Pictures at an Exhibition Karl Sigmund n 1965 Kurt Gödel wrote to his mother Mari- place other than the Institute for Advanced Study anne: “I am happy not to have to take part in (IAS) could have provided him with more peace and the Viennese festivities, as I hate these things.” ease, or better intellectual companionship. Yet So we must concede: the Viennese festivities within a dozen years his productivity trickled off, Iplanned for April 2006, on the occasion of his although he certainly did not relax in either ambi- centenary, would probably have made him wince. tion or hard work. In April 2006 a large scientific congress will be The city of Vienna cannot boast about the way held at the University of Vienna, organized by the it treated Gödel, but his centenary is a good occa- International Kurt Gödel Society and generously sion for making amends. The same applies to sponsored by the Templeton Foundation (see Mozart. And as luck will have it, Mozart’s 250th an- http://www.logic.at/goedel2006/). It will be niversary also takes place next year. And Freud’s attended by the few scientists who had close per- 150th. Some competition! sonal exchanges with Gödel, such as Georg Kreisel, Exhibitions are costly. Aspiring to just one or two Dana Scott, and Gaisi Takeuti. There will also be an percent of the sum lavished by Berlin, for example, exhibition on the life and times of Gödel, and this on its splendid Albert Einstein Exhibition 2005 is provides me, who rashly volunteered for the job, not a trivial matter. Fortunately, among officials in with a new set of experiences. some ministries and magistrates I found several The University of Vienna is well-advised, of dedicated enthusiasts, true crypto-Gödelians who course, to celebrate Kurt Gödel as much as it can. were ready to help. I also encountered some who The game theorist Oskar Morgenstern, one of had never heard of him: but as soon as I men- Gödel’s few friends in later years, was surely right tioned that Time magazine had listed Gödel among when he wrote: “Among all those who taught at the the hundred most important persons of the twen- University of Vienna, there is probably nobody tieth century, conversation flowed more easily. whose name outshines that of Gödel.” Gödel did Whoever drew up that list deserves an accolade! most of his best work in Vienna. The university did Exhibitions also need space. Eventually, the list not exactly pamper him, however. He remained a of possible locations boiled down to three candi- lowly Privatdozent (meaning he had the right to lec- dates. One was the main building of the University ture, but no salary worth speaking of), and he even- of Vienna. During the Congress, in the week of tually had to escape, under hair-raising circum- Gödel’s birthday (April 28), hundreds of experts stances, to the safety offered by Princeton. No from set theory and mathematical logic will stroll Karl Sigmund is professor of mathematics at the Univer- its neo-Renaissance arcades, in addition to the sity of Vienna and a research scholar at the Institute for daily stream of students; but many other Viennese Applied Systems Analysis in Laxenburg, Austria. His email will be reticent to cross the university’s entrance address is [email protected]. stairs. The second location is Palais Pallfy, on the 426 NOTICES OF THE AMS VOLUME 53, NUMBER 4 Josefsplatz, the most beautiful piazza in town, Next to the univer- just opposite the Hofburg of the Habsburgs. Since sity, the richest source this will be the venue of many high-level confer- on Gödel is in City Hall: ences in the first half of 2006 (when Austria pre- the municipality sides over the council of the European Union), one bought hundreds of let- hopes that some visitors will take a look at Gödel. ters which he wrote to But people around the Josefsplatz are usually busy. his mother on every Finally, there is the beautiful MuseumsQuarter, other Sunday evening, whose baroque halls are available during the sum- for the first twenty mer months, when flocks of tourists throng be- years after the war. tween the Museum for the History of Art, the They were bought, Leopold Museum with its collections of Klimt and thanks to Werner Schi- Schiele, and a lively scene of bars and restaurants. manovich and Peter No drawback here, except that Gödel’s birthday Weibel (producers of a documentary on does not fall in summer. It finally was decided that Gödel), from the heirs the exhibition will travel and visit all three spots of Gödel’s brother in different incarnations, from the end of April to Rudolf. Unfortunately, mid-August 2006. there is no trace of the What can one show in an exhibition on Kurt letters Gödel must have Gödel? His work was abstract and his life with- sent from Princeton drawn. There is nothing equivalent to, say, the during his visits there STAMP OF APPROVAL. “I replied very couch of Sigmund Freud, or the fiddle of Albert Ein- in the 1930s, and after gently to the magistrate, saying that I stein. Gödel’s famous spectacles have not been Gödel’s death his wife owed my education to the University”, preserved, so it seems, but his optometric pre- Adele destroyed all let- wrote Gödel to his mother. He had scription from 1925 has survived. For Gödel, who ters by her mother-in- experienced superb teachers but grew up as an avid stamp collector, was not one to law. obnoxious administration. During his throw things lightly away. He kept the bill for his The gist of Gödel’s time as Privatdozent, he mostly was wedding meal, for instance, as well as the testy re- major discoveries can on leave, either in Princeton or in minder, signed by Helmut Hasse, that he had not be explained fairly eas- sanatoria, and lectured only for three paid his membership dues for the German Mathe- ily to a large public: (a) semesters altogether. matical Society. Gödel also kept the receipt for the incompleteness, (b) the purchase of Principia Mathematica, acquired dur- consistency of the continuum hypothesis, and (c) ing his student days. The Gödel’s Nachlass, which time travel in rotating universes. But I do not be- belongs to the IAS and is kept at Princeton Uni- lieve that an exhibition can explain the finer points versity’s Firestone Library, is a gold mine of tidbits of “Gödel’s proof” at the level of detail which sev- like these, but also of more serious information, and eral trade books have achieved. Visitors stroll from Gödel’s biographer John Dawson, who knows that one spot to another. Exhibitions are meant for me- Nachlass like no one else, has kindly agreed to co- andering around. This implies some superficiality. curate the exhibition. He writes, in this issue of the Anyone wanting greater depth should sit down to Notices, about his experiences cataloguing the boxes read or listen to a lecture. In contrast, the format of Nachlass material (see also Dawson 1997). of an exhibition seems well suited to giving an idea The only other place with a sizeable amount of of Gödel’s intellectual surroundings. That is the information on Kurt Gödel is Vienna (Köhler at al, right topic for an easy stroll. 2002). There are the archives of the university, So let us take a stroll through Gödel’s Vienna, containing much on his brilliant Ph.D. thesis, on his even if that means walking in a Circle. Gödel was epochal Habilitation, and on the sinister corre- an unusually quiet and withdrawn person, but by spondence between academic officials and high- no means a hermit in his Viennese years. He was level Nazis after 1938. Gödel managed twice, after a member of the Vienna Circle. This shaped him Hitler annexed Austria, to go on leave to visit the profoundly, but in an indirect, almost contrary way. In a questionnaire that Gödel filled out much U.S., first at the height of the Munich crisis and again later (but which he never sent off—Dawson exca- in the tense months of the “phony war”. More than vated it from the Nachlass), he states that the most a year after Gödel had settled down for good in the decisive influences on his intellectual development U.S., the German ministry sent him (c/o University were the lectures by Heinrich Gomperz in philos- of Vienna) a lavishly emblazoned diploma with his ophy and Philipp Furtwängler in mathematics. One promotion to “Dozent Neuer Ordnung” and the would have expected the names of Moritz Schlick pompous guarantee of the Führer’s special pro- and Hans Hahn instead, the professors of philos- tection. The document was never collected, though, ophy and mathematics who had founded the Vienna and the receipt still waits to be signed. APRIL 2006 NOTICES OF THE AMS 427 Circle (and were certainly no including Georg Nöbeling, Franz Alt, and Abraham mean lecturers). But no: Gom- Wald. It was to this group that Gödel lectured first perz and Furtwängler, who on incompleteness. “That’s very interesting,” said held the introductory lec- a voice in the awestruck silence ending Gödel’s tures for Gödel’s cohort, im- lecture. “You should publish that.” (Alt, 1998) “I am printed him for life. There is consumed with unjustifiable pride,” wrote Natkin little reason to doubt that from Paris. “So you have proved that Hilbert’s sys- Gödel was a Platonist by the tem of axioms contains unsolvable problems— age of nineteen and never wa- why, this is not a trifling matter.” vered in this conviction (Fe- The young prodigy was soon pointed out by ferman 1984).