Max Dehn, Kurt Godel, and the Trans-Siberian Escape Route, Volume 49, Number 9

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Max Dehn, Kurt Gödel,

and the Trans-Siberian

Escape Route

John W. Dawson Jr.

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he careers of Max Dehn and Kurt Gödel

followed very different trajectories. Yet

Dehn and Gödel were linked by one his-

torical circumstance: They were the only

mathematicians of stature to flee the

scourge of Nazism via the trans-Siberian railway.

The stories of their escapes and the contrasts in

their situations before and after their emigration

exemplify both the perils and the limited range of

opportunities that confronted intellectual refugees

of the Holocaust.

In 1940 Max Dehn and Kurt Gödel each left Eu-

rope, never to return. Dehn was then a distin-

guished topologist nearing the end of his academic

career, while Gödel was a young Privatdozent who

had only recently burst into prominence for his star-

tling discoveries in mathematical logic. Dehn was

a Jew. Gödel was not. And their personalities were

starkly opposed: Whereas Dehn was an outgoing,

generous man, esteemed by students and col-

leagues alike for his humanity, his breadth of in-

tellectual and cultural interests, and his love and

knowledge of the outdoors, Gödel was a reclusive

hypochondriac who had few close friends, worked

in isolation, and suffered recurrent bouts of men-

tal illness. Nevertheless, in a few respects their ca-

reers were similar: Both solved problems on

Hilbert’s famous list [16]; both published important

papers on decision problems; and both, by force

of circumstance, emigrated to America via the

trans-Siberian railway.

The disparity between the situations of Dehn and

Gödel prior to their emigration exemplifies the di-

versity of backgrounds among the mathematicians

who fled Hitler. The circumstances of their escapes

highlight the dislocations, difficulties, and dan-

gers such emigrés faced. And the contrast in their

subsequent careers in America is illustrative of

the range of institutions in the United States that

provided havens for intellectual refugees.

Dehn’s European Career

As yet there is no full-length biography of Max

Dehn, nor a collective edition of all of his pub-

lished works. But several shorter articles provide

details of his life and mathematical accomplish-

ments. For the present brief survey I have drawn

primarily on [13], [15], and, especially, the chapter

on Hilbert’s third problem in [16].

Dehn was born November 13, 1878, in Hamburg,

one of eight children of a physician, Maximilian

Moses Dehn. According to Max’s son Helmut, the

family were secularized Jews who “lived by princi-

ples that some…would call ‘good Christian’”, and

who did not think of themselves as Jewish until the

Nazis came to power [16, p. 118]. After graduating

from the Gymnasium in Hamburg, Max went first

to Freiburg and later to Göttingen, where he

John W. Dawson Jr. is professor of mathematics at Penn-

sylvania State University. His e-mail address is

jwd7@psu.edu.

This article contains the text of an invited address prepared for a special session on the exodus of math-

ematicians from Nazi-occupied territories, held in Vienna in mid-September 2001 as part of a joint meet-

ing of the Deutsche Mathematiker-Vereinigung and the Österreichische Mathematische Gesellschaft. Aware-

ness of how difficult it was for those caught up in the rise of Nazism to escape from the terrors they

experienced was reinforced by the terrorist attacks of September 11, which prevented the author’s at-

tendance at the conference. He is grateful to Professor Karl Sigmund of the University of Vienna for

having read the paper in his absence and to Professor Michael Drmota for granting permission for its

reprinting here. It originally appeared in the April 2002 issue of the Internationale Mathematische

Nachrichten.

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received his doctorate in 1900 under Hilbert’s su-

pervision. In his dissertation he established that the

Archimedean postulate is essential in order to

prove in neutral geometry that the sum of the an-

gles of a triangle does not exceed 180

◦

(Legendre’s

theorem).

Later that same year, soon after Hilbert’s address

on “Problems of Mathematics” at the International

Congress of Mathematicians in Paris (and before the

appearance of its printed version, in which the list

of problems was expanded from ten to twenty-

three), Dehn established a related result that solved

the third of the published problems (one of those

left unstated during the lecture [8]): By exhibiting

two tetrahedra with the same base and height that

are neither equidecomposable into finite, congru-

ent parts nor equicomplementable by such parts

to produce two polyhedra that are equidecom-

posable, he demonstrated that the Archimedean

postulate is also needed in order to prove that two

tetrahedra of equal base and height have equal

volumes.

For his solution of Hilbert’s third problem Dehn

was awarded his Habilitation at Münster, where he

served as a Privatdozent from 1901 until 1911. In

1907 he was coauthor with Poul Heegaard of the

influential survey article “Analysis situs” in the

Enzyklopädie der mathematischen Wissenschaften.

In 1910 he introduced the so-called “Dehn dia-

grams” for groups and published a fundamental

paper on the topology of 3-dimensional space,

which included the result that has since come to

be known as “Dehn’s lemma” (though with a proof

later seen to be faulty) and the technique now

called “Dehn surgery”. That paper also introduced

the word and conjugacy (decision) problems for

groups, which Dehn explored further in two sub-

sequent papers, the second of which employed an

algorithm now named after him.

From 1911–1913 Dehn was Extraordinarius at

Kiel, and from 1913–1921 Ordinarius at Breslau. On

August 23, 1912, he married Toni Landau, who

bore him three children during their years in Bres-

lau. In 1914 Dehn published a proof that a trefoil

knot is not continuously deformable into its mir-

ror image—an important early result in knot the-

ory. Then, from 1915–1918, his work was inter-

rupted by army service.

In 1921 Dehn succeeded Ludwig Bieberbach as

Ordinarius at Frankfurt, and the following year he

founded a seminar there on the history of mathe-

matics, whose history and significance, as well as

Dehn’s leadership role in it, is poignantly recounted

in the memoir by Siegel cited above [13]. Dehn con-

tinued to direct the seminar until 1935, when, at

age 56, the Nazis forced him to retire (later than

most, due to his earlier war service).

After his removal from the university Dehn con-

tinued to live in Frankfurt for another three years.

For a time he received a pension and traveled to

various European countries to lecture. He also con-

tinued to publish, including an important paper that

appeared in 1938, in which he introduced the no-

tion now referred to as “Dehn twists”. By 1936,

however, he had prudently sent his children out of

reach of the Nazis, his son Helmut to the United

States and his daughters Maria and Eva to a board-

ing school in Kent, England, where Dehn himself

taught from January to April of 1938.

Later that spring Dehn returned to Frankfurt —

a fateful act, as it turned out, for on November 11,

1938 (the morning after Kristallnacht) he was ar-

rested by Nazi agents and taken to a local deten-

tion center. Providentially, however, he was re-

leased later that day, so many having been rounded

up that there was no place to hold them all.

Subject to imminent re-arrest and deportation,

Dehn and his wife immediately fled to Bad Hom-

burg, where they were given shelter by his friend

and colleague Willi Hartner; and there, in the com-

pany of Hartner and Siegel, Dehn celebrated his six-

tieth birthday. Hartner recalled the occasion years

later in a newspaper tribute to Dehn [9]: “Unfor-

gettable for those who saw him at the time was his

calmness, his philosophical composure. For the

conversations centered not on the events of the day,

but on the relationship of mathematics to art, on

problems of archaeology, and finally on the con-

cept of humanity of Confucius.”

Once the brutal initial phase of the pogrom in

Frankfurt ended, Dehn and his wife, with the as-

sistance of Albert Magnus (son of Dehn’s student

and colleague, Wilhelm Magnus), managed to escape

by train through Frankfurt to Hamburg, where they

hid for a few weeks at the home of one of Dehn’s

older sisters who had been left unmolested be-

cause of her age. From there, with further help

from Siegel and “a Danish colleague and former stu-

dent of Dehn’s” [15] — perhaps Jakob Nielsen — a

way was found for the Dehns to escape to Denmark

and from there to Norway. In January 1939 they

reached Copenhagen, and not long afterward Dehn

secured a temporary position at the Technische

Hochschule in Trondheim as a replacement for

Viggo Brun, who was then on leave.

Until March 1, 1940, when the Nazis invaded Nor-

way, the Dehns were relatively safe. Financially,

however, their situation was precarious. Before

leaving Germany Dehn had been forced to sell his

library and much of his furniture at great loss. He

was, of course, paid by the Hochschule in Trond-

heim, and from the university in Frankfurt he some-

how managed to obtain an official leave of ab-

sence, valid from April 1, 1939, until June 30, 1940,

that enabled his pension payments to continue.

They were credited, however, to an account in Ham-

burg from which disbursements could only be

made to parties within the Reich, so that he was

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unable to pay storage charges on what little furni-

ture and other personal effects he had been able

to ship to London. Consequently, they too were lost.

When the Nazis invaded Trondheim, the Dehns

fled to the nearby countryside. But actions against

the Jews there quickly subsided, so after a short

time the Dehns moved back to the city, apparently

with little effort at concealment. Indeed, corre-

spondence preserved among Dehn’s papers at the

University of Texas includes a letter he wrote from

Trondheim on June 5, 1940, requesting an exten-

sion of his leave of absence, and another dated Au-

gust 29, 1940, informing the German authorities

of his move to Hvalstad, near Oslo.

Under the circumstances it seems extraordinary

that Dehn continued to behave as “a good Ger-

man”, dutifully making his whereabouts known

and seeking official permission to remain longer

in Norway. Perhaps he knew how long it would

take for the Nazi bureaucracy to respond. In the

meantime, with the help of Ernst Hellinger and

other former colleagues who had escaped to the

United States, he was making preparations for his

own long journey to America.

Gödel’s Life Prior to Emigration

Several sources provide details of Gödel’s life and

work. [1] is a full-length biography, while the in-

troductory essay [6] in the first volume of Gödel’s

Collected Works is an excellent shorter survey.

Briefly, Gödel was born April 28, 1906, in Brno,

Moravia, where he spent his youth. After graduat-

ing from the Realgymnasium there, he entered the

University of Vienna in the autumn of 1924. Influ-

enced especially by the lectures of Phillip Furtwän-

gler and Hans Hahn, he soon switched from physics

to mathematics and became active in the mathe-

matical colloquium directed by Karl Menger. For a

time he also attended meetings of Moritz Schlick’s

seminar, later to become famous as the Vienna

Circle.

Unusually for the time, Gödel never enrolled in

courses at any other university. In 1929 he was

granted Austrian citizenship, and that same year

he submitted his doctoral dissertation to Hahn. In

it he established the semantic completeness of

countable first-order theories. He was awarded the

degree of Dr.Phil. on February 6, 1930.

The following September, at a conference in

Königsberg, Gödel gave the first, somewhat veiled,

announcement of his first incompleteness theorem.

The second followed soon thereafter, and both

were published in his epochal paper [7], which be-

came his Habilitationsschrift. In 1933 he was

granted his Dozentur, and that fall he accepted an

invitation to spend the academic year 1933–1934

in Princeton, at the newly founded Institute for

Advanced Study.

Shortly after his return to Austria in the spring

of 1934 Gödel suffered a serious bout of depres-

sion and was admitted to a sanatorium in Purk-

ersdorf bei Wien. By 1935 he had recovered enough

to prove the relative consistency of the axiom of

choice with the axioms of Zermelo-Fraenkel set

theory, but a subsequent relapse left him inca-

pacitated until the spring of 1937, when he finally

succeeded in proving the relative consistency of the

generalized continuum hypothesis as well.

Gödel taught for the last time in Vienna during

the summer of 1937. The following spring, not

long after the Anschluß, his authorization to teach

was withdrawn and the unpaid rank of Dozent was

abolished and replaced by that of Dozent neuer Ord-

nung—a salaried rank, but one that required vet-

ting by the Nazi authorities. Gödel applied for the

new title, but by the time it was granted he had al-

ready emigrated. ([14, p. 29], reproduces one of the

letters evaluating Gödel’s application.) In the mean-

time, while the financial situation in Austria dete-

riorated, Gödel was left unemployed.

Despite the uncertainty, in September of 1938

Gödel married, and soon thereafter he returned

once more to America. He lectured that fall at the

Institute for Advanced Study and went on in the

spring of 1939 to the University of Notre Dame. He

planned to return to the IAS again the following au-

tumn, but on his return to Vienna he was called up

for a military physical and declared fit for Nazi mil-

itary service.

Even then, Gödel seemed strikingly oblivious to

what was happening around him: In a letter to

John von Neumann of September 17, 1939, he

wrote, “Bei mir gibt es nicht viel Neues; ich hatte

in letzter Zeit eine Menge mit Behörden zu tun. Ende

September hoffe ich wieder in Princeton zu sein.”

(“There’s not much news around here; recently I had

a lot of dealings with the authorities. I hope to be

in Princeton again around the end of September.”)

On September 30, in a letter to Karl Menger that

Menger thought “set a record for non-involvement

on the threshold of historic events”, Gödel wrote,

“Ich bin seit Ende Juni wieder hier in Wien u. hatte

in den letzten Wochen eine Menge Laufereien, so

dass es mir bisher leider nicht möglich war, etwas

für das Kolloquium zusammenzuschreiben.” (“Since

the end of June I’ve again been here in Vienna, and

in recent weeks I’ve had a lot of running around to

do, so that up to now it was unfortunately impos-

sible for me to compile anything for the collo-

quium.”) And after his emigration, when asked by

Oskar Morgenstern how things were in Vienna, he

offhandedly replied, “Der Kaffee ist erbärmlich.”

(“The coffee is wretched.”)

At the same time, however, Gödel had begun try-

ing to find a way out: He applied both for a leave

of absence from the university and an exit visa

from the Reich, on the grounds that he had no

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means of support in Austria but had been offered

temporary employment by the IAS. Given his mil-

itary status, the likelihood of his obtaining per-

mission to return to the United States must have

seemed remote; and there were difficulties on the

American side as well. For although he had earlier

possessed a U.S. immigration visa, he had forfeited

it on his return to Austria in 1938, and thereafter

U.S. policy stipulated that visas for those in teach-

ing or research positions would be “granted only

to applicants…who ha[d] had such positions…in the

country they c[a]me from” in the “two years…im-

mediately preceding their application.”

In the end Gödel succeeded in obtaining the

necessary documents, in large part due to the ef-

forts of IAS director Frank Aydelotte, who inter-

ceded on Gödel’s behalf with consular and immi-

gration authorities in both Austria and the United

States. (For details of the negotiations involved see

[1, chapter VII].) Exit permits for Gödel and his

wife were finally issued in December 1939, and the

two left Europe in mid-January. By then, however,

crossing the Atlantic had become quite risky. The

alternative—explicitly stipulated by their exit per-

mits—was to take the trans-Siberian railway, from

whose terminus at Vladivostok they could cross the

Sea of Japan and then voyage from there across the

Pacific.

The Trans-Siberian Escape Route

Begun in 1891, the trans-Siberian railway was con-

structed in stages. From Moscow the tracks extended

some 9,200 km to Vladivostok, via one of two routes.

The first, completed in 1901, crossed Manchuria. The

second, following the course of the Amur river and

lying entirely within Siberia, was built out of concern

that the Japanese might take control of Manchuria

(as they later did) and was completed in 1916.

Always a route of last resort, during the early

years of the Third Reich the trans-Siberian railway

was nonetheless taken by thousands of Holocaust

refugees, most of whom emigrated in large groups

either to Kobe, Japan, or Shanghai, China. (Among

the former, the several thousand Polish Jews issued

visas by the Japanese diplomat Chiune Sugihara are

perhaps best known.) Later, after the last sea routes

out of Europe were closed off in June 1940, and

until June 1941, when Hitler violated the German-

Soviet nonaggression pact by invading Russia, it was

the only avenue of escape available to Europe’s

Jews.

The trip across the vast Russian taiga was long

and grueling, especially during the winter, when

there were long hours of darkness and tempera-

tures sometimes fell to

−50

◦

C. Few emigrés left any

account of their trans-Siberian experiences, and

the Gödels were no exception. But from entries in

Gödel’s passport (see [14, p. 32]) and other docu-

ments in his Nachlaß we know that on January 18

he and his wife crossed from Latvia into Russia at

Bigosovo and boarded a train for Moscow. Follow-

ing the Manchurian route, they arrived in Yokohama

on February 2, too late for the ship they intended

to take, and remained there until February 20,

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when they were at last able to board the President

Cleveland. After an intermediate stop in Hawaii

they debarked in San Francisco on March 4 and went

on to Princeton by train. Altogether, their emigra-

tion took nearly two months. Yet, remarkably, de-

spite his hypochondria and earlier mental health

crises, Gödel apparently came through the long

journey in good physical and mental condition.

The Gödels’ departure was precipitate. Dehn

and his wife, however, planned their escape with

deliberation. How they procured the necessary doc-

uments to emigrate to the U.S. is unclear, but it is

known that Dehn secured an academic post in

America—a prerequisite to his admission as an

immigrant—through the efforts of Clare Haas, a

physician the Dehns had known in Frankfurt. Haas

had found a position as a psychiatrist in Pocatello,

Idaho, and she was able to arrange a temporary ap-

pointment for Dehn at Idaho Southern University

(now Idaho State), where he served as associate pro-

fessor of mathematics and philosophy from Feb-

ruary 1941 through the spring of 1942 [16, p.129]

The Dehns finally left Norway in late October,

and Dehn chronicled their journey in a talk he gave

at Idaho Southern not long after his arrival there,

the text of which is preserved as an eight-page

typescript among his papers at the University of

Texas [2]. According to that narrative, a small group

of friends saw them off at the station in Oslo. At

the frontier between Norway and Sweden their lug-

gage was “ransacked” and they were treated “ex-

tremely unkind[ly] and rough[ly]” by the border

guards—actions that led Dehn to wonder how

“young people could exult in [such] unkindness

without any real profit for themselves or their com-

munity.” They were delayed three weeks in Stock-

holm, allegedly because of an outbreak of plague

in Manchukuo and Vladivostok, but actually, Dehn

thought, for “obscure political” reasons. In the end

they took the Amur River route and so did not

pass through Manchukuo. Meanwhile they found

Stockholm a pleasant place to stay, not least

because it was “splendidly illuminated”, in con-

trast to the blackout throughout the rest of west-

ern Europe.

At last the necessary tickets and travel docu-

ments were issued, the Dehns were vaccinated

against smallpox, typhoid, paratyphoid, and plague,

and they flew on to Moscow, where Dehn found it

necessary to consult a doctor. Three more days

elapsed there before the departure of the next

trans-Siberian train—an interlude that gave them

time to explore the city and even attend the opera

and ballet. Dehn noted that there were long lines

in the stores, but that food was not rationed.

During the several days they spent crossing the

“endless Russian plain”, the temperature at times

fell so low that the only liquid that could be used

for bathing was cologne (though hot water was

available in samovars for tea), and Dehn devel-

oped a life-threatening combination of influenza

and pneumonia, for which he was treated in Irkutsk.

Yet in his account he dwelt hardly at all on the hard-

ships they experienced, describing instead the

grand railway station in Novosibirsk, the great

Siberian rivers, frozen Lake Baikal, and “the hand-

some settlements…in the capital of the…[nomi-

nally] Jewish state of Birobidjan”, founded in 1934

as one of several “autonomous” states that were

intended as ethnic havens for Russian minority

groups but that never succeeded in attracting many

settlers.

When the Dehns finally reached Vladivostok,

they were forced to remain six more days while

waiting for a ship to Kobe. Dehn took the oppor-

tunity to visit the Pedagogical Institute there and

was surprised to find a good mathematical library,

whose holdings included a text by Courant.

The crossing to Japan proved to be very rough

and cramped, but the gentle climate in Kobe offered

welcome relief and a chance for Dehn to recover

his health. He said nothing about the subsequent

voyage to San Francisco, where he and his wife ar-

rived on New Year’s Day, 1941.

Contrasting Refuges: The Institute for

Advanced Study and Black Mountain

College

The subsequent careers of Dehn and Gödel were

markedly different, yet also parallel in certain re-

spects. Both had difficulty securing permanent ap-

pointments, and both were supported at first

through funds for refugee scholars. Gödel remained

at the IAS the rest of his life, but he was not made

a permanent member there until 1946. He was

named a professor only in 1953 (the same year he

was elected to membership in the National Acad-

emy of Sciences), after the departure of Carl Lud-

wig Siegel, a close friend of Dehn’s who had him-

self found sanctuary at the IAS but who resolutely

opposed Gödel’s advancement there. For the first

Kurt Gödel and wife Adele, in Vienna prior to emigration.

Photograph courtesy of the Institute for Advanced Study.

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six years Gödel’s contract was renewed on an an-

nual basis, and at one point his name was sent to

the University of Wyoming as one still seeking a per-

manent position. But Gödel seems never to have

complained about his status. The Institute gave

him freedom to pursue his intellectual interests as

he saw fit, without any obligation to lecture. He was

not under pressure to publish, and he did so only

occasionally. He also preferred not being obliged,

as faculty were, to take part in matters of IAS gov-

ernance; and even as a temporary member he was

relatively well paid. (His annual stipend in

1940–1941 was $4,000.)

Dehn, on the other hand, arrived penniless in

Pocatello, where he was paid a salary of only $100

per month. His teaching duties at Idaho Southern

were not excessive, and he enjoyed hiking in the

nearby mountains, but Pocatello was an intellectual

backwater, and his short-term appointment forced

him to begin searching for a position elsewhere al-

most immediately. He went next to the Illinois In-

stitute of Technology, where he served as a visit-

ing professor of mathematics. The pay was better

there, but the lecture duties were more onerous,

and Dehn disliked the busy Chicago urban/indus-

trial environment. So, after only a year at IIT, he ac-

cepted a position as tutor at St. John’s College in

Annapolis, Maryland.

One of the oldest colleges in the United States,

St. John’s was distinguished by its curriculum,

which focused (as it still does today) on the Great

Books of western culture (based on a list of one hun-

dred such drawn up at the University of Chicago).

It was Dehn’s task to teach mathematics directly

from the texts of Euclid, Apollonius, Newton, etc.,

ending with Principia Mathematica (!), but he quickly

realized that his students were young (most of

those over eighteen having been called up for mil-

itary service) and their preparation weak. Frus-

trated by the attempt to uphold an absurd pretense,

he therefore sought yet another position.

Despite his eminence, Dehn’s age (66) made it

difficult for him to obtain a permanent appointment

at an established institution. The Depression years,

however, had spawned the creation of a few ex-

perimental academic enterprises. The Institute for

Advanced Study, which began operations in 1933,

was one such. Another, founded that same year, was

Black Mountain College, located outside the com-

munity of Black Mountain, North Carolina, a few

miles northeast of Asheville. There, in March of

1944, Dehn delivered a pair of guest lectures. And

there, from 1945 until his death in 1952, he served

as the sole faculty member in mathematics.

Black Mountain College was a unique institution,

about which much has been written. ([4] provides

a detailed history of the college, [10] is a collection

of reminiscences by former students and faculty,

and [12] describes Dehn’s career there.) Founded

by dissident faculty who had

resigned or been fired from

Rollins College in Winter Park,

Florida, BMC was an experi-

mental college of the arts that

began life in rented quarters (as

did the IAS) and moved six

years later (as did the IAS) to a

permanent location nearby (in

the forest on the site of a for-

mer summer camp). Like the

IAS, it served as a haven for

many refugees of the Holocaust,

including, besides Dehn, the

artists Anni and Josef Albers

and Willem de Kooning; the mu-

sicians Heinrich and Johanna

Jalowetz, Stefan Wolpe, and Erwin Bodky; the mu-

sicologist Edward Lowinsky; the psychiatrist Erwin

Straus; the physicist Peter Bergmann; and the an-

thropologist Paul Leser. Also like the IAS, BMC was

founded on the principle of faculty governance,

which (in both cases) all too often led not to con-

sensus but to clashes and changes of leadership.

Unlike the IAS, however, BMC had no endowment,

so its finances were always precarious. Students and

faculty collaborated in the construction of campus

facilities and the growing of crops for food, and fac-

ulty received little (and sometimes nothing at all)

beyond their room and board. Dehn’s initial salary

there was $40 per month. Moreover, whereas the

IAS was authorized to offer degrees (but never

has), BMC was never accredited. Instead, its grad-

uates were certified through examinations con-

ducted by outside scholars.

BMC was, in effect, an educational commune,

which attracted self-reliant students seeking an

alternative to a traditional college education. It was

an environment in which Gödel could not have sur-

vived. Dehn, however, thrived there. In addition

to mathematics he taught philosophy, Latin, and

Greek, and as several student memoirs attest, he

became a revered and beloved figure, remem-

bered especially for his love of the outdoors, the

impromptu natural history lessons he gave on

hikes in the nearby mountains, his unorthodox ap-

proach to the teaching of philosophy (via the So-

cratic method), and his friendly attitude toward

students, among whom were two (Peter Nemenyi

and Trueman MacHenry) who went on to receive

Ph.D.’s in mathematics. (For their graduations

from BMC, Nemenyi was examined by Emil Artin

and MacHenry by Ruth Moufang.) Nemenyi later

taught statistics in Mississippi and Nicaragua,

while MacHenry became a professor at York Uni-

versity in Canada [16, p. 133].

One might expect Dehn to have been frustrated

by the paucity of serious mathematics students at

Black Mountain; yet when queried about that, he

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replied, “Not at all. In fact, I have been very fortu-

nate. In my sixty years of teaching I have had at least

fifteen real students” [10, p. 298).

Dehn’s intellectual isolation at BMC was miti-

gated by two leaves of absence (for the fall se-

mester of 1946–1947 and the academic year

1948–1949) that he spent at the University of Wis-

consin in Madison. Nevertheless, he retained his at-

tachment to Black Mountain. Indeed, among the

documents preserved in the archives of the college

is a letter Dehn wrote from Chicago on July 13,

1946, thanking the board of BMC for granting his

upcoming leave. In it he lamented that he would

“miss the flaming October and the dark and cozy

time before Xmas” at Black Mountain, and he ex-

pressed the hope that when he returned there later

that summer there would be “some nice work” for

him to do, such as “geometry for artists or hoeing

potatoes.”

Remarkably, during his leaves at Wisconsin Dehn

directed one final doctoral student: Joseph Engel,

who later became prominent in the operations re-

search community. In an unpublished memoir

about Dehn [5], Engel describes him as “small and

frail”, “an idealistic man” distinguished by “his

inner peace, …good humor, and innocence.” Engel

recalls how, on one occasion, following a very in-

formal final examination that took place at the

University of Wisconsin Ratskeller, Dehn suggested

they walk across the frozen Lake Mendota. As they

did so, Engel “noticed that the wind had built up

a small ice barrier bordering the shoreline,” and he

warned Dehn, “Be careful crossing that ice.” Dehn,

however, ignored the warning. “He fell through the

ice…[and] was in water up to his waist.” His small

size enabled the accompanying students to

“grab…him under the armpits and yank…him out,”

but he was soaked, and it was bitterly cold. “To keep

him from freezing” the students “made him walk

briskly back to the nearest building”—and all the

while Dehn “continued to chat…in his usual cheery

and benevolent manner.”

Engel goes on to say that “Working under

[Dehn’s] kind and understanding guidance was a

joy and a privilege. …Looking back at that wondrous

time, I still love him, and am in awe of his wisdom

and humanity and humor and compassion.”

Final Years

By the time of their emigrations, the greatest works

of both Gödel and Dehn were behind them. Both,

however, continued to publish works of substance.

Gödel’s interests turned increasingly to philosophy

and, for a time, to relativity theory. During the

1940s he contributed important essays on Rus-

sell’s mathematical logic and Cantor’s continuum

problem, and in 1949 he published the first of

three papers in which he described his discovery

of radical solutions to Einstein’s field equations of

gravitation (rotating universes, in some of which

time travel was possible). In December 1951 he

delivered the prestigious Gibbs Lecture to the Amer-

ican Mathematical Society (concerning some philo-

sophical implications of his incompleteness theo-

rems), and in 1958 he outlined a consistency proof

for arithmetic (originally obtained in the period

1938–1941) based on the notion “computable func-

tional of finite type”. After that, apart from revi-

sions to earlier papers, he published no more and

became increasingly reclusive. During the 1960s

and early 1970s he was awarded several honorary

degrees and memberships, and in 1975 he received

the National Medal of Science. By then, however, his

physical and mental deterioration had progressed

to an alarming degree. He retired from the IAS in

1976 and died two years later of self-starvation.

As for Dehn, in the years 1943 and 1944 he

published a series of five historical articles in the

American Mathematical Monthly. In 1947 he con-

tributed a short paper “On the approximation of a

function by power series” to the pedagogical jour-

nal The Mathematics Student. And in 1950 his last

publication, “Über Abbildungen geschlossener

Flächen auf sich” appeared in a Norwegian journal.

According to the obituary memoir [9], “After

the end of the war, [Dehn] immediately resumed

his contacts with his German friends” and “inau-

gurated a magnanimous relief program for his for-

mer Frankfurt colleagues.” In June of 1952 he re-

tired from Black Mountain College as Professor

Emeritus, with the expectation that he would con-

tinue to “serve as an advisor and…live on the cam-

pus” [12]. Hartner reports that he also “planned [to]

return to the University of Frankfurt” in the win-

ter of 1953. But it was not to be. For on July 27,

1952, apparently as the result of his overstrenu-

ous efforts the previous day to protect some

beloved trees from being cut down by loggers,

Dehn developed a coronary embolism and died. He

was buried in the woods at a spot marked by a

stoneware tablet made in the college’s pot shop. (His

wife Toni lived on to become a centenarian, and fol-

lowing her death in 1996 her ashes were buried at

the same site.)

Black Mountain College itself survived only four

years beyond Dehn’s death. Unable to raise funds

for its continued operation, it closed abruptly in

1956. Its buildings were sold to pay its debts, and

the site reverted once again to a summer camp.

Acknowledgments: I am indebted to Dr. Dallas

Webster of Austin, Texas, for assistance in ob-

taining documents from the Archives of American

Mathematics at the University of Texas; to Profes-

sor John Stillwell for providing copies of Dehn

materials from Idaho State University; to Dr. Joseph

H. Engel of Bethesda, Maryland, for his recollections

of Dehn; and to Mrs. Maria Peters, daughter of Max

CTOBER

2002

OTICES OF THE

AMS

1075

Dehn, for her reply to my inquiries about her fa-

ther.

Sources