surprised him by his scientific

achievement, his reply was “Friedrichs.”)

While still a student, Friedrichs solved a problem of relativity theory. His dissertation (1925) treated the theory of elastic plates. Courant,

his “doctor-father,” found it an “admirably powerful” work and, looking back, later, was to see it as “the point of departure for

[Friedrichs’s] further development as one of the most fruitful and successful representatives of the field of partial differential equations of

mathematical physics.”

During the next two years, while Otto Neugebauer served as assistant in administrative matters, Friedrichs was Courant’s assistant in

mathematics and was beginning to work with him on the second volume of Courant-Hilbert. It was this period that saw the production of

the now classic Courant-Friedrichs-Lewy paper. The primary goal of the work was purely theoretical. At Courant’s suggestion, Friedrichs

and Lewy used finite differences to develop an existence theory of hyperbolic equations of the first order. The result which was to be

significant for numerical analysis — but only after the development of the modern high-speed computer — was the observation that a

hyperbolic differential equation cannot be replaced by a difference equation in an arbitrary manner without a severe restriction on the ratio

of the time difference to the space difference. Friedrichs was always very modest about his share in this work, crediting Courant with

great intuition in suggesting the direction of the research and Lewy with great originality in making the observation mentioned above.

According to Lewy, what Friedrichs himself brought to the collaboration was his orderly mind and his gift for seeing formal relationships:

“He was a thoroughly independent and original thinker with a way of making penetrating remarks which seemed at first contradictory.”

In 1927, after Friedrichs had been an assistant in Gottingen for two years, Courant arranged for him to go to Aachen as assistant to

Theodor von Karmin, the director of the aerodynamics institute there and a former “G6ttinger.” Although Friedrichs was not happy at the

thought of leaving the congenial “mathematical family” he had found in Gottingen, he recognized the force of Courant’s argument that it

would be good for him to get experience in applied mathematics, since otherwise — as they both believed at the time — he would not be

able to compete against the many gifted pure mathematicians then in Germany.

“Courant forced him out into what at the time were unpleasant situations,” Lewy says. “I remember saying goodbye to Friedrichs at the

station when he left for Aachen, and he was in a daze and very unhappy. He was a man, you see, who wouldn’t want to change, who

would, so you would say, gradually have reduced to smaller and smaller the radius of the circle in which he was operating. I think if it had

not been for Courant he would have become a gymnasium teacher.”

Friedrichs spent two years in Aachen with von Karmin. By the time he returned to G6ttingen in 1929, he had published several works and

had several more awaiting publication. Courant, recommending his Habilitation, pointed out to the faculty that Friedrichs was the only one

among the young mathematicians in Germany who was qualified “to build the bridge from modern analysis to mechanics and to hammer

out its applications.” It was true that he still made a somewhat poor first impression because of his shyness, “but in spite of that he pleases

on account of his excellent character and his helpfulness to colleagues and students and enjoys a special popularity.” He was sure

Gottingen would not be able to keep him for long; and, in fact, within a year Friedrichs was “called” to a full professorship at the

Technische Hochschule in Braunschweig.

The Hochschule was a comparatively small institution, but Friedrichs (the youngest full professor on the faculty) had to teach several

hundred first- and second-year students.

“A tremendous teaching load, many hours, and I had never taught the courses before so I had to work from morning to night to prepare

them. Yet I have never done scientific work more intensely than during that year. It’s a general observation of mine that if you have all

the time you want for your scientific research, you just end up consulting a psychiatrist. If you have to fight against obstacles, if you have

to fight for your time, you do much better. Unless, of course, it goes too far.”

Also contributing decisively to Friedrichs’s creativity at the time was his belated discovery of the great paper in which John von Neumann

introduced the modern theory of operators in Hilbert space.

“I had known von Neumann in Gottingen in 1926. His main interest then had been logic, and we in the group around Courant were

somewhat doubtful about him. He offered a very abstract approach. Brilliant, but is it really substantial? We wondered. And I remember

having discussions with Courant about von Neumann at that time. Oh well, this abstractness for its own sake — we don’t believe in that!

But we didn’t know it. And when I got hold of von Neumann’s paper, it opened my eyes. It was a revelation. And I immediately

translated a paper I had written earlier into von Neumann’s language of general Hilbert space.”

Years later he remarked to Peter Lax that all he needed mathematically he got from Hermann Weyl — “except for Hilbert space, and that

I got from von Neumann.” In 1931 he became the first to apply the von Neumann theory to partial differential operators, showing that the

initial-value problem for linear hyperbolic equations could be solved by using energy integrals and, later, showing that the same method

could be applied to elliptic equations.

“In this work Lebesgue theory played no role,” he noted in the account of his scientific work for Modern Scientists and Engineers, “the

underlying Hilbert spaces were defined by completion of spaces of smooth functions. Operators were defined by completion (strong

extension) or by adjointness (weak extension); the identity of these two extensions is one of the fundamental results, proved with the aid

of so-called mollifiers. These methods are rather simple and direct; they preceded the development of the theory of distributions of

Laurent Schwartz as applied to partial differential equations.”

Somewhat later, after Franz Rellich’s discovery that the spectrum is moved smoothly by specified smooth perturbations for an operator

with only a discrete spectrum, Friedrichs treated the problem for an operator with a continuous spectrum. He found that, again under

appropriate conditions, the character of the spectrum is unchanged; however, in general drastic changes are possible. In 1948 he showed

that the theory of these perturbations is fundamental to the theory of scattering. Later, as he pointed out, the pair of operators he had

introduced turned out to be identical with the forward- and backward-wave operators which formed the basis for subsequent development.

Although living in Braunschweig, Friedrichs continued to visit Gottingen, giving talks in the seminar on occasion and working with Courant

on the second volume of Courant-Hilbert. He was disturbed, however, by a change he sensed in the atmosphere. “The easy carefree

attitude of earlier days was no longer so common.” The students in Gottingen — as well as his students in Braunschweig —were

different.” Some even protested against relativity theory: “For us Germans, there is something absolute!” Then — on January 31, 1933 —

Adolf Hitler was named chancellor of the Reich.

‘It was for many a great surprise. Many couldn’t believe that it would mean too much.”

But Lewy left Germany immediately; and Friedrichs, who had carefully read Mein Kampf, could not share the optimistic hope of many

that governmental responsibility would now temper the rowdy radicalism of Hitler’s brown shirts, especially in regard to the Jews.

‘Still also I myself didn’t realize how deep all this would go.”

It was only four days after Hitler became chancellor that Friedrichs attended a benefit theatrical ball — the social event of the year in

Braunschweig — in the hope of seeing there a young Jewish girl whom he had noticed each day on his way home from his morning

lecture. He immediately spotted her dark straight hair, bobbed in the style of the American movie actress Colleen Moore; and, after the

entertainment of the evening, never having spoken a word to her before, he marched determinedly across the ballroom and invited Nellie

Bruell to dance. Thus began the great romantic adventure of his life — a romance and adventure story which is told in charming detail by

Nellie Bruell Friedrichs in her Erinnerungen aus meinem Leben in Braunschweig, 1912—193 7 (No. 4 in the Kleine Shrissten of the

Stadtarchiv und Stadtbibliothek of Braunschweig).

Although the new regime took no interest at the time in the budding romance of the Aryan professor and the young Jewish woman,

Courant and a number of other Jewish professors were very soon dismissed from their positions. Friedrichs and Neugebauer circulated a

petition in support of Courant and submitted it to the ministry but without success. After a year’s sojourn in England as a visiting

professor, Courant emigrated to the United States and a modest position at New York University. By that time Nellie Bruell had had to

abandon her position as an assistant at the Hochschule and was giving English lessons to Jews who were desirous of emigrating. She had

no problem keeping busy. It was clear to Friedrichs that for personal and political reasons he was going to have to leave Germany soon.

In the summer of 1935 he visited Courant in New York, ostensibly to continue work on the second volume of Courant-Hilbert but in

actuality “to see ifl could emigrate.” He concluded that he “had very definite feelings that this is a country where I could live.” Courant

promised to see what he could do about finding an academic position for him in the United States, no easy task at a time when most

young American Ph.D.’s were without jobs.

While Friedrichs was on his way back to Braunschweig, the Nurnberg laws, which forbade marriage between Aryans and non-Aryans,

were passed. From that time on, he was able to meet with Nellie Bruell only infrequently and then secretly at the apartment of a friend of

hers who was not Jewish.

In the spring of 1936 Courant wired an invitation to give a few lectures at NYU during the coming summer. When word of the invitation

reached the Nazi minister of education, he wrote angrily to the Braunschweig rector: “I can find no explanation why Professor Friedrichs

has not already declined the invitation from Professor Courant, one of the Jewish emigrees who, although he knows German, writes in

English.”

Friedrichs dutifully refused the invitation — in German; but he added in a note to the rector that he saw no reason why an invitation

should not be written in the language of the institution extending it, even when a Jewish emigrant from Germany was a member of the

administration of the institution. That summer, with great secrecy, he materialized at the Czechoslovakian spa where Courant was

vacationing and announced that he was now willing to take any American job he could get, except possibly construction work, which he

didn’t think he could do very well.

Back in Germany, in the fall of 1936, he began surreptitiously to arrange to emigrate during the following spring vacation. He told even his

parents nothing of his plans so that, if they were questioned later, they could truthfully say that they had not known he was going to go.

For their sake, he was determined that everything he did would be done according to the law and whatever he said or wrote would be

factually correct. To get permission to leave the country (necessary because he was of military age), he explained that he wanted to visit

his sister, who was at the time in Paris. To obtain a visa from the American consul in Hamburg, he produced the required documents

showing that he had permanent residence and employment in Germany. These had been signed by landlady and a clerk at the

Hochschule. He was certain that both of them suspected that he was not planning to return.

As soon as she heard that Friedrichs was safely across the German border, Nellie Bruell, who had a French passport and could still travel

freely, left for her father’s home in Lyon to wait until Friedrichs had obtained a job in the United States and could send for her.

On March 4, 1937, Friedrichs arrived in New York, essentially penniless, since he had been permitted to take only 10 marks out of

Germany. Courant found him a place to live.

“So I was his assistant again. I lived in a room near him in New Rochelle. In fact, I didn’t even know the precise details of that. I was not

too concerned. I thought that somehow it would work out.”

A few days after his arrival he sent a letter to Germany formally resigning his position as a German professor. Still concerned about the

possible effect of his emigration upon his parents, he took the letter to Princeton to mail so that it would not bear a New Rochelle

postmark, which would connect him with Courant.

During the spring and summer of 1937, after a dozen years of more or less unproductive effort, Courant with Friedrichs’s help completed

the second volume of Courant-Hilbert. In the course of the writing, however, Friedrichs had recognized that they had grown so far apart

mathematically that they would never be able to work together on the projected third volume.

Courant wrote letters about Friedrichs’s presence in the United States to everyone he knew who was interested in the development of

applied mathematics. In fact, he campaigned so energetically on Friedrichs’s behalf that Lewy, who was by then an assistant professor at

Berkeley, warned him that as a recent arrival from Europe he might jeopardize his own position at NYU. Undeterred, he continued to

“spread the news” about Friedrichs.

“That was something Courant always did for Friedrichs,” Lewy says. “I have known few people among gifted mathematicians who were

as adverse as Friedrichs was to putting themselves forward.”

In trying to place Friedrichs in America, Courant emphasized also to him the importance of his work in applied mathematics.

“He told me, look, the situation is not easy in America to get positions for mathematicians, but there is a great need in America to develop

applied mathematics; and since I had a background in applied mathematics, that was my best chance. And, in fact, Courant wanted —

independent of me — to develop applied mathematics here. So in a way my coming fitted his plans.”

That summer, with some help from people interested in aeronautics —“including, I always understood, Lindbergh” — Friedrichs was

appointed to a temporary professorship at NYU. Nellie Bruell was immediately sent for. In August, following the complicated procedure

recommended at the time, she and Friedrichs drove to Canada so that he, officially emigrating, could truthfully say (since he had not yet

married a non-Aryan) that there existed no reason why he could not return to Germany if he so wished. As soon as they could find a

justice of the peace on the American side of the border, they were married.

It was a well made and fortunate marriage for both of them, her outgoing and supportive nature and her exceptional talent for friendship

perfectly complementing his needs and gifts.

“Due to Courant and to Nellie, his wife — and also due to Hitler probably —Friedrichs really blossomed,” Lewy says. “He became a

different person from what he was as a student.”

The same year that Friedrichs came to NYU, James J. Stoker, a young applied mathematician from Pittsburgh, a former mining engineer,

also joined the faculty. For the next quarter of a century, until Courant’s retirement in 1961, these three very different men and very

different mathematicians were to be the core of the development which became the Courant Institute of Mathematical Sciences.

In spite of their different national and scientific backgrounds, Friedrichs and Stoker were able to collaborate very effectively. Friedrichs

always said that, as in the case of Lewy, his attitude toward mathematics was strongly influenced by working with Stoker. He spoke with

special pleasure of their collaboration on the boundary problem of the buckled plate with large deflections.

“I think that piece of work I did with Stoker is a piece of work I like myself more than Stoker does. I had more mathematical background,

he had more engineering, and we worked very well together. In any case the main point is that there was a piece of work where

mathematical methods were used, and still it clarified an issue of significance in mechanical engineering.”

Stoker — who did in fact recall this same work with special pleasure at the memorial service held for Friedrichs at NYU — emphasized

on that occasion the quality of daring in Friedrichs’s life and in his mathematics:

“[He] always picked out the dangerous problems to work on, the really tough ones, in which there was no certainty of getting through,

and then he would push them through.”

Friedrichs later published several other papers having to do with plate theory. In fact, throughout his career in America, he alternated

periods of working on more applied problems with periods of working on problems which were of a purely mathematical character.

He considered, so he wrote, that probably the most significant work he did after 1937 was that on symmetric hyperbolic linear differential

equations. The work, in which he utilized powerful tools which he had developed earlier, is considered a breakthrough in many ways.

Later he extended the theory to accretive equations.

During World War II Friedrichs returned to fluid dynamics. In spite of a number of contributions to theory made while working on

problems of flow past airfoils, shock waves, and combustion, he considered that his most valuable wartime contribution was the manual

Supersonic Flow and Shock Waves, which he and Courant wrote. After the war, when it had been declassified, the two authors decided

to publish it as a book. Cathleen Morawetz, then a graduate mathematics student at NYU, was selected to edit the volume. She has

described the process of collaboration in a way that highlights the difference in the approaches of the two men:

“One or the other of them would take a section from the manual and rewrite it. If Courant did it, then it went to Friedrichs. And

Friedrichs would look at it and grumble that it wasn’t sufficiently exact. He would rewrite it, and it would become all “ifs” and “buts”.

Then Courant would take it and he would mumble and groan that it was much too complicated. Then he would rewrite it. Then Friedrichs

would take it back and say it wasn’t precise enough. The process went on many, many times for each section. When it came back to

Friedrichs, he would put in again some of what he had had before, but not so much. Then the next time Courant wouldn’t take out so

much. They were both pretty determined about what the end product should be, and they were both quite willing to do an awful lot of

work. But I never remember a single session where they both sat down together over the manuscript.”

During the war and after, Friedrichs also analyzed the mathematical aspects of deflagrations and detonations. He had always been

interested in what goes on in the boundary layer. “He put it under the microscope, so to speak,” his long-time colleague Fritz John

explains. Now he showed that a boundary-layer type of argument, which he had introduced earlier in airfoil theory, would explain why

certain types of detonations (weak) and deflagrations (strong) would not occur. Later he showed that the Lundquist equation which

governs magneto-fluid dynamics could be written as a symmetric hyperbolic system and, still later, that the same is true in the relativistic

case.

In a series of five papers on the quantum theory of fields, he attempted to put that theory on a sound mathematical foundation. These

papers appear in his book, Mathematical Aspects of the Quantum Theory of Fields. A somewhat different approach to the theory is

contained in his later book, Perturbations of Spectra in Hi/bert Space.

Between 1940 and 1950 Friedrichs and his wife became the parents of four sons and one daughter; and these members of the household

in New Rochelle provided the obstacles to uninterrupted research which he had recognized since his Braunschweig days as being

conducive rather than detrimental to his mathematical productivity. Organization and self-discipline, as well as an exceptionally

understanding and cooperative wife, enabled him to protect himself from any interruption during the time which he set aside for writing

and research. Even Courant, who liked to drop in on neighboring colleagues in New Rochelle, never got beyond the living room and a cup

of tea with Nellie Friedrichs unless he had a previous appointment.

Friedrichs’s five children, in short talks which each gave at the memorial service in New Rochelle two days after his death, recalled a

father whose earliest individual contacts with them had been “lessons” on his lap in his study. Christopher, the second son, who spoke

last, expanded upon these recollections.

“To a large extent I think my father’s very idea of what it meant to be a parent was bound up with the idea of educating his children,” he

said. “. . . In our youngest years, of course, there was not much ‘educational content’ in these lessons, but I don’t think that mattered to

Dad at all — the important thing was that a ‘lesson’ seemed to him to be a very natural form of interaction between a parent and a child.

And, of course, as we grew a bit older some more real content was slipped into these lessons. Eventually the ‘lessons’ were dropped, but

teaching and learning continued.”

Very much in the same way Friedrichs’s idea of being a mathematician was bound up with the idea of being a teacher. He considered the

expression “mathematician and educator” redundant.

Thoroughly prepared, he would start his lectures at one side of the blackboard with a series of little boxes which by the end of the hour

would stretch to the other side. Although he was not a showman, he would sometimes leave a box empty until he could fill it at exactly the

moment when the information he gave would have the maximum effect.

Former students who spoke at the NYU service recalled that his lectures were not polished performances. He was often difficult to follow

because of the originality of his thought and his willingness “to make a mess.”

“He believed that the first part of a course should be confusion,” Jerome Berkowitz explained. The student should get the feel of the

problem and learn what would not work. “[The second part] should be deconfusion, clarification, and illumination. ‘Of course,’ he said, ‘I

sometimes don’t have time for the second part.’’’

(Peter Lax recalls that Friedrichs sometimes described himself as a great teacher “in the weak sense.”)

Friedrichs’s teaching was not limited to his courses. Especially after his retirement, he enjoyed giving expository lectures. These would

range from a single talk to a mathematical “mini series.” In them he would try always to reach a wider public than that of the specialist.

(Fritz John thinks that he would have agreed with the statement that no mathematical theory is completely realized until you can explain it

to the first man you meet on the street.)

In 1965 he published a little book entitled From Pythagoras to Einstein. Typically, he wrote in the preface that the book was not

addressed to a “well defined” audience. The first chapter, in fact, was based on a talk he had given to a special sixth grade math class, the

middle chapters were hopefully intended for high school students, and the last chapter “might just as well be read by college seniors.”

“Professionally, of course, it was hard to imagine Dad as anything other than a mathematician..., Christopher Friedrichs recalled. “Yet at

the very same time, he had such a wide range of knowledge and talent that he could, I think, have followed many other paths. I think, for

example, that he could also have been a great physicist. He could have been a good philologist and certainly ... he could have been a very

good historian. He would have been a better than average naturalist. He had a solid knowledge of philosophy and a sophisticated interest

in things like archeology and modern German literature. And he had also a deep and fundamental concern with the problems of society

and political ethics.”

Since his youth Friedrichs had had a general philosophical bent. This had made him concentrate in his work, as he said, “as much on

points of view as on proofs.” When Lewy asked what he intended to do when he retired, he replied promptly, “Go back to philosophy.”

He found it personally significant that, unlike most scientists, he was not attracted to positivism or pragmatism: “the effect was, so to say,

not to be doctrinaire, as so many scientists are.” He often remarked, “A question which has an answer does not belong to philosophy.”

Lewy also remembers his “smiling” paradox: “Philosophy is the growing recognition of the impossibility of reducing known facts to

unknown ones. The science which does that is called theoretical physics.”

According to Fritz John, it was Friedrichs’s philosophical propensity which drove him to search for the deeper reasons for the occurrence

of symmetric hyperbolic systems in physics in connection with the conservation laws. In a note in 1970 with Lax and in a later paper he

was able to establish that general systems of conservation equations which possess a convex extension can be reduced to symmetric

hyperbolic systems. He also became very interested in the “observable quantities” of physicists. He thought that these were misused or

wrongly interpreted. Trying to clarify the subject in a 1979 paper, “On the Notion of State in Quantum Mechanics,” he showed that the

future values of unobserved observables are determined in terms of their unobserved initial values, “thus in some sense validating

causality.”

From 1971 to 1976 he devoted a great deal of time and effort to working with me on the book Courant in Gottingen and New York, the

writing of which he had suggested. He thought it was important to keep alive for future generations of young mathematicians the unique

scientific spirit of Richard Courant, which had played such an important role in his own life and career. Appropriately, the last talk which

Courant himself ever gave was at the celebration of Friedrichs’s seventieth birthday. On that occasion he spoke with great feeling of the

man whom he had known for almost half a century as student, colleague, and friend:

“He is one of the rare scientists whose intellectual and scientific development has never slackened but has gone forward continually. ...

One of the very wonderful aspects of all this is the fact that even now, at the age of seventy years, Friedrichs has not stopped or

slackened in his endeavors and the radiant inspiration that emanates from him. All his friends and many others in many countries in the

world are profoundly aware of the fact that he has been and has become steadily more truly a great man of science. What a great human

being he is everybody near to him knows very well.”

There were, of course, many honors bestowed on Friedrichs during the course of his career. Writing the account of himself for Modern

Scientists and Engineers, he mentioned particularly Director and Distinguished Professor of the Courant Institute of New York University,

Josiah Willard Gibbs Lecturer of the American Mathematical Society, election to the National Academy of Sciences and to the American

Academy of Arts and Sciences, the Applied Mathematics and Numerical Analysis Award of the National Academy, and (in 1977) the

National Medal of Science, the nation’s highest scientific award.

There were also honorary doctorates from Aachen, Uppsala, Braunschweig, Columbia, and NYU.

During the last decades he received invitations to lecture in many different parts of the world. He had always been interested in seeing

new places; and he and his wife were now able to travel even more extensively than in the past — to Israel, Japan, India, Africa — but

also, many times, back to Germany. Because of the asthma with which he was still afflicted, although not nearly so severely as in his

youth, it was his custom to leave New Rochelle during the ragweed season. In 1982 he spent most of that time in Braunschweig, where

he had begun his professional career.

When he returned in October, he was mortally ill. Increasing deafness had already cut him off from many social contacts, and in the next

few months he gradually and quietly withdrew from life itself He died at his home in New Rochelle in the final moments of 1982, with his

wife and two of his sons at his side.

Richard Courant. Since his life and Courant’s were intimately connected, he told me a great deal about himself in the course of telling me

about Courant. I have drawn also on the recollections of his family and a few colleagues — especially Hans Lewy — and on the account

of his scientific work which he himself wrote for McGraw-Hill’s Modern Scientists and Engineers.

Friedrichs was born on September 28, 1901, in Kiel, a Baltic port and the capital of the German state of Schleswig-Holstein. He was

christened Kurt Otto, but in later years he objected to the sharp, abrupt sound of “Kurt,” which he felt didn’t suit him, and preferred to be

called “Frieder”.

He was the second of three children. (An older sister became a teacher of English and a brother, a distinguished English translator and

interpreter.) The mother, Elisabeth Entel Friedrichs, was from Silesia. She was an exceptionally lovely woman whom the boy Friedrichs

adored and for whom he was to name his only daughter. The father, Karl Friedrichs, was a lawyer and legal writer, an expert on laws

affecting the Civil Service. He could be maddeningly fussy in small matters — “quite impossible” — but superb and very wise in the big

things, so Friedrichs described him. It was a description which his own sons would later feel could be even more appropriately applied to

him.

The Friedrichs family had long been established and politically active in Schleswig and Holstein — the great-grandfather having fought for

their independence from Denmark — but the family left Kiel shortly after Friedrichs’s birth and by the time he was ready for school had

settled in Dusseldorf. There the elder Friedrichs became acquainted with another lawyer, the brother of the mathematician Felix Klein, the

powerful director of mathematics at the University of Gottingen — commonly known, even beyond the borders of Germany, as “the

mecca of mathematics”.

Throughout his youth, Friedrichs was plagued by asthma and rarely able to participate in the activities of the other young people. He

remembered himself as very timid; however, after he had made the Abitur at the Realgymnasium in Dusseldorf, he moved — following

the custom of the day — from university to university: to Greifswald for a term, to Freiburg for a year, and to the Austrian university of

Graz for a term.

“Then I said to myself, ‘Now I must go to the mecca of mathematics!”’

In the fall of 1922 he arrived in G6ttingen with a letter of introduction from Felix Klein’s lawyer brother. Richard Courant had just

recently succeeded Klein as director of mathematics and was now attempting in his own way to recreate the scientifically stimulating

environment which he had known at the university during his student days.

The times had become much harder since the war of 1914—1918. Inflation had reached staggering proportions. A university mess hail

had replaced glamorous dining clubs; and, as unappetizing soups and stews were ladled from a long trough, students flirted with serving

girls in the most often unfulfilled hope of getting larger portions. Constantly thinking about food, they found it impossible to concentrate

on their books. Friedrichs, like many others, lived in a former prisoner-of-war camp.

“[Yet] in spite of a high degree of enforced frugality,” Courant later recalled, “the general intellectual life in the university was intense,

idealistic, permeated by profound desires to find a firm position in the struggle with the problems of the times, political, philosophical,

religious, humanistic, artistic, and literary, not to speak of the challenges which came from the new emerging scientific fields of relativity,

quantum mechanics, genetics, aerodynamics, etc.”

Friedrichs did not come unprepared for such an intellectual life. In Freiburg he had been “infected,” as he put it, by the philosophy of

Husseri and Heidegger. His original scientific interest had been mathematical physics; and his mathematical hero was Hermann Weyl, who

was making contributions to the foundations of mathematics as well as to relativity theory in the early 1920’s.

Another student who arrived in Gottingen the same year as Friedrichs was Hans Lewy, with whom he later collaborated on several

important papers. Lewy, two years younger, was impressed by Friedrichs’s “vast and well organized” knowledge; but Friedrichs himself

was overwhelmed by the superior knowledge of the young lecturers and assistants in Gdttingen. These included such future luminaries as

Carl Ludwig Siegel and Emil Artin — “such a bunch of people who knew everything about everything!”

He was also captivated by the informal and scientifically exciting atmosphere which existed around Courant and by Courant’s approach to

mathematics (although it would always be quite different from his own). Reading the Hurwitz-Courant book on function theory, which

appeared in 1922, he found the two sections by Hurwitz “very neat, very clear, to the point, you could learn from them,” but the third

section by Courant on geometric function theory— “I started reading one morning, I read morning and night without stopping. It was the

most breathtaking book I have ever read in mathematics.” Inaccuracies which would bother other mathematicians did not faze him —

“because, in spite of them, the essence came through so marvelously!”

On his side, Courant quickly recognized Friedriclis’s gifts in spite of the first impression which the young man made (“as if he could not

‘his drei zahien”’). Only a few years later, in 1929, he noted that even as a student Friedrichs had stood out because of the independence

and originality of his observations and the seriousness of his scientific aspirations.

It is the opinion of Lewy that a less keen observer of human abilities and human nature than Courant would not have put much stock in

Friedrichs at that time.

“He was a very retiring person, not much at ease with himself or the rest of the world. I guess on most people he would have made a

negative impression as to his abilities. Oh yes, I was impressed by him; but I was, you see, a student and on the same level with him. But

thinking how he would have appeared to a teacher. I think it took keen observation as well as a really intense human interest on Courant’s

part to see what was there.”

(However, when Courant was asked a year before his death who of all hismany students had most surprised him by his scientific

achievement, his reply was “Friedrichs.”)

While still a student, Friedrichs solved a problem of relativity theory. His dissertation (1925) treated the theory of elastic plates. Courant,

his “doctor-father,” found it an “admirably powerful” work and, looking back, later, was to see it as “the point of departure for

[Friedrichs’s] further development as one of the most fruitful and successful representatives of the field of partial differential equations of

mathematical physics.”

During the next two years, while Otto Neugebauer served as assistant in administrative matters, Friedrichs was Courant’s assistant in

mathematics and was beginning to work with him on the second volume of Courant-Hilbert. It was this period that saw the production of

the now classic Courant-Friedrichs-Lewy paper. The primary goal of the work was purely theoretical. At Courant’s suggestion, Friedrichs

and Lewy used finite differences to develop an existence theory of hyperbolic equations of the first order. The result which was to be

significant for numerical analysis — but only after the development of the modern high-speed computer — was the observation that a

hyperbolic differential equation cannot be replaced by a difference equation in an arbitrary manner without a severe restriction on the ratio

of the time difference to the space difference. Friedrichs was always very modest about his share in this work, crediting Courant with

great intuition in suggesting the direction of the research and Lewy with great originality in making the observation mentioned above.

According to Lewy, what Friedrichs himself brought to the collaboration was his orderly mind and his gift for seeing formal relationships:

“He was a thoroughly independent and original thinker with a way of making penetrating remarks which seemed at first contradictory.”

In 1927, after Friedrichs had been an assistant in Gottingen for two years, Courant arranged for him to go to Aachen as assistant to

Theodor von Karmin, the director of the aerodynamics institute there and a former “G6ttinger.” Although Friedrichs was not happy at the

thought of leaving the congenial “mathematical family” he had found in Gottingen, he recognized the force of Courant’s argument that it

would be good for him to get experience in applied mathematics, since otherwise — as they both believed at the time — he would not be

able to compete against the many gifted pure mathematicians then in Germany.

“Courant forced him out into what at the time were unpleasant situations,” Lewy says. “I remember saying goodbye to Friedrichs at the

station when he left for Aachen, and he was in a daze and very unhappy. He was a man, you see, who wouldn’t want to change, who

would, so you would say, gradually have reduced to smaller and smaller the radius of the circle in which he was operating. I think if it had

not been for Courant he would have become a gymnasium teacher.”

Friedrichs spent two years in Aachen with von Karmin. By the time he returned to G6ttingen in 1929, he had published several works and

had several more awaiting publication. Courant, recommending his Habilitation, pointed out to the faculty that Friedrichs was the only one

among the young mathematicians in Germany who was qualified “to build the bridge from modern analysis to mechanics and to hammer

out its applications.” It was true that he still made a somewhat poor first impression because of his shyness, “but in spite of that he pleases

on account of his excellent character and his helpfulness to colleagues and students and enjoys a special popularity.” He was sure

Gottingen would not be able to keep him for long; and, in fact, within a year Friedrichs was “called” to a full professorship at the

Technische Hochschule in Braunschweig.

The Hochschule was a comparatively small institution, but Friedrichs (the youngest full professor on the faculty) had to teach several

hundred first- and second-year students.

“A tremendous teaching load, many hours, and I had never taught the courses before so I had to work from morning to night to prepare

them. Yet I have never done scientific work more intensely than during that year. It’s a general observation of mine that if you have all

the time you want for your scientific research, you just end up consulting a psychiatrist. If you have to fight against obstacles, if you have

to fight for your time, you do much better. Unless, of course, it goes too far.”

Also contributing decisively to Friedrichs’s creativity at the time was his belated discovery of the great paper in which John von Neumann

introduced the modern theory of operators in Hilbert space.

“I had known von Neumann in Gottingen in 1926. His main interest then had been logic, and we in the group around Courant were

somewhat doubtful about him. He offered a very abstract approach. Brilliant, but is it really substantial? We wondered. And I remember

having discussions with Courant about von Neumann at that time. Oh well, this abstractness for its own sake — we don’t believe in that!

But we didn’t know it. And when I got hold of von Neumann’s paper, it opened my eyes. It was a revelation. And I immediately

translated a paper I had written earlier into von Neumann’s language of general Hilbert space.”

Years later he remarked to Peter Lax that all he needed mathematically he got from Hermann Weyl — “except for Hilbert space, and that

I got from von Neumann.” In 1931 he became the first to apply the von Neumann theory to partial differential operators, showing that the

initial-value problem for linear hyperbolic equations could be solved by using energy integrals and, later, showing that the same method

could be applied to elliptic equations.

“In this work Lebesgue theory played no role,” he noted in the account of his scientific work for Modern Scientists and Engineers, “the

underlying Hilbert spaces were defined by completion of spaces of smooth functions. Operators were defined by completion (strong

extension) or by adjointness (weak extension); the identity of these two extensions is one of the fundamental results, proved with the aid

of so-called mollifiers. These methods are rather simple and direct; they preceded the development of the theory of distributions of

Laurent Schwartz as applied to partial differential equations.”

Somewhat later, after Franz Rellich’s discovery that the spectrum is moved smoothly by specified smooth perturbations for an operator

with only a discrete spectrum, Friedrichs treated the problem for an operator with a continuous spectrum. He found that, again under

appropriate conditions, the character of the spectrum is unchanged; however, in general drastic changes are possible. In 1948 he showed

that the theory of these perturbations is fundamental to the theory of scattering. Later, as he pointed out, the pair of operators he had

introduced turned out to be identical with the forward- and backward-wave operators which formed the basis for subsequent development.

Although living in Braunschweig, Friedrichs continued to visit Gottingen, giving talks in the seminar on occasion and working with Courant

on the second volume of Courant-Hilbert. He was disturbed, however, by a change he sensed in the atmosphere. “The easy carefree

attitude of earlier days was no longer so common.” The students in Gottingen — as well as his students in Braunschweig —were

different.” Some even protested against relativity theory: “For us Germans, there is something absolute!” Then — on January 31, 1933 —

Adolf Hitler was named chancellor of the Reich.

‘It was for many a great surprise. Many couldn’t believe that it would mean too much.”

But Lewy left Germany immediately; and Friedrichs, who had carefully read Mein Kampf, could not share the optimistic hope of many

that governmental responsibility would now temper the rowdy radicalism of Hitler’s brown shirts, especially in regard to the Jews.

‘Still also I myself didn’t realize how deep all this would go.”

It was only four days after Hitler became chancellor that Friedrichs attended a benefit theatrical ball — the social event of the year in

Braunschweig — in the hope of seeing there a young Jewish girl whom he had noticed each day on his way home from his morning

lecture. He immediately spotted her dark straight hair, bobbed in the style of the American movie actress Colleen Moore; and, after the

entertainment of the evening, never having spoken a word to her before, he marched determinedly across the ballroom and invited Nellie

Bruell to dance. Thus began the great romantic adventure of his life — a romance and adventure story which is told in charming detail by

Nellie Bruell Friedrichs in her Erinnerungen aus meinem Leben in Braunschweig, 1912—193 7 (No. 4 in the Kleine Shrissten of the

Stadtarchiv und Stadtbibliothek of Braunschweig).

Although the new regime took no interest at the time in the budding romance of the Aryan professor and the young Jewish woman,

Courant and a number of other Jewish professors were very soon dismissed from their positions. Friedrichs and Neugebauer circulated a

petition in support of Courant and submitted it to the ministry but without success. After a year’s sojourn in England as a visiting

professor, Courant emigrated to the United States and a modest position at New York University. By that time Nellie Bruell had had to

abandon her position as an assistant at the Hochschule and was giving English lessons to Jews who were desirous of emigrating. She had

no problem keeping busy. It was clear to Friedrichs that for personal and political reasons he was going to have to leave Germany soon.

In the summer of 1935 he visited Courant in New York, ostensibly to continue work on the second volume of Courant-Hilbert but in

actuality “to see ifl could emigrate.” He concluded that he “had very definite feelings that this is a country where I could live.” Courant

promised to see what he could do about finding an academic position for him in the United States, no easy task at a time when most

young American Ph.D.’s were without jobs.

While Friedrichs was on his way back to Braunschweig, the Nurnberg laws, which forbade marriage between Aryans and non-Aryans,

were passed. From that time on, he was able to meet with Nellie Bruell only infrequently and then secretly at the apartment of a friend of

hers who was not Jewish.

In the spring of 1936 Courant wired an invitation to give a few lectures at NYU during the coming summer. When word of the invitation

reached the Nazi minister of education, he wrote angrily to the Braunschweig rector: “I can find no explanation why Professor Friedrichs

has not already declined the invitation from Professor Courant, one of the Jewish emigrees who, although he knows German, writes in

English.”

Friedrichs dutifully refused the invitation — in German; but he added in a note to the rector that he saw no reason why an invitation

should not be written in the language of the institution extending it, even when a Jewish emigrant from Germany was a member of the

administration of the institution. That summer, with great secrecy, he materialized at the Czechoslovakian spa where Courant was

vacationing and announced that he was now willing to take any American job he could get, except possibly construction work, which he

didn’t think he could do very well.

Back in Germany, in the fall of 1936, he began surreptitiously to arrange to emigrate during the following spring vacation. He told even his

parents nothing of his plans so that, if they were questioned later, they could truthfully say that they had not known he was going to go.

For their sake, he was determined that everything he did would be done according to the law and whatever he said or wrote would be

factually correct. To get permission to leave the country (necessary because he was of military age), he explained that he wanted to visit

his sister, who was at the time in Paris. To obtain a visa from the American consul in Hamburg, he produced the required documents

showing that he had permanent residence and employment in Germany. These had been signed by landlady and a clerk at the

Hochschule. He was certain that both of them suspected that he was not planning to return.

As soon as she heard that Friedrichs was safely across the German border, Nellie Bruell, who had a French passport and could still travel

freely, left for her father’s home in Lyon to wait until Friedrichs had obtained a job in the United States and could send for her.

On March 4, 1937, Friedrichs arrived in New York, essentially penniless, since he had been permitted to take only 10 marks out of

Germany. Courant found him a place to live.

“So I was his assistant again. I lived in a room near him in New Rochelle. In fact, I didn’t even know the precise details of that. I was not

too concerned. I thought that somehow it would work out.”

A few days after his arrival he sent a letter to Germany formally resigning his position as a German professor. Still concerned about the

possible effect of his emigration upon his parents, he took the letter to Princeton to mail so that it would not bear a New Rochelle

postmark, which would connect him with Courant.

During the spring and summer of 1937, after a dozen years of more or less unproductive effort, Courant with Friedrichs’s help completed

the second volume of Courant-Hilbert. In the course of the writing, however, Friedrichs had recognized that they had grown so far apart

mathematically that they would never be able to work together on the projected third volume.

Courant wrote letters about Friedrichs’s presence in the United States to everyone he knew who was interested in the development of

applied mathematics. In fact, he campaigned so energetically on Friedrichs’s behalf that Lewy, who was by then an assistant professor at

Berkeley, warned him that as a recent arrival from Europe he might jeopardize his own position at NYU. Undeterred, he continued to

“spread the news” about Friedrichs.

“That was something Courant always did for Friedrichs,” Lewy says. “I have known few people among gifted mathematicians who were

as adverse as Friedrichs was to putting themselves forward.”

In trying to place Friedrichs in America, Courant emphasized also to him the importance of his work in applied mathematics.

“He told me, look, the situation is not easy in America to get positions for mathematicians, but there is a great need in America to develop

applied mathematics; and since I had a background in applied mathematics, that was my best chance. And, in fact, Courant wanted —

independent of me — to develop applied mathematics here. So in a way my coming fitted his plans.”

That summer, with some help from people interested in aeronautics —“including, I always understood, Lindbergh” — Friedrichs was

appointed to a temporary professorship at NYU. Nellie Bruell was immediately sent for. In August, following the complicated procedure

recommended at the time, she and Friedrichs drove to Canada so that he, officially emigrating, could truthfully say (since he had not yet

married a non-Aryan) that there existed no reason why he could not return to Germany if he so wished. As soon as they could find a

justice of the peace on the American side of the border, they were married.

It was a well made and fortunate marriage for both of them, her outgoing and supportive nature and her exceptional talent for friendship

perfectly complementing his needs and gifts.

“Due to Courant and to Nellie, his wife — and also due to Hitler probably —Friedrichs really blossomed,” Lewy says. “He became a

different person from what he was as a student.”

The same year that Friedrichs came to NYU, James J. Stoker, a young applied mathematician from Pittsburgh, a former mining engineer,

also joined the faculty. For the next quarter of a century, until Courant’s retirement in 1961, these three very different men and very

different mathematicians were to be the core of the development which became the Courant Institute of Mathematical Sciences.

In spite of their different national and scientific backgrounds, Friedrichs and Stoker were able to collaborate very effectively. Friedrichs

always said that, as in the case of Lewy, his attitude toward mathematics was strongly influenced by working with Stoker. He spoke with

special pleasure of their collaboration on the boundary problem of the buckled plate with large deflections.

“I think that piece of work I did with Stoker is a piece of work I like myself more than Stoker does. I had more mathematical background,

he had more engineering, and we worked very well together. In any case the main point is that there was a piece of work where

mathematical methods were used, and still it clarified an issue of significance in mechanical engineering.”

Stoker — who did in fact recall this same work with special pleasure at the memorial service held for Friedrichs at NYU — emphasized

on that occasion the quality of daring in Friedrichs’s life and in his mathematics:

“[He] always picked out the dangerous problems to work on, the really tough ones, in which there was no certainty of getting through,

and then he would push them through.”

Friedrichs later published several other papers having to do with plate theory. In fact, throughout his career in America, he alternated

periods of working on more applied problems with periods of working on problems which were of a purely mathematical character.

He considered, so he wrote, that probably the most significant work he did after 1937 was that on symmetric hyperbolic linear differential

equations. The work, in which he utilized powerful tools which he had developed earlier, is considered a breakthrough in many ways.

Later he extended the theory to accretive equations.

During World War II Friedrichs returned to fluid dynamics. In spite of a number of contributions to theory made while working on

problems of flow past airfoils, shock waves, and combustion, he considered that his most valuable wartime contribution was the manual

Supersonic Flow and Shock Waves, which he and Courant wrote. After the war, when it had been declassified, the two authors decided

to publish it as a book. Cathleen Morawetz, then a graduate mathematics student at NYU, was selected to edit the volume. She has

described the process of collaboration in a way that highlights the difference in the approaches of the two men:

“One or the other of them would take a section from the manual and rewrite it. If Courant did it, then it went to Friedrichs. And

Friedrichs would look at it and grumble that it wasn’t sufficiently exact. He would rewrite it, and it would become all “ifs” and “buts”.

Then Courant would take it and he would mumble and groan that it was much too complicated. Then he would rewrite it. Then Friedrichs

would take it back and say it wasn’t precise enough. The process went on many, many times for each section. When it came back to

Friedrichs, he would put in again some of what he had had before, but not so much. Then the next time Courant wouldn’t take out so

much. They were both pretty determined about what the end product should be, and they were both quite willing to do an awful lot of

work. But I never remember a single session where they both sat down together over the manuscript.”

During the war and after, Friedrichs also analyzed the mathematical aspects of deflagrations and detonations. He had always been

interested in what goes on in the boundary layer. “He put it under the microscope, so to speak,” his long-time colleague Fritz John

explains. Now he showed that a boundary-layer type of argument, which he had introduced earlier in airfoil theory, would explain why

certain types of detonations (weak) and deflagrations (strong) would not occur. Later he showed that the Lundquist equation which

governs magneto-fluid dynamics could be written as a symmetric hyperbolic system and, still later, that the same is true in the relativistic

case.

In a series of five papers on the quantum theory of fields, he attempted to put that theory on a sound mathematical foundation. These

papers appear in his book, Mathematical Aspects of the Quantum Theory of Fields. A somewhat different approach to the theory is

contained in his later book, Perturbations of Spectra in Hi/bert Space.

Between 1940 and 1950 Friedrichs and his wife became the parents of four sons and one daughter; and these members of the household

in New Rochelle provided the obstacles to uninterrupted research which he had recognized since his Braunschweig days as being

conducive rather than detrimental to his mathematical productivity. Organization and self-discipline, as well as an exceptionally

understanding and cooperative wife, enabled him to protect himself from any interruption during the time which he set aside for writing

and research. Even Courant, who liked to drop in on neighboring colleagues in New Rochelle, never got beyond the living room and a cup

of tea with Nellie Friedrichs unless he had a previous appointment.

Friedrichs’s five children, in short talks which each gave at the memorial service in New Rochelle two days after his death, recalled a

father whose earliest individual contacts with them had been “lessons” on his lap in his study. Christopher, the second son, who spoke

last, expanded upon these recollections.

“To a large extent I think my father’s very idea of what it meant to be a parent was bound up with the idea of educating his children,” he

said. “. . . In our youngest years, of course, there was not much ‘educational content’ in these lessons, but I don’t think that mattered to

Dad at all — the important thing was that a ‘lesson’ seemed to him to be a very natural form of interaction between a parent and a child.

And, of course, as we grew a bit older some more real content was slipped into these lessons. Eventually the ‘lessons’ were dropped, but

teaching and learning continued.”

Very much in the same way Friedrichs’s idea of being a mathematician was bound up with the idea of being a teacher. He considered the

expression “mathematician and educator” redundant.

Thoroughly prepared, he would start his lectures at one side of the blackboard with a series of little boxes which by the end of the hour

would stretch to the other side. Although he was not a showman, he would sometimes leave a box empty until he could fill it at exactly the

moment when the information he gave would have the maximum effect.

Former students who spoke at the NYU service recalled that his lectures were not polished performances. He was often difficult to follow

because of the originality of his thought and his willingness “to make a mess.”

“He believed that the first part of a course should be confusion,” Jerome Berkowitz explained. The student should get the feel of the

problem and learn what would not work. “[The second part] should be deconfusion, clarification, and illumination. ‘Of course,’ he said, ‘I

sometimes don’t have time for the second part.’’’

(Peter Lax recalls that Friedrichs sometimes described himself as a great teacher “in the weak sense.”)

Friedrichs’s teaching was not limited to his courses. Especially after his retirement, he enjoyed giving expository lectures. These would

range from a single talk to a mathematical “mini series.” In them he would try always to reach a wider public than that of the specialist.

(Fritz John thinks that he would have agreed with the statement that no mathematical theory is completely realized until you can explain it

to the first man you meet on the street.)

In 1965 he published a little book entitled From Pythagoras to Einstein. Typically, he wrote in the preface that the book was not

addressed to a “well defined” audience. The first chapter, in fact, was based on a talk he had given to a special sixth grade math class, the

middle chapters were hopefully intended for high school students, and the last chapter “might just as well be read by college seniors.”

“Professionally, of course, it was hard to imagine Dad as anything other than a mathematician..., Christopher Friedrichs recalled. “Yet at

the very same time, he had such a wide range of knowledge and talent that he could, I think, have followed many other paths. I think, for

example, that he could also have been a great physicist. He could have been a good philologist and certainly ... he could have been a very

good historian. He would have been a better than average naturalist. He had a solid knowledge of philosophy and a sophisticated interest

in things like archeology and modern German literature. And he had also a deep and fundamental concern with the problems of society

and political ethics.”

Since his youth Friedrichs had had a general philosophical bent. This had made him concentrate in his work, as he said, “as much on

points of view as on proofs.” When Lewy asked what he intended to do when he retired, he replied promptly, “Go back to philosophy.”

He found it personally significant that, unlike most scientists, he was not attracted to positivism or pragmatism: “the effect was, so to say,

not to be doctrinaire, as so many scientists are.” He often remarked, “A question which has an answer does not belong to philosophy.”

Lewy also remembers his “smiling” paradox: “Philosophy is the growing recognition of the impossibility of reducing known facts to

unknown ones. The science which does that is called theoretical physics.”

According to Fritz John, it was Friedrichs’s philosophical propensity which drove him to search for the deeper reasons for the occurrence

of symmetric hyperbolic systems in physics in connection with the conservation laws. In a note in 1970 with Lax and in a later paper he

was able to establish that general systems of conservation equations which possess a convex extension can be reduced to symmetric

hyperbolic systems. He also became very interested in the “observable quantities” of physicists. He thought that these were misused or

wrongly interpreted. Trying to clarify the subject in a 1979 paper, “On the Notion of State in Quantum Mechanics,” he showed that the

future values of unobserved observables are determined in terms of their unobserved initial values, “thus in some sense validating

causality.”

From 1971 to 1976 he devoted a great deal of time and effort to working with me on the book Courant in Gottingen and New York, the

writing of which he had suggested. He thought it was important to keep alive for future generations of young mathematicians the unique

scientific spirit of Richard Courant, which had played such an important role in his own life and career. Appropriately, the last talk which

Courant himself ever gave was at the celebration of Friedrichs’s seventieth birthday. On that occasion he spoke with great feeling of the

man whom he had known for almost half a century as student, colleague, and friend:

“He is one of the rare scientists whose intellectual and scientific development has never slackened but has gone forward continually. ...

One of the very wonderful aspects of all this is the fact that even now, at the age of seventy years, Friedrichs has not stopped or

slackened in his endeavors and the radiant inspiration that emanates from him. All his friends and many others in many countries in the

world are profoundly aware of the fact that he has been and has become steadily more truly a great man of science. What a great human

being he is everybody near to him knows very well.”

There were, of course, many honors bestowed on Friedrichs during the course of his career. Writing the account of himself for Modern

Scientists and Engineers, he mentioned particularly Director and Distinguished Professor of the Courant Institute of New York University,

Josiah Willard Gibbs Lecturer of the American Mathematical Society, election to the National Academy of Sciences and to the American

Academy of Arts and Sciences, the Applied Mathematics and Numerical Analysis Award of the National Academy, and (in 1977) the

National Medal of Science, the nation’s highest scientific award.

There were also honorary doctorates from Aachen, Uppsala, Braunschweig, Columbia, and NYU.

During the last decades he received invitations to lecture in many different parts of the world. He had always been interested in seeing

new places; and he and his wife were now able to travel even more extensively than in the past — to Israel, Japan, India, Africa — but

also, many times, back to Germany. Because of the asthma with which he was still afflicted, although not nearly so severely as in his

youth, it was his custom to leave New Rochelle during the ragweed season. In 1982 he spent most of that time in Braunschweig, where

he had begun his professional career.

When he returned in October, he was mortally ill. Increasing deafness had already cut him off from many social contacts, and in the next

few months he gradually and quietly withdrew from life itself He died at his home in New Rochelle in the final moments of 1982, with his

wife and two of his sons at his side.

THE FRIEDRICHS FAMILY WEB SITE Contact: Marty .Friedrichs@Gmail.com |

with Richard Courant 1965