Theodore Von Karman

Heilbron:

Let us begin with the origin of your own interest in science.

Von Karman:

Of early life and family I can say a few words. I was born in Budapest in 1881. My father, Maurice von Karman, was professor at the University, for philosophy and pedagogies. Sometimes he was called Preceptor Hungarian, the teacher of Hungary, because he founded a gymnasium for the candidates for high school teachers. This was also called the model gymnasium. I studies there. I decided to be really a teacher, but the question was in what subjects. Now I had an early inclination for mathematics. When I was quite young I multiplied numbers with four or five digits in my head, but my father was very wise and forbid it. So I forgot it. Now I can only multiply in Hungarian. My students here at Cal Tech were often wondering what I am mumbling when I made a multiplication on the blackboard, but I can do it only with Hungarian numbers. When I was about 14 or 16 years, I decided not become a pure mathematician but an applied mathematician and an engineer. And in 1902 I received a mechanical engineering degree at the so-called Royal Technical University in Budapest. I had, very good teachers, and especially I was close in collaboration with Professor Banki, who worked on internal combustion engines; and with Professor Schimanek, who was professor of machine elements. Then I started to work half-time in industry, half-time in the University, especially on problems of elasticity and stability of constructions.

Heilbron:

Was there much pure mathematics and pure physics in the course you took at the University?

Von Karman:

Oh ja, the mathematics and physics courses were very good. And I took also courses at the university from the famous Eotvos, who worked on gravitation. He was a very good friend of my father so I went to his lectures. In mathematics we had Julius, Konig, and Rados, all very good men. And of course my main interest was the accordance between mathematical theory and experiments. Now my father thought that I should not consider my education finished by the Technical University but should go to Germany for more fundamental studies. He himself studied in Germany and was Privatodozent and lecturer in Leipzig. So I decided to go to Gottingen, especially because I was interested in Felix Klein. Of course it is difficult to go from Hungary to Germany financially so I got from the National Academy in Budapest a fellowship for two years in 1906.

Heilbron:

Were there many of those available? Were there many such fellowships available?

Von Karman:

Ja, for the fellowships you had to have published something. I published a few things in Hungarian, and so the Academy decided to send me to Gottingen. This was for two years. Now because my main interest was applied mechanics, I joined Prandtl. In 1906 there was very little aerodynamics; flight theory was at the beginning. But elasticity and strength of materials was very well-known. My first work in Gottingen was on materials. I published in Budapest a short theoretical paper to explain why the theory of buckling of Euler cannot be applied to columns which are not very slender. I gave a theory which is based on the plastic behavior of this material beyond the elastic limit. But I had not in Budapest the means to prove it, so when I came to Gottingen, I asked Prandtl to do this. And we got from the Krupp Company a machine especially for buckling experiments. This was also my thesis for the Doctor’s degree. So I got in 1908 a Doctor’s degree, and because in 1908 my fellowship went, Prandtl offered me a place as assistant — about like assistant professor in this country — so I could stay. My next work was also a practical engineering problem. Namely, the condition is the difference of the principal stresses. I made the following experiment; I took a material which is quite plastic, really not brittle, marble. I made a marble cylinder and then exerted lateral pressure, and the marble was deformed like a metal. Twice the stress which you get if you just compress the marble, and it was then increasing with the lateral pressure. It was deformed like you can deform lead and had yet the original strength. I made similar experiments on sandstone, and so on. Then I got with a few mathematicians and especially got very near to two men, David Hilbert and Carl Runge, applied mathematicians.

The Privatdozent at the same time was Max Born, and we became very close friends and decided to form a group of bachelors. Max was not married at that time, and I was never married. And the other two who were with us when we founded a joint household was first, a fellow named Bolza, a nephew of the mathematician. He was a rich fellow — I see him sometimes now — who owns a printing machine factory. The printing machine factory is called Konig und Bauer, and as a matter of fact, the American dollars are printed on these machines. I always tell him, you are responsible for the whole inflation because without your machines there would not be inflation. The second was a friend of mine who unfortunately died, Dr. Renner, a medical man. And a sister, a nurse, was his housekeeper. As we started, I told Renner, who was a candidate for the M.D. degree, “look for somebody who’ll be our housekeeper.” He came back and said, “There is only one trouble. This nurse said that her plan was to have a house outside of the city and where she’d take care of four or five mentally disturbed people.” I told him, “Tell her that the house is near the University in the city, but otherwise there is very little difference. Now one good friend who came to meals is Peter Paul Ewald, an expert in solid state physics. Now, this time Hilbert got interested in physics, especially because he was interested in principles of variation calculus. He said that physics is too difficult for the physicists, we mathematicians must do something. And the big question was, at that time of course, whether the quantum theory is an independent principle or a modification of the Boltzmann theory.

Heilbron:

When did people become really concerned with the quantum at Gottingen? Was it discussed when you arrived at first in I906?

Von Karman:

Ja. I did not know about it, but it was already discussed because Nernst was interested. Nernst left Gottingen I think a year after I arrived 1907. And Nernst found empirical formulae for specific heats based on the quantum formula. But I must say, Born — maybe he will not remember or will not like to — Born for example, when we started to discuss these matters, believed that if we made really a theory taking into account the molecular build-up, then the famous deviations from the specific heat will come out automatically. He did not believe it — he wanted to save the Boltzmann theory. And Hilbert was also dubious. Hilbert said, “Well, maybe if we make a real good theory for the Boltzmann equation, then maybe it will modify it.” Hilbert had the idea, somewhat naive, that the linearization is what fails, that if we make an exact theory for the Boltzmann equation for the equilibrium, maybe it will come out.

Heilbron:

What was your opinion at the time?

Von Karman:

My opinion was that it is a quite new thing and quite necessary. So you know now that Einstein believed of course in the quantum theory, and he made the first theory for the specific heat, assuming one frequency. Now it was Born’s idea that we should calculate the spectrum by calculating the lattice exactly. But he wanted to calculate these to show that the quantum theory is not necessary. I told him, “Max, I don’t follow you. There are so big deviations that if I have a continuum or a lattice when I got to the limit, it must be the same. We started to work, he of course said, “You are right.” Later he became very famous for his theory of liquids and so on, which all used the quantum theory. Now Klein did not go into details. You know Klein was a wonderful teacher, you never heard such good lectures as Felix Klein’s. But, he was too broad. He was interested in so many things. He had a wonderful talent to explain something. I always thought if I don’t understand something, then I go to Felix Klein. He does not give me the solution, but after he analyzed it, I know the way to get the solution.

Heilbron:

That was the attitude of the more experimental and old-time physicists at Gottingen? How did people like Riecke, Wiechert, and Abraham, who were there at the same time, feel about the quantum?

Von Karman:

Abraham was very enthusiastic about the quantum…

Heilbron:

I understand that Born met Einstein at the famous meeting in Salzburg in 1909 of the Naturforscher Versammlung, where Einstein argued very strongly for the quantum. Do you remember if Born came back much impressed or enthusiastic or interested after that?

Von Karman:

Ja, but he did not believe that in 1909.

Heilbron:

His interest though in the quantum dated from before he met Einstein, or was it Einstein who interested him in it?

Von Karman:

No, I think he was interested, because Nernst was there, and everybody talked about it… Now I think that Debye’s theory of specific heat really took away the value of our paper. Debye real1y had good luck. Debye made a simple formula, and the simple formula was much easier than our complicated formula, so he really took away our value. Before Debye’s paper came out, our paper was already ready, but it was not yet printed. I think that the approximation for very low temperatures is only correct after our theory. The variation is the difference in the exponent.

Heilbron:

Let me ask you once again to make certain I have this correct, that it was Born’s idea originally to go after calculating the spectrum accurately for the lattice?

Von Karman:

Ja, it was Born’s idea to do it, but I had perhaps a little more experience or knowledge of lattice structure, because you see I worked on lattice structure in connection with deformation, slipping and so on, for the condition of fracture. But after we decided not to make the multi-lattice, I mean the real lattice which consists of single crystals, but a single crystal alone.

Heilbron:

According to Ewald, when von Laue heard about Ewald’s work on a crystal, he was much amazed to find out about this lattice structure. Was it generally the case that physicists were ignorant of this old 19th century work on the lattices?

Von Karman:

Ja, it is very true. They were not interested in the lattice. Take Woldemar Voigt for example — this is a very interesting fact. Once when I gave a lecture in the Physikalische Gesellschaft, he said, “But listen, you really believe in this lattice business?” He said, “This is only a working hypothesis.” This is a true story. Ja, this was the attitude of the older generation. He wrote a book on crystal physics, and he told me, “It is a working hypothesis. You see, I came to the interest for crystal lattice from the strength point of view. My general philosophy was perhaps very different from most of the physicists. Most of the physicists believe there is a truth that the world is made in a certain way. And I, following my father’s philosophy, said, “It is a very funny point of view. Why is the good lord hiding … why does he not tell us?” So my father said that all science is only an organization of our observation. This is also Poincare’s view, and Ernst Mach said also that it has nothing to do with the truth, that we believe in an explanation that is the most economic as far as thinking is concerned. That everything depends on our senses is self-evident. Poincare says the following example: that if a worm would be two dimensional, and you make a curve on the surface, then he believes he is closed in. And if another worm comes from the third dimension, he says it is a miracle. I think our present philosophers and our present physicists don’t give attention to this. This is the last century’s philosophy, but there is very much in it. The whole world of physics has changed so much. I feel like Yukawa. We lectured together at Columbia University, and I congratulated him that he found really the meson. He said, “Ja, but there are four or five different ones.” He was really disturbed. He says, “Now, I predicted one, but now there are…”

Heilbron:

How did Max Born feel about that von Laue discovery? Was there much concern at Gottingen about X-rays at all?

Von Karman:

At that time I don’t think so… Lenard was also a great enemy of x-rays and so on. You know what happened to him? His mechanic told him, “Professor, I found the following: I left the camera out near the cathode, and as we opened it, it was part black, and I saw a key which I left there.” And Lenard, instead of recognizing it, said, “Keep the camera closed and don’t let it lie around.” That is true.

Heilbron:

There were a number of people who missed that discovery. What did you feel about the Bohr atom when it came out?

Von Karman:

Well, I was very enthusiastic. I knew Bohr and his brother. The brother was my very close friend, the mathematician, but I knew Niels also very well. I think the brother and I studied together, but he died very early. I was in Aachen in 1913, but I remember I went to Gottingen and met Bohr. Then we became very good friends after the war, here in Pasadena. Bohr came very often. I remember I went to Gottingen and met Bohr. I remember the following funny thing. Niels Bohr came here in my house and I invited all the physicists and mathematicians here. I had a glass with two walls — it looks as though it might be cognac or brandy — I gave this to Bohr, and Bohr three times took it up and did not notice. And I told him, Niels, how do you like my cognac?”

Heilbron:

Had you known Epstein before you began to exchange visits?

Von Karman:

Ja, I knew him. Epstein is responsible that I came here. I knew Epstein from Gottingen, and then he was in Munchen. I knew him very well from that time. And then, you know, in 1926 the Guggenheims started to be interested in aeronautical research, and gave money to American schools. And then Robert A. Millikan, as he told me, went to Long Island where old Guggenheim lived and told him that he makes the mistake of his life if he does not give a few millions to Cal Tech. You see in ‘26 he had the vision to say that the American aeronautical industry will be concentrated in California. And old Guggenheim told him, “All right, you can have the money for a laboratory, two million or so, if you bring me from Europe somebody who knows the theoretical part of it.” Then he talked with Epstein. He thought Prandtl, but Epstein told him, “You will never get Prandtl — Prandtl is very influential in Germany.” And he proposed me. They say that Millikan said, “I wanted Prandtl and settled on Karman.

Heilbron:

As long as we’ve started to talk about the organization of the Institute here in Pasadena, I wonder if you could tell us something about the general organization of German applied science at the time you were there, the relationships between the various institutes, where the money came from, and so forth.

Von Karman:

You see there were also in Germany very different schools. The idea of applied sciences and who made applied sciences respectable and so on was Felix Klein. Felix Klein told to the people at the Technische Hochschule, “You will educate the engineers and we at the universities will educate technical experts and engineers with scientific background. In that way, said Felix Klein, “as the army has officers on the line and a general staff, we will educate for you the general staff.” This met a great resistance in the Technische Hochschule. They attacked Klein and said, “This is impossible. We have exactly as talented people as at the University. And in this army this also does not work, because the general staff sometimes contributes more to losing battles than to winning.” Especially in Hanover there was great resistance. I remember that in the early ‘20’s Felix Klein asked David Hilbert to go to Hanover and make peace. David Hilbert went there and said, “No, Klein has no right. You are right. Mathematics and science have nothing to do with engineering.” You see, Hanover and Gottingen are neighbors, and Hanover was offended that Klein said they were only second class.

Heilbron:

Klein was also effective in getting money from industry, wasn’t he?

Von Karman:

Ja, he started … Ja, I think he was the first one to do that in Germany. Maybe not the first one, but he was very successful at it … The minister Althoff was also a great friend of Felix Klein, they were working together. He was also for application of science. Some of the physics professors were very much against it. They said good physics is done in a small laboratory, and they will have large laboratories; science will suffer. To some extent they were right. You know now in the nuclear age a physics laboratory looks like a big factory, and maybe in the small laboratory they found out more.

Heilbron:

Were there more means of support for people interested in the more applied physics and. science than there were for people who intended to work in so-called pure science?

Von Karman:

No, I don’t think so because there were people who gave money really for fundamental research. There were many people in industry who were very broad-minded. Well you see the student’s life was not very expensive at that time. You could exist. I find that now we have too many fellowships. I think if you worked in the old Gottingen University, you worked in the physics laboratory in theoretical things, and you worked also so much that you could support yourself. I have an interesting example for the different philosophy. There is a Hungarian conductor named Sebastian who was a prisoner of war in Russia. There he married a Russian girl who was a great communist. They came in this country, and I invited them here to the Athenaeum, Faculty Club. And I told the lady, “Now don’t you think this is an interesting example of democracy. Those fellows who serve us? They are students, and there is no stigma connected with it. They will be big professors and directors someday.” And she told me, “You mean to say that these waiters are students? And this rich country of yours,” she said, “has not enough money to feed them?” And. I must say, to some extent she was right. To some extent it has no sense that they serve the lunch and. dinner instead of learning or enjoying themselves.

Heilbron:

Did the First World War change the pattern of support of science much in Germany?

Von Karman:

Ja, I think so. Ja, it multiplied the numbers. After the First World War in Aachen I had no difficulty to get money for research. One third came from the government, two thirds from industry. But Aachen is an industrial place. I think Gottingen has now more difficulties than Aachen; you know the west has much more means. But it is not only because it is industrial. Before, Gottingen belonged to Prussia, and in Berlin were very good people in the Ministry in the pre-Hitler time. Now Prussia does not exist anymore because of military security, and Gottingen belongs to lower Saxonia. They have no sense for… So Gottingen really lives now on the Max-Planck Gesellschaft, which was the Kaiser-Wilhelm Gesellschaft.

Heilbron:

Where did the Kaiser-Wilhelm Gesellschaft get its money from? Was that entirely government supported?

Von Karman:

No. I think three-quarters industry supported. I don’t know what it was at the end. Perhaps they paid more because the people worked on orders.

Heilbron:

Let me ask you another question. What sort of relations did Prandtl have with the big mathematicians at Gottingen? Was there any slight feeling of inferiority because he was doing these mechanical things?

Von Karman:

Ja, also Hubert had not a great opinion of those things, and Prandtl did not have the talent to explain what he really does. He did not like the mathematician very much. His own mathematical training was not very good. On the other hand, there were mathematicians like Zermelo who were more on the philosophical side. I never will forget that once we had, a Kneipe called the Black Bear, where Zermelo, some other mathematicians and Caratheodory liked to get together. I liked these people because I had some inclination to philosophy. And Zermelo told me once, “Now listen, from all these applied idiots, you are the only one who could be educated.” I was very proud. Also, Hubert and Klein had a very good friendship but were very different. Hilbert was very impractical, a wonderful personality. He had a wife who wanted to educate him in a literary and social sense. I remember the following case. The German writer Zahn was invited by the faculty ladies to give a lecture. And Katie, Mrs. Hilbert, told Hubert, “You must come to the party and be kind and polite to Zahn because he is one of the most excellent present German authors.” So Hubert meets Zahn and says, “I am very glad to meet you, Mr. Zahn. You write wonderful books. Mr. Zahn we are very really honored that you come to us” And Zahn knew that he was one of the greatest living mathematicians and said, “What did you read from me, Herr Geheimrat?” And then you heard a long, long call, through the whole hall, Hilbert saying, “Katie, Katie, what did Zahn write?” Hilbert you never forgot. We noticed one day that Hilbert came with a rip in his pants, and we said we ought to tell him. Courant was his assistant at that time. And after the seminar we always took a walk in the woods. Hilbert jumped over a fence, and Courant thought, “Well, this is the time to tell him,” and said, “Herr Geheimrat, you ruined your pants.” And Hilbert says, “What the hell. I told three days ago to my wife she should repair them.” That is very characteristic of the Gottingen time.

Heilbron:

Did you go to the seminars of both Hilbert and Klein?

Von Karman:

Ja, both of those seminars. Hilbert was a little too difficult for me. Hilbert read the formula automatically, so he did not explain sometimes. If you had the art that while you write the formula, you at the same time check in your head what the terms are then you had no great difficulty. But some people, even mathematicians, don’t have that. Klein explained every term. And I learned this from Klein. I think my lectures were not very good, but this way of explaining was. I have also one very nice story about Boltzmann. In the Boltzmann seminar in Vienna, where a fellow took me, Boltzmann said, “I learned very much to keep apart. I even learned to keep apart Ehrenhaft from Ehrenfest. But I never understood. What is the difference between axial and polar vector?” That is true.

Heilbron:

Let me ask you a question. It’s really a minute point, but it made me very curious. In your bibliography in Poggendorff’s volume, your papers with Born are not listed. It’s particularly interesting because the section which covers those years is marked “eigene Mitteilung.” [gets out paper]

Von Karman:

Eigene Mitteilung. I have no idea. I don’t think I saw that. I don’t think I saw that. I don’t think I had anything against Born. I once told Einstein when we talked about Born, “You know, Dr. Einstein, my friendship with Max is handicapped by the fact that I cannot stand his wife, and his wife cannot stand me.” Einstein answered, “Karman, you are much happier than I am. She loves me.” The real Einstein. The real Einstein.

Heilbron:

If you would let me take two or three minutes more of your time, I would like to ask you once again about the immediate background of your paper with Born. There was a lot of literature on specific heats at the time, and people had tried to calculate the υ that goes into the Einstein formula, connecting it with the elastic properties of bodies and so forth. Madelung, for instance, had a paper. Had that played no role in getting you people interested at all?

Von Karman:

I think that Madelung influenced us. I remember that Madelung told me that the Einstein cannot be correct, the deviations are too great. And Lindemann and Nernst also, I believe, influenced us.

Heilbron:

Did people take that very seriously? Were people very much interested in that Nernst and Lindemann half quanta idea?

Von Karman:

No, I think at that time I visited Nernst in Berlin. He told me that and I thought it cannot be.

Heilbron:

I’m now a little bit confused because earlier you said that the original impulse to the work was that Born thought he could avoid the quantum that way; and now you say that it was perhaps, Lindemann and Nernst’ s previous work that might have got you started in that direction.

Von Karman:

Ja, because my interest after all was to generalize the Einstein. So, I had known of Lindemann. And of course, Born too, but Born had a secret hope that it will perhaps eliminate the quantum. I don’t say that he did this to this purpose, but he was uncertain: shall we believe quantum theory, or perhaps we can eliminate it. As we worked on it, he saw that it is essential. We had great difficulty, and I think this is really Debye’s achievement. You see, for the spectrum we had a kind of parabolic curve; the energy is function of the frequency. Now there is a maximum frequency, and on the other hand, the energy must be finite. And we lost very much time with trying to find out what happens to the wave at the limiting frequency. I don’t think that we solved it; I don’t know if anybody has. Now look what Debye said… He made a curve like that, quit, and said, “This is now the distribution.” But that was I believe the influence of Born against such simplification. I really am inclined to such simplification. Born wanted really here the correct character of the curve. We sometimes were in conflict. I told this in a little article I wrote about Gottingen in the Deutsche Universitats-Zeitung. I talked about the time I worked with Born. I was told, he did not tell me, that Born said, “I like to work with Karman. He had very good ideas. Fortunately I did not learn his Schlamperei.” But as you included here the Born-Karman articles, I will tell you, the article in which there was the most Schlamperei – 2π instead of π/2, in an exponent a factor of 2 left out — was Born’s. So it was some satisfaction (to me).

Heilbron:

How close were you to the mathematicians when you were working this out to people like Toeplitz?

Von Karman:

I was very close to Runge, and I was very close, if you can be close, to Felix Klein. Runge’s was a real friendship, Karl Runge; maybe the only real close friendship. You know with Felix Klein, this was very difficult because Felix Klein gave appointments. You have to come exactly, and he says you have twenty minutes. But I did not mind because once I was working with him or had these twenty minutes, and I looked over his shoulder to see is program, and next was his daughter, fifteen minutes, to talk over plans for a trip to the United States. He was really not an earthly man… Now Hilbert and I had one common sickness, he liked pretty girls and me too. So we sometimes… he was much older, but… Then I was very close to Caratheodory, Zermelo, this was the Schwarze-Bar club. You know, the house where I lived with Born was called El Borkarrebo –- El, that was Mrs. Ewald, Bor -– Born, Kar –- Karman, Re -– Renner, Bo -– Bolza. We organized Hilbert’s 60th birthday. We gave many parties, and I found recently the manuscripts for a long poem we gave then. It was a dramatic story. Albert Renner played the’ good lord, and Ewald the archangel Gabriel, and I was Lucifer. All the persons who were invited were treated — what shall happen with them in the last judgment. And Ewald was a blonde young man, as the archangel Gabriel he says, “Oh, she is wonderful” and so on. And then came Lucifer, “Yes this is true, but…” And, then we were, two together, all condemned to go to hell. And this was the table order. I will send it to you.

Heilbron:

Do you happen to have other manuscripts or letters from that time?

Von Karman:

I will give you an address where you can find letters. You Know Lee Edson? He is my co-author for my autobiography. And this address is a Hungarian lady who types and if it is necessary translates my letters. The letters will not be published. They are only for my use. But sometimes you can write them and ask whether they have data from these periods.

Heilbron:

I can just write them directly?

Von Karman:

Ja.