I consider that particular book as one of the most influential I have read in my life, so far. But from the standpoint of genealogy, Gödel presents an example of the problems we can encounter with shifting jurisdictions.
As genealogists, we need to be acutely aware that jurisdictions change over time, but can change suddenly and without notice. Each time there is a change in jurisdictions, there will be a adjustment to the existing records, as well as future records created by the newer jurisdictional entities. Gödel's escape from Nazi Germany, just at the outbreak of World War II, gives an extreme example of what can happen to an individual as these jurisdictional boundaries change.
In 1938, Austria became part of Nazi Germany. In the Fall of 1939, as the War started, he and his wife attempted to leave the country for the United States. Due to the fact that the country of his citizenship was Austria and that the country no longer existed, he had great difficulty in obtaining a Visa for the U.S. Ultimately, he had to circumnavigate the globe and travel to the United States by way of the Trans-Siberian Railroad to ultimately reach Princeton, New Jersey where he would be employed during the War at the Institute for Advanced Studies.
When he arrived in the United States, he was a declared an enemy alien and the U.S. Government refused to allow him to leave Princeton without formal permission from the Department of Justice, even to visit a doctor in New York. A more complete description of his difficulties in obtaining U.S. residency is set forth in the following book:
Since the Kurt Gödel was a naturalized Austrian citizen and his wife was an Austrian citizen by birth and since the U.S. Government had recognized the overthrow of Austria by the German Reich, they were both considered German citizens. The Government based this holding, in part, on the fact that they had obtained German Passports to come to the United States. Finally, he was allowed to apply for permanent residency in the U.S. and immediately became eligible for the Draft and was classified 1A.
After a great deal of paper work, Gödel was finally allowed to continue his work at the Institute for Advanced Studies at Princeton University.
Unfortunately, Gödel's experiences with changing jurisdictions is neither unique nor uncommon. Further, unfortunately, few genealogical researchers avail themselves of the historical background necessary to sort out similar experiences of their own ancestors. It is imperative, when you have immigrant ancestors, to become fully acquainted with the historical circumstances surrounding their immigration. This is sometimes the only way of finding their original records and understanding how and why they came to the United States (or any other country, for that matter).
Question: Where are Kurt Gödel's genealogically significant records now? Of course, I do not have the answer, but remember he was born in what is now the Czech Republic.