Richard Courant

Kuhn:

Professor Courant, we'd really like to start out with your education. I've got nothing but a list of Breslau, Zurich, Göttingen, with no notion of the order or of how long you spent at these places.

Courant:

I personally am quite unimportant in this picture. I can tell you all about that I know, that I remember. But what do you want to know?

Kuhn:

Let me start out by asking you where you studied.

Courant:

I ran away from high school because it was intolerable for me. And I started studying mathematics, physics in Breslau. My teachers in mathematics were old Kneser, really a very original man, and then Lanzberg of Heinz and Lanzberg, who was a very impressive lecturer, and some algebras. I was trained profoundly and really drilled in projective geometry of the old-fashioned, 19th century type. But then there were my deeper philosophical interests. First I was interested in philosophy — but all this (???) did not really catch me — and in physics. That was my motivation, scientific and not modern, as it is so called, in today's sense of modern mathematics. And so I studied physics quite intensively, but then that was the time with the old physics dying out. The physicists in Breslau were Fringsheim; a very nice, extremely boring man, Clemens Schafer ... and Lummer, the optics man. He was a show man, he wanted to imitate Knudt, the great experimentalist , and he was one of the people who turned his lectures into a show. The main thing is to produce eruptions of volcanoes and things of this type. But one didn't learn what it was all about. And so I did more mathematics, only for a very short time. Then I studied in Zurich. Well, first I had to pick up my high school diploma, I did that (on the side) ... I was at the University for a year and a half or so. But then I went to Zurich, where I studied with (???). But I didn't do anything. I did mostly mountain-climbing and so on. I studied also a little bit. I had personal problems, I had even great economic problems, because I was completely dependent on what I could earn by tutoring. But anyhow, from there I went to Göttingen ... It must have been 1910, or 1909. And that was very interesting for me. I really wanted to do physics, but I was very frustrated by my experience with the physicists in Breslau. And trying to read a little physics was also not so easy. Planck's lectures helped me a little bit. I don't think they are so very good, illuminating. In Göttingen I got into the hands of some older mathematicians of whom you konw. Toeplitz was my mentor first, and then Fred (Hart). I was a completely green, naive boy. I came there two weeks or three weeks before the semester started just to prepare myself for the possibility to follow classes. Then I got in the Hilbert-Minkowski seminar on the mathematical foundations of physics. It was an idea of Hilbert, he wanted to study electro-dynamics. He alined to know what was done by Lorentz, Einstein's paper was relatively new and unknown. And this was a very great experience. I didn't know anything, I didn't know any electro-dynamics. For these two weeks I spent all my time studying out of Föppl and also looking through some classical papers. So I could at least at the beginning follow. Then I (gave some talks) which were successful. At least minkowski became suddenly interested. And then Haar shortly afterwards left Göttingen to take care of his vineyards His father was one of the great wine growers in Hungary. Haar was really one of the first-rate mathematicians. He was Hilbert's assistant. Then Hilbert couldn't find anybody, and I was suddenly in the vicinity of Hilbert and that was decisive for me. Physics in Göttingen as very weak then, or very much along the lines of 19th century classical physics.

Kuhn:

This Hilbert-Minkowski seminar; had that been going on for some time, or was that new?

Courant:

There was a steady Hilbert-Minkowski seminar on all kinds of topics. It was extremely stimulating. Hilbert prepared a number of topics. Usually the seminar was different. Not necessarily connected topics, which were at the beginning of the term distributed among the students. They had to give talks, discuss different theories. Then Hilbert and Minkowski criticized, and very good work came from this Hilbert seminar, by and large. But also quite poor work. I mean it was very uneven. But that semester — I think it was the first semester when I was in Göttingen — they had decided to look into physics, electro-dynamics, with a view to understanding Einstein's theory. And that was the semester, or the year, in which Minkowski wrote, conceived, his approach to the formalism of the special theory of relativity. And I was involved in that as an astonished witness, because the seminars generated into talks by Minkowski. The students could not participate. But at the beginning it started on a very low level, electro-statics, which are stationary electro-dynamic. I was the reporter on this. And then gradually wave propagation and so on ... Hilbert of course was one of the mathematicians who were scientists primarily. He had been interested in physics forever. I do not quite recall when his very active interest in physics started. You knew that Hilbert always later had one assistant who was his private tutor in physics? Pauli. I don't know whether Pauli was officially Hilbert 's assistant. The best of all, the most effective of all, was Stern ... He was not an assistant. He didn't get paid on this title, but he was the one whom Hilbert always praised as the physicist from whom he could learn most, because he was not super-mathematical. He said, Mathematics I can do myself. I would like to understand what is behind it." And Stern had a wonderful way of explaining that did not compromise physical reality and still made things accessible to a mind like Hilbert's. He had a very great influence in this respect.

Kuhn:

I think the first of those assistants was in 1912. I think was P.P. Ewald.

Courant:

Oh yes. But Ewald came, I don't know whether he was around when I came, but he came in a very short time certainly. He was also my teacher. He taught me throwing stones. He was a very sporting type, and Ewald and I, we were very intimate friends ... I remember that Ewald, whom I knew quite well, came to Göttingen. He was assistant of Hilbert's then I think. And from the station he came to my little Studentenbüde, quite excited. He said, Oh, I come with something very exciting. Here I have an envelope with some photographs. He brought me the first photographs of the Laue experiments. And he just had witnessed some first experiments of Laue and Knipping. He was quite excited. He came directly from the station. He lived up from me a little. He was then Hilbert's assistant. He did mostly crystal optics for Hilbert. Hilbert was interested in crystal optics, from the point of view of the energy of vibra-tions. And then Born-Kármán — these papers came from this ...

Kuhn:

Let me just ask a couple of other questions in this same period of your education. When talking about Breslau, you say this is the period when the old phy ics is declining. Now with men like Lummer and Pringsheim at Breslau, was it clear that a corner had been turned?

Courant:

Oh, not at all, not at all. I mean one was taught physics — phenomenological radiation, which is what Pringsheim did, and you know Pringsheim's law. I learned these things. They didn't go deep below the surface.

Kuhn:

Did these men themselves take the quantum seriously?

Courant:

That I don't know. Quantum theory, when I was in Breslau ... Then nothing was known there. Pringsheim probably knew of the existence of such things. I had listened to a lecture of Planck in Berlin. Some students took me there. This was a strange thing, in this country, when this quantum paper appeared. It is of course seen from today a detour through the forest. But people did not appreciate it. Of course Planck started from a slightly phenomenological point of view. I mean he had these facts, But of course these questions of the two ends of the radiation spectrum, the paradoxes, this was already known. I remember that I learned about them, I heard about them at an early stage. But only in Göttingen. In Breslau all these things were completely outside acquaintance ... It was a provincial university. There was research — Lummer did very good work in optics. And Pringsheim also. But the researches were rather divorced from teaching.

Kuhn:

This raises a question. A lot of the people did start at Breslau. Born came from Breslau.

Courant:

Born was in the same school. He had the same mathematics teacher. He inspired Born, as he did later inspire me. And I looked up. Born was much older and I had no personal contact in school withhim in the gymnasium. But then later I met him, and he was a great help for me. We have been close friends ever since.

Kuhn:

Was there anything particular about the university, that should account for there having been that large a cluster of people who went on to do famous things?

Courant:

I think I can say this about Born. There was another mathematician who was not so close to physics, Hellinger. He came from the same school and from the same teacher. There was one teacher in our gymnasium who was enormously inspiring. Also, he was largely ignorant. He didn't know mere than the elements of differential calculus. Integral calculus was hazy for him. But he was very inspired, and I got a big kick out of his lectures and classes, so did Born and so did Hellinger. There was another man who died. He became mentally disabled. He started very brilliantly. Wolfgang Sternberg ... He degenerated completely later, but he was also a product of this Professor (Maachkin). Max Born came from an intellectual family his father was a physiologist, and he was very much interested. He was very rich. He lived on what we thought then was an extremely lavish social plane. So he could indulge in many scientific hobbies and he had a wonderful education. But in Breslau at the University there was very little for physics. Mathematics was different. I mean there was Kneser. He was one of the moving forces at that time; and Lanzberg. So it was not a place where one could develop scientifically. Clemens Schafer I think later went to Cologne, or to Bonn. And he was very nice, but also as a teacher very uninspiring.

Kuhn:

Would people come from all over Germany in mathematics to go to Breslau?

Courant:

No, no. It was a strictly provincial place. Breslau was, as Mark knows, the intellectual center of the Near East. Many people came from Upper Silesia, where I was born as a little infant. This was a reservoir for Poland, and they got quite a number of good people. It was a high intellectual level. Art, music was very good at Breslau.

Kac:

You don't think that the fact that Dirichlet was there at one time could account for the tradition?

Courant:

No, no no tradition. The mathematics tradition in Breslau was established. There was this very strange high school — (???). There was Sturm, who taught projective geometry. And he was such an intense Pauker — drill master, that he had a very great influence. He just forced — students could not follow in his classes, unless they worked very hard. The best teacher, the most successful teacher I had at Breslau, was typical of the point of view of education, was a man in algebra, his name was Rosanes. His name is not known any more. His great success as a teacher was really due to the fact that he didn't teach things very well. He came to the platform. There was a blackboard. In his right hand he had some chalk, in the left hand he had a wet sponge. He turns his back to the audience, and he mumbled something towards the blackboard, and scribbled something in small letters on the blackboard, cover it up with his body. And as he roved along he erased what he had written. And then the student always had to try to snatch a few words. Then there was an enormous task after class, one sat there for another half hour to try to put together the pieces. If one succeeded, one really had learned enormously much. This was the basis for my learning algebra. And one of the other students, who came a little later, was Hecke ... He came when I was drafted for the army, and then Hecke was my successor with Hilbert. I made Hecke come, I wrote him that if he could he should come here because it was so much better than in Breslau. Hecke didn't come from the same high school, nor did Toeplitz. There was another center in Göttingen [Breslau], an inspiring center for young scientists, mostly mathematicians. That was a gymnasium, Magdalene Gymnasium, I think. And the father of Toeplitz was the chief Mathematics teacher there, and this had a very great influence also ...

Kuhn:

The seminar must have been 1909-1910, the Hilber -Minkowski seminar? ... You spoke of the Einstein paper. And I take it this is the first — the 1905 — paper And its being not well-known at that time.

Courant:

The first paper I remember. It was not well known. I saw it first when I visited Max Born in his house in Breslau, and he said this is a very interesting paper. I never had seen scientific papers really. So he showed me this Einstein paper. In fact I'll explain it. He was also struggling with it. But that was still in my Breslau time, before I went to Göttingen.

Kuhn:

Born himself then seemed very much impressed with it?

Courant:

Born was impressed. And he also met Einstein later. I also met Einstein later then. I had some very interesting, humamly interesting, encounters with him. But no, Born was quite impressed. Then he went to Göttingen. He went really to study these things. But it was the first time in his life, that he was forced by Felix Klein to get his doctors' degree in something not in relativity, but in elasticity. Euler's theory of the elastic. ... As a student he was very independent; also in his personal life ... He was invited by Klein to participate in the Mathematische Gesellschaft. For somebody who had not gotten his doctors' degree, this was a very great distinction. So he came. Klein always dominated the scene. The Academy of the University each year set some prize for mathematics. And the prize winner got for his prize paper the degree, the doctors' degree. And Klein was interested in all kinds of things, so in this year he wanted that somebody should study, from the point of view of the variational calculus, Euler's theory of elastic! It's really the first theory of buckling. And Born was not interested. He wanted to learn relativity. Well Klein invited Born, "Wouldn't you come some day, tomorrow afternoon? And then Klein told him, "Herr Born" — Klein was very imperious. "I've just set the prize paper, and of course you know that we have to be sure that somebody does the paper and gets his degree, and I've selected you for that." And then Born rebelled, and said "'No, but I am not interested in this. I want to do relativity." Klein: "What, you are not interested in it? This is of course a most interesting thing, of course you should do this." And Born stood on his hind legs: "Herr Geheimrat, ich kann das nicht tun." Klein was very (primitive). Klein said, "Well Herr Born, dies zeigt dass Sie doch nicht so reich sind wie ich gedacht habe, vielleicht kommen Sie da lieber nicht mehr in die Mathematische Gesellschaft." So Born was ejected from the Mathematics Society, by Klein personally. He was the president of course, in Göttingen. And Born was heartbroken. He met his friends. I remember how Toeplitz insisted then, "Oh, why don't you do that? "You can do it very quickly." And so Born, after a week, went back to Klein and said, "I thought it over, I will write this paper." And Klein said, "Oh, I'm so glad, because it would be nice if you could continue in the Mathematisc Gesellschaft." It was really like this ... I mean Klein, he was just shy, he didn't know how to reach people. But from time to time his wife, who was a grand-daughter of Hegel, said we must invite young people from time to time. She gave dinner parties, very stiff. I was invited, and I still see this dinner table, Klein at one end and Frau Klein at the other end, and all the young assistants and Privatdozenten very shy and intimidated. It was really deadly silence, and then Frau Klein finally broke the silence, shouting to her husband, "Du musst doch mit den jungen Leuten sprechen." It was really like this. So Klein pulled himself together, and next to Klein was a Privatdozent, (Prandtl), a statistician. Oh, they were sitting at the table, and then not to make a faux pas, "Ja, Herr College (Prandtl), wie geht es Ihnen?" or, rather "Wie ist es lhnen gegangen?" That's it! "Gut, Herr Geheimrat". That was the effect that Klein had. And so Born also gave in. And he wrote this paper; he got his doctor's degree; and he missed — or he thought he missed — on the early relativity developments. He wanted to write, to do the same kind of thing that Herglotz did later on the relativistic theory of rigid bodies. There wasn't very much to it. And so he was very unhappy that he had missed out on that, and then did not work in the field, but went into crystal structures and such ... He felt beaten in the beginning by Herglotz. It hurt him deeply. But whether he ascribes that to Klein's interference or to Herglotz' brilliance, I mean this is very difficult psychologically to say ... But I do think that his enthusiasm was broken by this. It may have been just as well, because Born was of course a member of this small inner circle of really very good people. With Haar. Then he did all this crystal structure stuff. And he learned very much from Hilbert. And that was the time when hilbert's theory of functions of quadratic forms of infinitely many variables blossomed. The ultimate result — this was also a big disappointment — was this paper that Born and Kármán wrote on the specific heat. It was a little later, but it grew out organically from this contact with Hilbert, and with Kármán, who also belonged to the group. Kármán is really, in my opinion, one of the geniuses of physics in this era. He didn't happen to work in the fashionable center, not interested in some of the fashionable people, so he never won the Nobel Prize, nor did Prandtl. This is one of the great injustices of this prize-awarding... He is a genius who deviated very much, by becoming the early pioneer of the commercialism of science. I mean it is a tragedy, because it is not in his heart, he just turned to that. But anyhow, Kármán and Born were good friends, this idea of doing better on the specific heats than Einstein in his first paper — Einstein of course had the basic idea, this is only when we look at it in perspective. But then he worked on this, with this very nice idea to take an infinite array of atoms. Then their paper came out. This was wonderful, great excitement. We all participated violently in this ... It was a close community and we saw Born; we talked about these things, and with Kármán. But then Debye, who was in Munich, he also hit on the same problem. It was a very central problem of course, with the experiments by Eucken and by Nernst and Lindemann. And we saw Nernst very often. He came to visit Hilbert. And I would say Debye went after this problem with a very similar idea, only he did it more primitively, and got just as good results. They came out almost simultaneously. And it was a big tragedy. I mean the Born-Kármán paper was printed in the Physikalische Zeitschrift. Two columns each page in bad print. And many misprints; Kármán didn't read the proofs very carefully. Debye's paper was printed in a new, much nicer looking journal, and very carefully proofread and so on. So it was an immediate Impression. Also it was more accessible. It didn't make use of the sophisticated Hilbert theory. So the immediate impression of Debye's paper was greater, except in the Göttingen circle. I mean, they kind of berated Kármán and Born for having made errors in proofing and printing. So this was a big disappointment in the beginning. Of course in the end it didn't make any difference. And the collaboration between Born and Kármán ended right then ... I don't want to be too personal, but it also ended because Mrs. Born, whom you don't know, she hated Kármán. It didn't end in any drastic sense. They remained friends, but Mrs. Born always felt that Kármán's sloppiness deprived her from attaining the same glory that the Debye family attained. But this is a small item .

Kuhn:

Now as you describe the Göttingen situation around 1912, clearly at least this younger group of theoretical physicists were very close to the mathemiticians.

Courant:

Very close, yes.

Kuhn:

What was their relation with the experimental physicists?

Courant:

Quite good. Let's see, who was the experimental physicists? There was Voigt. As a matter of fact, I was quite interested in crystal optics, and I took an advanced laboratory course and did many different experiments, and measuring bi-axial crystals, and so on. It was quite interesting. But Voigt was interested first in crystal optics, and then also in these effects. I remember that in my doctors examination I gave a little expose of (???) and (carbino) experiments. No student now would know about these things ... But there was not too much collaboration, except later when Debye came. of course with Scherrer, they did these wonderful experiments. Debye was not an experimentalist, Scherrer also not really, in the beginning. He mastered the X-ray ideas, X-ray techniques, very early. But there was a very close connection. Scherrer was in our seminar. I had later a seminar — when I was Privatdozent — with Weyl. Scherrer took part in the seminar. It was a very close connection. Of course when Scherrer and Debye were in Göttingen and worked on the experiments, we always spent hours in the physics institute talking to them.

Kuhn:

Now this is a good deal later.

Courant:

It was later, yes ... what happened later was that the theorists, such as Debye and Scherrer, went into experimental physics themselves to a certain extent. When I came as a student to Göttingen, the theoretical physicist, Voigt, but he also did experiments. The experimental physicist was Riecke. He was a dull, boring, uninspiring man. I don't know what he has done. There was some man in applied physics, (Sieman) I think it was; and there was of course Prandtl. He came there early. Prandtl was a great physicist, in fact. But Prandtl was a little bit outside. He was very inarticulate and "linkisch" this is a German word — for "awkward." And always was stepped on by the big shots in the faculty. I remember, he never got this point. People would send out students - what is called here faculty adviser — they would only send the worst students to Prandtl. It's really fantastic ... There was an inner circle of people who really ruled the place. In the old times it was Hibert. There was a circle around Hilbert, but Hilbert was very open. There was no politics, no ulterior motives involved in Hilbert. (He worked very hard governing the place ...) And he had conscientious assistants, so this worked all right. But in physics it was different, more ambitious young people ...

Kuhn:

Then there was none of the sort of separation between the mathematicians and the physicists?

Courant:

No, not at all. Hilbert of course set the tone by becoming more and more interested in physics, the quantum theory. Relativity was the beginning of his deep interest. Of course you knew, Hilbert had studied physics as a young man. He knew about old physics quite a bit. But then relativity came in, and Minkowski made all the difference. And ever since he had this series of assistants who came to Göttingen who became part of the whole picture. I mean, Pauli was in Göttingen, very much drawn in by Hilbert also, he was Privatdozent in Physics. Then, Heisenberg was a little later, I can tell you the beginning of this. Nordheim, (Peierls), Wigner, were all in this same group ... There was this whole (circle. John von neumann) spent much time in Göttingen, although he was a product of Berlin. He was in Göttingen very often ... But there was no difference, no barrier between the physicists and (mathematicians). Of course later there were experimental physicists like Pohl, who were very anti-intellectual. And there was not such a close connection. And even in the Göttingen faculty some acidity(?) developed against the long-haired mathematicians, among (???). They wanted to have the mathematicians teach courses just for physicists ... Do you remember the (???) book. A famous book on Mathematik der Naturwissenschaften, by Nernst and Schönfliess. But there again Nernst was a physicist, a physical chemist. Schönfliess was a Mathematician, quite a good mathematician, but also deeply interested in some aspects of physics. They wrote an elementary textbook, quite good. Now this book became the core, the basis of which courses were given in universities. The physicists and chemists demanded that the mathematics group provide such a course. This was called, by the more haughty mathematicians, Das IdiotenKolleg — a class for idiots. And that was the title. The physicists like Pohl and Tammann, a physical chemist, a very outstanding man, were outraged that their baby was called IdiotenKolleg . And this was always shifted to the least experienced Privatdozent. But such fighting went on, also internally. But contact was very good, and also centered very much around Hilbert. Hilbert was a close friend of Nernst's from their young years on ... And the young people (was one family).

Kuhn:

How would you compare that with other places in Germany?

Courant:

There was nothing like this in Germany. There was a little bit in a very different way — it was in the center, with much contact — in Berlin. Frankfurt had quite a number of mathematicians, but not the same momentum came out of it. Planck was much more aloof, although he had students. Laue also I think was in Berlin. He also came to Göttingen often as an extended visitor, at least. He came from München as a matter of fact. And Ewald. Sommerfeld of course was an old Göttinger. And Sommerfeld's influence on this inter-connection between mathematicis and physics cannot be overestimated. He also kept his contact with Göttingen. Sommerfeld always provided Hilbert with assistants. They were very close friends, and Sommerfeld took an enormous interest in this, and was at Göttingen quite often. There was really very much communication. And Hilbert's personality was quite, instrumental in this ... A very important element in all this, if you want to know more about Göttingen, was the direct, and more indirect, influence of Niels Bohr. And this is really a most important feature in this whole affair. There was an extremely close connection in Göttingen between the Göttingen group and Harald Bohr, Niels' two year younger brother. He was a very, very close friend of mine. He came to Göttingen and he was really the most wonderful phenomenon. Now Harald was greatly admired by everybody. He came from month to month to Göttingen for visits. This was before the first World War, and he told told me always — (he admired me very much). I even wrote a paper with him ... But Harald Bohr, he always praised me, but that's nonsense. I mean, I am nobody. And he was just about the greatest genius in physics and in natural philosophy. He was completely (unaware) of his superiority. And finally he said, "You must meet Niels." Niels didn't come to Göttingen then ... And then I met him in Cambridge; that's where I met Niels first. This was about at the same time when his first paper came out, on the. Balmer spectrum. We became very close very soon. But then he came to visit us in Göttingen. We went skiing, Niels and Harald and I in Arosa. I was going to show you some movies I made then. (I saw him quite a bit) also in Copenhagen. But the interesting thing is that Niels became very well-liked in Göttingen by everybody. He came for some visits of a week or so. We played tennis. We played a double game in which Harald (???), and Niels used his tennis racket — like this. (But Niels taught me physics.) Carl Runge was between physics and mathematics. He was the great spectroscopist. He knew more about the spectra than anybody else. I mean he, and Kayser did, just deciphering complicated spectra without seeing what it was all about. And Ritz also was in Göttingen, dying at that timel already, from tuberculosis. But he was of course a man who invented the fundamental combination principle. Then Niels came with his model. And I remember that Runge was completely upset. He said, "Well, such a nice man, and so intelligent. But this man has become completely crazy. This is the shearest nonsense." It was a violent criticism and opposition. And he berated Harald for praising his brother, at the moment when he really had become insane.

Kuhn:

Do you remember how other people felt?

Courant:

They were astonished. Except Harald. Harald played a very great role in convincing people, because everybody was completely convinced that what Harald said, was so reliable. Harald said, "You don't understand it yet, but you will really see this is one of the most important steps in physics. He told people, and they didn't believe quite, but thought one must take Harold seriously....it is sometimes nonsense, and thought — and derided it as nonsense. Next day it is accepted in sociology that one has no influence forever. That happened with ... Of course later after it was seen that a little bit more than the Balmer spectrum was covered by these ideas, then their resistance broke down ... If you are used to the Helmholtz kind of physics, everything deduced log- ically, not so tremendously big steps from what existed, it was an enormous step. And we discussed that with Harald. The philosophy of that. He said, "Yes, Niels is really somebody who has a more immediate access to the secrets of nature. He sees these things and then this logical, deductive thinking comes only afterwards. He just is sure, he is sure." "And I, Harald , also don't understand about it. But since Niels says it, and considers it so important and decisive and complete, I know that it is really the great progress in physics." That was the way Harald said it ... This was the beginning. But then very soon the people said, "Well, this is wonderful. He must really study this." And then of course Sommerfeld came out very quickly. This was quite important. Also, Sommerfeld started as a mathematician, and was very much given to this deductive, step-wise attitude. But he saw something. And Sommerfeld had a young student — who as a matter of fact went to the same (???) Klasse as Mr. Himmler. A very brilliant young man. I forgot the year, but I was already professor, or at least Privatdozent. I don't know. But Hilbert insisted that we should invite Bohr. There was a series of lectures that Bohr gave in Göttingen — ... I just want to say that the ice was broken even before the war. And I think the m,ost effective protagonist of Niels' ideas was Harald ... He told everybody. He also told the physicists in Göttingen, everybody, that you are silly, you must really watch this. And since he was so absolutely trusted and believed, it made a big impression. Also on Hilbert.

Kuhn:

Do you remember at all how if Max Born felt about this?

Courant:

I don't know exactly any more. But then he was rather early in on that. Because Born and Karman were the ones who :ade very early use of these principles. Of course ' stein was the first, but that was before ... You see people who had s e close contact with quantum, the quantum idea, were more easily accessible ...

Kuhn:

What about Hilbert in this respect; exposure to the quantum and convictions about the quantum before Bohr? ...

Courant:

Of course, Hilbert's contact with Einstein was through the relativity theory. But then he had so great confidence in Einstein. It was also Einstein's famous paper, where he did photo-effect and these things, that was then discussed, and Hilbert was completely aware of this. But of course, Hilbert's idea always was that one could somehow have a bridge of rationality between the quantum idea and the classical continuum of physics. This he would have liked. But he never made a passionate statement. I mean he never committed himself ...

Kuhn:

There's a particularly interesting paper of Einstein's in 1909, which is the fluctuation paper, the one in which he does fluctuations in the electro-magnetic field? ...

Courant:

I am not aware at the moment of this.

Kuhn:

It occured to me as one that might well have been discussed in the seminars around that time.

Courant:

No, no. I mean, there was a seminar, which Hilbert started. It really was very interesting. When Born was there, and of course Minkowski, who died very soon afterwards. This seminar "Uber die Struktur der Materie" went through many years, with physicists, and Hilbert 's assistants, and all the new physical discoveries were discussed there. Always with the view, "Could one not bring Mathematics to bear on these problems?" It would be worthwhile to Nordheim ... The War of course was a big hole ... I spent all the time from the beginning, from the first day of the mobalization on to quite late, in the German army. First as an infantry soldier. Then I did some technical work.

Kuhn:

Where did you do the technical work?

Courant:

Oh, I was by that time a lieutenant in the infantry. I did it later, after I was almost shot dead. I was transferred to the central research laboratory of the postal office. And I did, I built microphones. I was involved in the first electronics, first amplifiers. That was in Berlin ... But then later I was transferred — I made what the military calls an "invention" — I built some devices to listen — which later had some bearing, some importance, some relation to geophysical questions. I built something to transmit and receive signals. Not radio signals. They couldn't build such things then. But signals through the earth. It was low frequency currents for communication between the front lines and the artillery and so on. And this then mushroomed into a bigger thing. It was the first taste I had of business people. So I was quite busy. And while I worked on this I had contact with geologists and acoustics people. Also at a very early stage I understood (???) in electronics, but then later I got completely involved in mathematics. And I did some theoretical work also, on amplifiers, tubes. With Born I had very little contact during the war. No, it's not quite so. Born was drafted after a while, and became a member of the Artillerie-Prufungs-Commission. That was a research group of the artillery. And there he did mostly acoustical, directional things. But he had a lot of time to do physics. I saw him. He had a uniform, but he was not very military. Generals in high offices talked to him on occasion. And there was a wonderful scene. I was a first lieutenant. I remember the scene. We met in Berlin. When he was in Berlin on this occasion he was in uniform. But he had a (lower rank). (It was a civilian uniform), and he tried to look military. And I know, I remember, in a big crowd, with many soldiers and officers, we said goodbye to each other. And then Born forgot completely that he was in uniform, he took his military cap and made a big bow, and waved it. It was the funniest eperience. He never went out in uniform again. He could have been arrested.

Kac:

Just to interrupt one second [3/4 hour to go.]

Kuhn:

There was a good deal of scientific work and following up of quantum done, and of the Bohr atom done in Germany during the war.

Courant:

But I don't know whether I even saw Sommerfeld. For the first two years of the war I was completely involved in strictly military service. And I was in the hospital. I had a very bad shot. It was a miracle that I survived. So I was for a while convalescent. During that time I worked in Berlin. And then I felt so disgusted about the (marching), and the (guys) at the front lines. I mean I was a very class-conscious front soldier. So when I made this invention, I decided, I have to see that it is being used properly. I had a very interesting time. I got myself a little detachment of people, a few non-commissioned officers and technically trained soldiers, and we experimented in the front lines with this communication. I took part in the Battle of Verdun in some way. I got gassed. But I was quite interested in these matters. I became an organizer. But I didn't have so very much time. My contact was with Hilbert. I mean I didn't see anybody during that time. One point may interest you. One feature in physics (very attractive) to Göttingen, were the lower echelons. Among the big shots there was nothing. But there was a younger, slightly diletantic but highly cultured physicist who was interested. in cosmic rays. That started as a hobby of this grand seigneur, Rausch von Traubenberg ... He was the protagonist of cosmic rays. And this was also disconnected with classical physics. One didn't understand, so serious people didn't pay too much attention to it. Mostly the link with that part of physics came much later.

Kuhn:

It appears, when you think of what was going on in Britain in this period, with radioactivity and radiations in general. There was remarkably little of it in Germany.

Courant:

Oh yes. Very little. There was of course Hahn in Berlin, with this group. But they weren't very prominent. Bohr was not connected with the Germans during the war. I lost contact with both. I remember I wrote at the beginning of the war (that I thought it would be a horrible thing.) And, when I marched through Belgium, one evening I wrote a long letter to Harald Bohr, My next contact with him was much later, at the end of the war.

Kuhn:

Let me switch the ground now, and ask you a question I'm terribly curious about, which is the background or foreground of the Methoden der Mathematischen Physik How did that project start?

Courant:

Yes, but that has very little to do with your project.

Kuhn:

Well, I'm not sure. This is one of the things I want to find out.

Courant:

So, I was always very much interested in those aspects of mathematics that provided some bridge to, (or criticism of) physicists. And, well, I was influenced by the seminars and my contact with Hilbert, and my great scientific seriousness at the beginning. Also may thesis was written under Hilbert, it was about Hilbert's paper on the Dirichlet Principle. And I also was personally influenced by Klein. Klein was the man who brought Riemann's complex functions theory to attention with younger people. So I became quite ineAed, again, in this aspect of the connection between the theory of functions of complex variables, and hydrodynamics, or electrodynamics, electrostatics. So then I studied the old papers and lecture notes of Riessnn, which later were expanded into Riemann —Weber and so on. And I was very much impressed by the style ...

Kuhn:

Had you used the Riemann-Weber as a student?

Courant:

Ja, I tried to learn things there. And then Hilbert after the war. I studied in Breslau with Rosanes and these people. Also with Kneser. I was very unhappy. I said, "Well these people — they know so much. But they don't know how to tell anybody else. So when I grow up I will try to do something about this." I think I can do that. Well, I can do a little bit. But of course, you lose your insight when you get older and you are transferred to the other side of the fence, and your perspective becomes a little bit blurred. But anyhow ... I must really tell how my first contact with Hilbert and Minkowski occurred. I was really a complete (greenhorn). I had not the slightest idea. I had two or three weeks before the semester started to learn this. I read as much Abraham-Föppel as I could to prepare myself for the seminar. In mathematics this was not so difficult, I picked it up. There was this distribution in the Hilbert-Minkowski seminar of subjects. The whole of electrodynamics was subdivided. It started with electrostatics, and then stationary phenomena. And I deliberated. At the beginning you can select, or you can apply to get your assignment. "Should I get an assignment the first time, the first two lectures. Maybe I should wait to see how the seminars go." Of course afterwards it becomes very difficult, so I thought it would be the safest to do (???) stationary phenomena. And I was given this assignment. And I was lucky. In two weeks time when my turn came, I had not only learned things, but I had thought a little bit — nothing original — but I did it a little different from Abraham-Föppel. I thought I was wonderfully prepared. But then Minkowski, who was a very sharp and really merciless critic, he interrupted me and said, "I don't understand that. Can you explain it again?" So I explained it again, and Minkowski became quite involved. He went to the blackboard and wanted to show that my argument cannot be correct. I was very sure of myself, so I became disappointed, but also stubborn. So this seminar really degenerated into a duel, between this little guttersnipe student, and Minkowski. And finally he asked me, "Where did you get all this nonsense from, that is not from Abraham-Föppel." And I said "Well no, I thought it out differently and I think I am right." "Oh," he said — the bell rang and we had to stop — "The next time you prepare better, and study your Abraham-Föppel better." And I was very offended, because I knew that I was right. But then I thought, well, I could have presented it better. I didn't know how to present it better. But then a few days later I met Minkowski on the street. And he crossed over and shook hands and said "I'm sorry, I should apologize. I was completely wrong." And then next time I had a great triumph There was really nothing, nothing to it, scientifically. But that was how I came to know Hilbert and Minkowski. And also, the first effect was that Hilbert asked me to tutor his son in mathematics, which was very good for me because I had no money. And then Haar left for the second time, and then Hilbert made me his assistant. And so we became very friendly, and had very good personal relations. And I saw very much of his whole life, not from the outside. Well then later — that was right at the beginning — before the first world war. And with Hil bert I always kept some contact during the war. As a matter of fact, I was by that time already Privatdozent. And so I had my household. I was married. I got divorced during the war. My household goods were stored partly in Hil bert's attic, so I saw quite a bit of Hilbert. During the war I met an artillery officer, with the name Ferdinand Springer. At that time the next generation of the Springer Publishing House was in a big fight with his uncle, who wanted to (throw him) out because he made big commitments — I think it was not the Handbuch der Physik — but to some journal. He made some comitment, very many hundred thousand marks. Springer was really a genius. I mean this combination of understanding for science and people and business. And so I met Springer, and we talked on some occasions about mathematics and religion And I was very unhappy about the existing textbooks. Of course Hilbert had always said, in the old times some good textbooks were written, Riemann-Weber, and Weber's algebra and so on. But now this generation must also do something And I felt inspired by this. I talked with Hilbert about this Springer, and this plan of the yellow series was conceived then. It s still during the war. I still have some old documents. I made my first proposals. In this connection I talked to Hilbert. I thought this Riemann-Weber had degenerated, and the whole spirit of Riemann-Hausdorf. "We can do things so much better, and shouldn't we do it together." Hilbert was rather enthusiastic, but he never did anything ... We never discussed it. He became quite ill. He had this pernicious anemia, and I don't think he has ever read any line, even the proofs of it. I don't want to sound somehow inappreciative. It as still with very much his spirit that I grew up under Hilbert. And also some of Hilbert's lecture notes played some role. First I tried to get Hilbert involved, but I gave that up. And so much was going on any way. And then I started with this first volume ...

Kuhn:

In the Preface to the English edition, you speak of the possibility of physics splitting into more and more little rivulets and drying up ...

Courant:

I don't know what made me express myself so sourly then. In Göttingen for example — to talk of mathematics — Landau had come to Göttingen. He was an exponent of completely, not perhaps of abstractism in the present sense — where you write books which haven't any sense. You have seen such things even in my own yellow series.... It is so highly evaporative in air, and so little relationship to substance.

Kuhn:

But this surely was not happening at Göttingen at the time you undertook to write the book?

Courant:

Oh no. There was Landau. He was a fanatic of purity. For example, (Prandtl) at this time wrote a very fundamental paper, "Die Theorie der Schmiröle." It is a theory, physically speaking, a theory of hydrodynamics, of viscous fluids where the elements are long molecules, essentially. Also Kármán was interested in this. But Schmiröle was something, of course you don't want to have your fingers dirtied. And as soon as somebody in mathematics said anything, even faintly reminding of applications, Landau said, "Schmieröle, I don't want to have anything to do with it." I mean that was an extreme point of view. And of course there was a big fight in the faculty, who could give the course on differential and integral calculus. And one year Landau or his group was given this course, and the other, alternating with somebody more closer to science in general. And Landau started his courses not with the theory of real numbers, with the Peano axioms.

Kuhn:

Well now, was this already beginning to happen to mathematics in Germany at the time you were working on Courant-Hilbert?

Courant:

Oh yes, yes. I mean, when I was a student Kneser still had the old-fashioned connection with mechanics and classical physics. But the mathematicians didn't. In Göttingen the symbol of this was (Hilbert's fight with Landau). There was a big fight about it, a friendly fight, but very intense ... Hilbert later even gave lecture courses for "Hörer von allen Fakultäten," about the mathematical elements in physics — a very interesting course.

Kuhn:

You also speak of the physicists turning somewhat from mathematics. And I'm surprised at this.

Courant:

Yes. But this is of course quite clear. In physics, after quantum physics, take a cosmic ray physicist, they didn't do it. I don't think that Traubenberg was able to recite the for for a plus b² ... Pohl. Pohl. Completely — not unmathimatical — but antimathematical. And of the experimentalists ... But in other places it was much worse. They were not like was at Göttingen. Göttingen was a place where this tradition was very strong, it couldn't be broken so easily. But take Berlin, for example. The mathematicians in Berlin didn't have contact with Planck, or in München, with Sommerfeld. Well, there were some people; but there was not this interaction.

Kac:

Who was the mathematician in Munich at that time?

Courant:

Lindemann ... played a very great role; he was a very big Bonze ... What the Italians call (prezzo grazo). Somebody whose importance has to be shown all the time to cover up something else. But in Berlin. Berlin was a big center for mathimatics, also a big center of physics. But there was not this interaction. I mean we mathematicians in Göttingen, many mathematicians, used to go to the physical colloquium. When Debye was in Göttingen, there was an enormous — with Debye many of the mathematicians came to his lectures. They were the most wonderful lecture courses, that Debye gave. Born was more mathematical than Debye, but he didn't have the same appeal with the students. Berlin was a big center, and there the seperation between mathematics and physics was much farther progressed. And, another center was Bonn; there was also no interaction. And in smaller universities, the provincial universities, there was no interaction. And if you take the modern development of algebra, the so-called abstract algebra, it goes back to the middle of the 19th century. But there was suddenly this flurry, this big drama.

Kuhn:

Let me just ask briefly on one other topic. This whole question of the years just before, and then the early years of the matrix mechanics. For example, the story that Heisenberg developed something very like matrix multiplication but didn't know anything about matrixes. Is that right, that he didn't?

Courant:

Yes, yes. This happened. Heisenberg, although he had been with sommerfeld, he didn't know anything about this. I remember very well when Heisenberg started this. But the good luck was that then there was Jordan, who was very much of a mathematician, and Max Born, who was a great artist in the methods. So these more perfect aspects were brought in at a very early stage.

Kuhn:

Did Born and Jordan themselves come talk to you?

Courant:

Oh yes, oh yes. Jordan even was my assistant for a while. When he originally was in Göttingen, I think he wrote notes for my courses, I forget. But I knew him very well. I had difficulties with him, because I am too neurotic myself to feel at ease with neurotics, with people who stammer. I have great difficulty to listen to Jordan even now. I see him occasionally. But Jordan took a very intense part and was very instrumental. Of course the idea to break away from no nal analytical algebraic operations was Heisenberg's, very definitely.

Kuhn:

I wonder, do you remember any conversations, reactions, what people said, felt, in that very hectic summer of '25?

Courant:

Oh yes, there was very great excitement all the time. We often had lunch together, Mittagessen — Born, Heisenberg. We met all the time, and there was excitement — Jordan and Born. I don't remember any specific detailed conversation. It vas a running battle, a running struggle. Everyone wanted to get into the act, you see. And Born became quite excited over that. (Heisenberg didn't). I remember now, Born didn't understand this kind of mysterious multiplication operation. Amd then I remember that Born came to me very soon afterwards, "Now I understand what Heisenberg was doing — matrix multiplication."

Kuhn:

Would matrixes of themselves, the matrix multiplications, have been standard, part of the curriculum, at Göttingen?

Courant:

It didn't play the same role. The matter of course attitude didn't exist with which one learns matrixes. I mean, there is a book by Kronecker.

Kuhn:

But it was something you would not have learned unless a Dozent had given a series of lectures on it?

Courant:

Yes, I remember even later, some mathematicians became very excited, even Herglotz, when he realized how much simpler the theory of ordinary differential equations can be written with matrices. I even have in my bookshelves some old lecture courses. I think one by Herglotz about the application of matrices. But the awareness of it came only when it became more widespread at this time.

Kac:

Correct me if I am wrong, because I came at a later period, but it was not an integral part of one's mathematical kit of tools ...

Courant:

Yes, of course. They were used in projective geometry. I remember the first courses that I gave. Maybe I gave one of the first systematic courses in linear algebra. I decided right at the beginning — it may have been even my first or second lecture course for Privatdozent in Göttingen. I have even notes of this; determinants and linear equations and their applications. That was matrix theory ... I don't know how much of this I did in my course. I can look that up. I was aware of it. I had studied Kronecker. But I remember when I first ran into it by reading Kronecker. Kronecker had given lectures in Berlin, which still are worthwhile reading. And I learned this aspect at an early stage, but I remember how enthusiastic some of my younger colleagues at that time, still younger than I, were when they discovered how much you can do with it. Mere was a man (Wägen) you don't remember him. He was a strange man. Heisenberg didn't know matrices. But in München, that didn't exist.

Kac:

Because Sommerfeld was the real classicist and that was the classical 19th century tradition in analysis.

Courant:

With enormous power. And of course he would write everything, with summation signs and so on. But somehow I don't think that he accepted these tools at that time. And Epstein was the guiding spirit in establishing bridges to more current developments ...

Kac:

May I ask one historical question? The interesting thing is, purely analogically, in treating quadratic forms of infinitely many variables, Hilbert called what is now spectra spectra.

Courant:

This was a visionary achievement ... I always quote his symptom of a deep, instinctive, intuitive — not insight — feeling ... I never talked about this with Hilbert. With Hilbert, it was just the fact that some discrete phenomena could be described, ,and all its different c acter, could be described by the same mathematical structures as the spectra. He knew about spectra from Runge and so on.

Kuhn:

But he did not see the Ritz —

Courant:

Oh no, the Ritz combination principle was a very strange thing. All the Mathematicians shrugged their shoulders ... It was so very phenomenological at first. And Ritz was very highly respected. Was an interesting, mysterious, and very much admired and intriguing character at Göttingen. But what made Ritz so famous around the Göttingen circle was his numerical treatment (by the variational calculus of the vibration of a plate). He understood the whole background. And Ritz was inspired by Hilbert 's papers on the Dirichlet principle.

Kuhn:

Hilbert never tried to grapple with the physical spectrum problem?

Courant:

No, not with Ritz' principle, no. But later he did not reject, as Runge did, the early Bohr work ...

Kac:

Of course Von Neumann was extr emely close to the Göttingen tradition in his work.

Courant:

Oh yes, Von Neumann's achievements, this is of course something else. Von Neumann of course grew up in this Göttingen tradition — spectral theory, quadratic forms — under Hilbert. But then he came under the influence of Erhardt Schmidt. I always count Von Neumann's achievement as one of the really wonderful achievements — positive, clear-cut achievments — of the abstract approach. You see what Hilbert did was generalize quadratic forms to infinite dimensional space, infinitely many variables. There it was difficult if not possible to visualize all the possibilities that could exist by direct passage to the limit of an explicit formula. And there it was the great merit of Von Neumann guided by Schmidt, to see that what matters really is the structural situation in abstract space.