John von Neumann's 1935 letter to Oswald Veblen
John von Neumann's 1935 letter to Oswald Veblen
The book John von Neumann: Selected Letters* by Miklós Rédei (2005) is a fascinating collection of 150 of John von Neumann (1903-57)’s correspondences from the period 1920 until his death in 1957. Among his extensive communications included in the book are:
Four letters to Kurt Gödel (1906–1978), from 1930-33
Two letters to Norbert Wiener (1964–1909), from 1945–46
One letter to J. Robert Oppenheimer (1903–1957), from 1948
Four letters to Stanislaw Ulam (1909–1984), from 1936–43
One letter to Paul Dirac (1902–1984), from 1934
One letter to Edwin Schrödinger (1887–1961), from 1936
One letter to Edward Teller (1908–2003), from 1947
One letter to Hans Bethe (1906–2005), from 1941
Two letter to Pascual Jordan (1902–1980), from 1949–50
Also included are seven letters to von Neumann’s friend and colleague at the Institute for Advanced Study, mathematician Oswald Veblen (1880–1960) from the period 1930 (when the IAS was founded, see essay below), to the end of the war.
One letter, written in the summer of 1935, stands out as a remarkable testament to von Neumann’s eclectic mind. The letter has it all: a discussion of the theory of spectra of Hermitean operators, a presentation of an idea connecting logic, quantum theory and projective geometry (including proof sketches), inquiries about spin-geometries and not least of all, gossip. Lots of gossip.
Context
By the summer of 1935, von Neumann had been employed at the Institute for Advanced Study (IAS) for two years. Founded by Abraham Flexner (1866–1959) with the help of Veblen, the IAS had been funded with money from Louis Bamberger (1855-1944) and his sister Caroline Bamberger-Fuld (1964-1944). “The Institute” was at that point still housed in Fine Hall at Princeton University (now Jones Hall). Indeed, the IAS would remain in Fine Hall until the fall of 1939, when its own campus and main building Fuld Hall was opened for professors and visiting researchers. von Neumann had been one of six professors offered lifetime appointments at the IAS in 1933. The other five were J. W. Alexander (1888–1971), Albert Einstein (1879–1955), Marston Morse (1892–1977), Hermann Weyl (1885–1955) and, Veblen himself.
A socialite who was both extroverted and worldly, von Neumann frequently spent time away from the IAS. A frequent traveller, he would in the period 1935-45 spend considerable amounts of time both in pre-war Europe (including to try to convince Gödel to come to the IAS) and Washington, where he held various consultancies. Indeed, his offer of employment at the IAS was offered following a three-year stay as a visiting professor at Princeton University in the period 1930-33. In 1935, von Nuemann was a visiting professor at Cambridge University. During the summer, he spent time in his native Budapest before returning to Princeton for the fall term. In between all his travels, he finds time to write Veblen:
Dear Oswald,
Please excuse the size of my letter, which will probably be quite considerable before I am through. But there is quite a number of things I should write about.
The first six pages of von Neumann’s letter regard mutual acquaintances, politics and current events. The first pages are primarily filled with gossip:
Proceeding from the subjective to the objective, I have to report first, that we are all well, although Mariette is again engaged in her usual battle wit her elders, wether to put on weight or not. Mariana is well, and even gained 1 lb. between New York and Budapest, so that there is every reason to assume that she crossed the ocean without noticing it.
Marietta Kövesi was von Neumann’s first wife. She had been a brilliant student of economics in Budapest, where the two met in their early childhood. They married in 1929 just before von Neumann first left for Princeton, and had one child, Marina von Neumann Whitman (1935-), a distinguished Professor at the University of Michigan whom I was fortunate enough to interview back in 2021 (see essay below).
von Neumann and Marietta split up in 1937. A year after that, in 1938, von Neumann went on to marry early computer scientist Klára Dán (1911–1963), whom he had met during one of his trips to Budapest. According to Macrae (1992), von Neumann and Dán married two weeks after Dán’s divorce from another man, Andor Rapoch, was final. Prior to Rapoch, she had also been married to a man named Ferenc Engel. Her marriage to von Neumann would be her third, but not final, as she also married physicist Carl Eckhart in 1958, a year after von Neumann passed. She herself died tragically in 1963, at the age of 52, from suicide as she “walked in to the surf and drowned” on a beach in La Jolla, California.
von Neumann goes on to report that “Cambridge was very beautiful and interesting”, and that
The main architectonic sensation is of course still Hardy. He was somewhat disturbed by Milne's theological amplifications of his (not so hot) cosmology, and in particular about the fun Milne seems to find in connecting Creation with a singularity at t = 0. Hardy wishes to avoid this by introducing a parameter tau = ln t, which begins with tau = -infty, and thus satisfies his philosophical needs.
By 1935, G.H. Hardy (1877–1947) was still considered one of the foremost mathematicians in England, if not the world. Edward Arthur Milne (1896–1950) was a British astrophysicist and mathematician who had entered Hardy’s orbit around 1914 and would later propose various mathematical arguments postulating the existence of God, some of which were based on Hardy’s mathematics. As von Neumann expresses, Hardy, a lifelong atheist, was not too pleased.
I met Newman several times, and I am very glad for having made his acquaintance, he is very attractive both from the topological and from the human side. He has postponed his sabbatical leave for 1936/37, and seems to be quite anxious to come to Princeton then.
Max Newman (1897–1984) was another mathematician at Cambridge who had been lecturing there since 1927. His lecture series on “The Foundations of Mathematics and Gödel’s Theorem” (1935) would inspire a young Alan Turing to embark on his pioneering work on the so-called Entscheidungsproblem. Newman helped Turing get his draft of “On Computable Numbers with an Application to the Entscheidungsproblem” into publication, as well as arrange for him to visit Alonzo Church (1903–1995) in Princeton, where he earned his Ph.D in 1938. As legend has it, von Neumann inquired about whether Turing would be interested in a position as a postdoctoral research assistant, but Turing declined and travelled back to England.
By the way, there seems to be quite a traffic-jam on the road to Princeton. There are 4 or more advanced students or PhD.'s who will come next year to Cambridge: A Commonwealth fellow M. Price, who is very able, he worked in quantum theory until now, but he wants to change to group theory; an NRC [National Research Council] fellow, whose name is, I think Lewinsohn, who is a pupil of Weiner (!) and spent this first year in Cambridge (Hardy thinks that he is very good), Touring who you mentioned, and who seems to be strongly supported by the Cambridge mathematicians, for the Proctor fellowship (I think that he is quite promising); and one or two more, whose names I forgot.
Besides Turing (notice von Neumann’s misspelling of his name), the two other graduate students he mentions are Maurice Pryce (1913-2003) and Norman Levinson (1912–1975). Pryce was a British physicist who went to Princeton in 1935 and earned his Ph.D. on the topic of “The Wave Mechanics of the Photon” under the supervision of an all-star cast featuring Max Born (1882–1970), Ralph Fowler (1889–1944), Wolfgang Pauli (1900–1958) and von Neumann himself. Levinson was an American mathematician in Cambridge on a Redfield Proctor Traveling Fellowship who in 1937 earned his Ph.D. at MIT (then mostly an engineering school). He was hired in the same year he graduated and remained at MIT for the rest of his career. The exclamation point von Neumann includes in parentheses is likely a comment on Levinson’s Ph.D. supervisor Norbert Wiener (1894–1964), who was known as famously eccentric and absent-minded, and so did not supervise many students (see essay below).
von Neumann goes on to comment further about the graduate group at Cambridge, mentioning several names which would later be well known:
There is quite a considerable number of good men in the young group in C. [Cambridge] I was particularly interested in 3 of them: Two fellows of Trinity: L.C. Young, who works in real functions, Stieltjes integrals, etc,; and S. Chandrasekhar (a Hindu) who is primarily an astrophysicist, but who also has a considerable knowledge of quantum theory and connected mathematics, too; and a fellow of Caius: a theoretical physicist with the name F.C. Powell.
Laurence C. Young (1905–2000) was a British mathematician known for his invention of the Young measure. Indian-American astrophysicist Subrahmanyan Chandrasekhar (1910–1995) later became the 1983 Nobel Laureate in Physics for his “theoretical studies of the physical processes of importance to the structure and evolution of the stars”. Another Nobel Laureate, English physicist Cecil Frank Powell (1903–1969) would win the prize in 1950 for his discovery of the pion.
I had the audience of ≥ 15, ≥ 20 people, which showed no "radioactive decay", until the examination period (around January 3.) came along. Then the number reduced by several orders of magnitude, until I closed on June 14.
One might perhaps excuse von Neumann’s graduate students for being unable to keep up with his lectures. His brother Nicholas later described the difficulties audiences sometimes had in following his lectures as follows:
“His fluid line of thought was difficult for those less gifted to follow. He was notorious for dashing out equations on a small portion of the available blackboard and erasing expressions before students could copy them.” — Vonneuman (1987)
Fowler is looking forward with much expectation to his expedition to Princeton. We made the acquaintance of the Cooks, who live with him, and who are very charming. They will come to America in April, to join him for a "transcontinental tour".
The views about Eddington are essentially homogeneous in C. [Cambridge].: The astrophysicist are scared, the physicists (like Fowler) very afflicted; and advanced students highly amused. Nb.. he is really going from bad to worse, he wrote lately a paper on "relativistic degeneracy of gases", which is almost worse than his quantumtheoretical papers - a scarcely credible feat! He seems to have lost his contact with theoretical physics, and the methods which are in use for the last 50 years, completely.
I met E. [Eddington] once or twice, but succeeded avoiding discussions on anything more serious than graphology.
Ralph H. Fowler (1889–1944) supervised the doctoral theses of Chandrasekhar, Pryce and Dirac. “The Cooks” von Neumann refers to are likely Derek and Phyllida Cook who cared for the Fowlers’ children. By 1935, Sir Arthur Eddington (1882–1944) had gone from being the hero astronomer who in 1919 had travelled to West Africa to confirm Einstein’s General Theory of Relativity (see essay below), to a somewhat controversial character.
This largely for his work, beginning in the 1920s on his own “fundamental theory”, which reduced to “almost numerological analyses of dimensionless ratios of fundamental constants”. Among other controversies, Eddington also famously disagreed with student Chandrasekhar’s early prediction of the existence of black holes.
Summing up, the entire experience was a very agreeable one, and the new people we met are interesting and nice throughout. We went to Oxford, too (for 3 days), where we saw Schrödinger, Whitehead and family. Mrs. Whitehead is very charming, but Whitehead's classical definition of her ("I married a pianist") although literally true, bears false implications: She has a definitely "bourgeois" background. We stayed at Whitehead's house, and had a wonderful time. Whitehead's chief occupation is presently to knot tori, he constructed some very funny examples. Weyl stayed for 3 days with us in Cambridge.
von Neumann had likely met Erwin Schrödinger (1887–1961) while he was a student in Göttingen, studying under David Hilbert (1862–1943). Schrödinger had won the Nobel Prize in physics two years before (with Dirac) and would be awarded the Max Planck Medal two years later. A strong opponent of nazism, he left Germany in 1933 for the University of Oxford (see essay below). In 1935, famous collaborator (and former advisor!) of Bertrand Russell (1872–1970), Alfred North Whitehead (1861–1947) was 74 years old, a professor at Harvard since 1924. He retired two years later.
“I preached a sermon in Paris. There seems to be there a considerable interest in operator theory, boosted by G. Julia, and the younger group. Nb. the latter includes several absolutely first class people (A. Weil, Leray), and some who are at least interesting (C. Chevalley, perhaps D. Possel). A. Weil's wish to have a chance to come to Princeton in 1936/37 is unchanged".
Gaston Julia (1893–1978) was a French mathematician whose works were later popularized by Benoit Mandelbrot (1924–2010). The other French mathematicians mentioned are the de-facto early leader of the Bourbaki group André Weil (1906-1998), who earned his Ph.D. in 1928 for his discovery of the connection between algebraic geometry and number theory. Jean Leray (1906–1998) worked on partial differential equations and algebraic topology, earning a Wolf Prize in 1979. Both Claude Chevalley (1909–1984) and René de Possel (1905–1974) were founding members of Bourbaki, the former whom would later go to Princeton and the latter a pioneering computer scientist.
Following thirteen pages of equations (on the theory of spectra of Hermitian operations), von Neumann ends his letter:
I hope that your extension of the home is completed and that you enjoy it. With many greetings, from Mariette and my mother, too.
Yours Truly,
John.
I hope you enjoyed this essay. Please consider supporting my writing:
Thank you for reading Privatdozent, Have a great weekend!
Sincerely,
Jørgen
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References
Rédei, M. 2005. John von Neumann: Selected Letters*. American Mathematical Society
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