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Hilbert-Courant
I am very pleased that my books about David Hilbert, published in 1970, and Richard Courant, published in 1976, are now being issued by Springer Verlag in a single volume. I have always felt that they belonged together, Courant being, as I have written, the natural and necessary sequel to Hilbert the rest of the story. To make the two volumes more compatible when published as one, we have combined and brought up to date the indexes of names and dates. U nfortu nately we have had to omit Hermann Weyl's article on "David Hilbert and his mathematical work," but the interested reader can always find it in the hard back edition of Hilbert and in Weyl's collected papers. At the request of a number of readers we have included a listing of all of Hilbert's famous Paris problems. It was, of course, inevitable that we would give the resulting joint volume the title Hilbert-Courant.
547 pages, Paperback
First published May 22, 1986
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August 5, 2022
One of the graduate students at my university was tasked with helping the department with all the books we've managed to accumulate over the years. Many of the books were old and outdated maths texts that use archaic notation that modern students might find baffling, so we were looking to recycle the lot of them. However, being the book worm I am, I was assisting with what we should keep as some of the classics are certainly worth keeping around. In our searches we found a couple non-mathematics texts. This was one of them. At first I thought it might be the joint book, since this was a Springer publication, I fully thought it was going to be quite the terse read, however, I was pleasantly surprise to find that this is was more a history book of these wonderful mathematicians.
This was originally published as two separate books and here is a reprinting as a collected works. I rather think these books may have been lost to the annals of history, but for interested parties I think it is worth turning your head to these absolutely amazing stories. Constance Reid does an amazing job of telling us a story, not only of mathematical achievement, but insight into the personalities of these two men and all those around them. The stories are rife with personal anecdotes and stories of the two growing up, the people they worked with and friends they made along the way. The tragedies of major wars that struck them both and the continuance of a discipline into the future.
The first book covers the story of David Hilbert. Many students will recognize his name for Hilbert Spaces, which is a fairly common thing to run into in graduate school, if not an ambitious undergrad. However, we only learn the name, but in this book we meet the man behind them and how he was responsible for so much more. Hilbert worked in the late 1800's/early 1900's for the majority of his life. He began in Konigsberg, which has now become a Russian territory post-World War II. From here he eventually found his way to Gottingen and under the mighty Felix Klein they would create one of the most formidable mathematics institutions in all of Germany. The famous mathematicians and physicists that have crossed path with Hilbert is simply incredible. He was very good friends with Minkowski! Reid's preservation of their letters to each other in this book were some of the more wonderful portions. Hilbert worked on a couple major projects that would influence the rest of math for the coming century. The first was to work with quite a few other big names out there to get mathematics on much more solid footing. Doing Set Theoretic constructions, tackling criticism from Russell and the like, but he was primarily focused on the realms of analysis and shoring up those areas. He also took an interest in physics, I wonder if partly due to Minkowski, who was, unhappily, not at Gottingen with Hilbert. Although, he eventually found his way there, but by then he had been working in the realms of mathematical physics for quite some time. Hilbert sought to bridge the gaps between the two disciplines as much as possible, he may have done this rather well, especially with the help of Courant. Together they wrote a joint book on the subject taking the academic world by storm.
One of the more fascinating parts of the book, which made this into quite the page turner is that Reid told the stories through the dates of their lives. In the early 1900's we all know what was eventually coming... World War I. I was surprised to see that World War I was not that disruptive to the life of Hilbert. Naturally student enrollment went down and it became difficult to purchase certain things, but all in all the mathematics continued to flow. The great depression had similar issues, of course.
The years kept on moving and the next big event, which, I imagined would be the most disruptive was the oncoming of the Nazi party in the 1930's. This would, sadly, be a death sentence for Gottingen and many other institutions around Germany. Hilbert, being quite old at this point, was unlikely to bother leaving the country at this point. He tried to continue teaching, but found it odious so retired instead of deal with the rules of the regime. He was once asked by a higher up how mathematics was now that the "Jewish influence" was gone. His response was that "Mathematics is no longer done there." Due to the policies enacted by Nazi Germany it simply gutted their faculty. Some of their most prodigious professors were Jewish and either escaped, with luck, or were simply fired. Richard Courant, being Jewish, would fall victim to these policies and more detail is given in his portion of the book.
Sadly, I believe Hilbert passed away without seeing any real resurrection of the mighty Gottingen that he had helped create with Felix Klein so long ago. Fascism would tear down all the work these men had done and simply undo the great the strides being made there seemingly overnight.
This brings us to Richard Courant. Courant eventually came to Gottingen and worked quite closely with Hilbert. He started out being an assistant to Hilbert, but eventually found his way amongst their celebrated faculty. He fought in World War I and was rather fiercly loyal to Germany. As Hitler rose to power, he had even been moved by some of the ideas being brought forth there. This was, naturally, before the horrifying undercurrent of Hitler's nationalism was truly well known. Sadly, for Courant he found himselves in the crossfire of the new regime. He commission was dismissed from Gottingen fairly early on. However, it was interesting to note that the pro-Aryan policies were not something that were enacted upon Hitler taking charge. It was a rather slow-burn over quite a few years. I think a lot of people read about World War II and think things happened very quickly, but Courant remained in Germany for quite a few years after his dismissal. Trying to appeal to the government to get his job back or trying to be hopeful about the situation. This all bore out in letters to his colleagues around the world. Eventually, as we know today, things took a much darker turn.
There is a story of a student by the name of Teichmuller who was after Landau. Landau was eventually dismissed from this students efforts. Teichmuller was described by the faculty as being insane. He was an absolute Nazi loyalities joining their paramilitary branch very early on. Landau, being Jewish, naturally wound up in Teichmuller's cross hairs and Teichmuller eventually won out. The interesting part of the letters that Reid dug up was that even though many described Teichmuller as being insane, they also noted he was a genius. There is a branch of mathematics called Teichmuller theory that still exists today and it is based on only five papers written by Teichmuller. Teichmuller would eventually meet his end fighting on the Eastern front, which he volunteered to do. However, I like to think he would have eventually been executed at the Nuremburg trials even if he had survived the warfare. When I was talking with another graduate student on the history of Teichmuller we both marvelled how someone could be so gifted in a subject like mathematics, which is based on incredible logic, and then be so out of their mind as to think their faculty needs to be purged of the teachers that taught them! We can both see why the faculty often referred to him as an insane person.
Despite the hardships imposed, Courant wound up being very lucky and managed to escape to the United States along with many other German scientists during the 30's as they sought to escape the turn in politics. Most of the faculty at places like Gottingen were not at all prejudiced, so things became more dangerous for those who even supported their colleagues. Luckily a large portion were able to escape to other areas before war would really break out.
Courant came here and founded an institute with the help of New York University at the time. It was a major player in bridging the gap between Pure Mathematics and Physics. Courant always pushed for an Applied Mathematics styled school and he eventually built one. Once again, the famous names that he surrounded himself with were quite incredible. Aside from his efforts to help the U.S. government fight the war with research, he also used his influence to save quite a few people from the Nazis after he left. He would pay for whoever he could to come over to the U.S. and reading about this effort to save others when he could was an amazing thing. It really showed the character of Courant and one hopes they can live up to such greatness in similarly trying times.
While I have paraphrased the overall story and offered some opinion of the tales where I found it interesting, I highly recommend reading these books. These are more than stories of mathematicians. These are stories that tell of a trying time in history. It gives us special insight into how the changes of political winds would affect others. How it wasn't just a sudden turn of events, but instead of a subtle threat at first turning into something much more dire as time went on. It was a rather incredible thing to see who was choosing to leave before the new regimes policies truly got out of hand. In sum... pay attention who is leaving your nation if you live to see such times.
Through it all was some wonderful mathematics. Tying together a joy that brought people together through one of the most creative disciplines one could devote themselves to. A truly wonderful story and it makes me want to track down and read more of Reid's books.
This was originally published as two separate books and here is a reprinting as a collected works. I rather think these books may have been lost to the annals of history, but for interested parties I think it is worth turning your head to these absolutely amazing stories. Constance Reid does an amazing job of telling us a story, not only of mathematical achievement, but insight into the personalities of these two men and all those around them. The stories are rife with personal anecdotes and stories of the two growing up, the people they worked with and friends they made along the way. The tragedies of major wars that struck them both and the continuance of a discipline into the future.
The first book covers the story of David Hilbert. Many students will recognize his name for Hilbert Spaces, which is a fairly common thing to run into in graduate school, if not an ambitious undergrad. However, we only learn the name, but in this book we meet the man behind them and how he was responsible for so much more. Hilbert worked in the late 1800's/early 1900's for the majority of his life. He began in Konigsberg, which has now become a Russian territory post-World War II. From here he eventually found his way to Gottingen and under the mighty Felix Klein they would create one of the most formidable mathematics institutions in all of Germany. The famous mathematicians and physicists that have crossed path with Hilbert is simply incredible. He was very good friends with Minkowski! Reid's preservation of their letters to each other in this book were some of the more wonderful portions. Hilbert worked on a couple major projects that would influence the rest of math for the coming century. The first was to work with quite a few other big names out there to get mathematics on much more solid footing. Doing Set Theoretic constructions, tackling criticism from Russell and the like, but he was primarily focused on the realms of analysis and shoring up those areas. He also took an interest in physics, I wonder if partly due to Minkowski, who was, unhappily, not at Gottingen with Hilbert. Although, he eventually found his way there, but by then he had been working in the realms of mathematical physics for quite some time. Hilbert sought to bridge the gaps between the two disciplines as much as possible, he may have done this rather well, especially with the help of Courant. Together they wrote a joint book on the subject taking the academic world by storm.
One of the more fascinating parts of the book, which made this into quite the page turner is that Reid told the stories through the dates of their lives. In the early 1900's we all know what was eventually coming... World War I. I was surprised to see that World War I was not that disruptive to the life of Hilbert. Naturally student enrollment went down and it became difficult to purchase certain things, but all in all the mathematics continued to flow. The great depression had similar issues, of course.
The years kept on moving and the next big event, which, I imagined would be the most disruptive was the oncoming of the Nazi party in the 1930's. This would, sadly, be a death sentence for Gottingen and many other institutions around Germany. Hilbert, being quite old at this point, was unlikely to bother leaving the country at this point. He tried to continue teaching, but found it odious so retired instead of deal with the rules of the regime. He was once asked by a higher up how mathematics was now that the "Jewish influence" was gone. His response was that "Mathematics is no longer done there." Due to the policies enacted by Nazi Germany it simply gutted their faculty. Some of their most prodigious professors were Jewish and either escaped, with luck, or were simply fired. Richard Courant, being Jewish, would fall victim to these policies and more detail is given in his portion of the book.
Sadly, I believe Hilbert passed away without seeing any real resurrection of the mighty Gottingen that he had helped create with Felix Klein so long ago. Fascism would tear down all the work these men had done and simply undo the great the strides being made there seemingly overnight.
This brings us to Richard Courant. Courant eventually came to Gottingen and worked quite closely with Hilbert. He started out being an assistant to Hilbert, but eventually found his way amongst their celebrated faculty. He fought in World War I and was rather fiercly loyal to Germany. As Hitler rose to power, he had even been moved by some of the ideas being brought forth there. This was, naturally, before the horrifying undercurrent of Hitler's nationalism was truly well known. Sadly, for Courant he found himselves in the crossfire of the new regime. He commission was dismissed from Gottingen fairly early on. However, it was interesting to note that the pro-Aryan policies were not something that were enacted upon Hitler taking charge. It was a rather slow-burn over quite a few years. I think a lot of people read about World War II and think things happened very quickly, but Courant remained in Germany for quite a few years after his dismissal. Trying to appeal to the government to get his job back or trying to be hopeful about the situation. This all bore out in letters to his colleagues around the world. Eventually, as we know today, things took a much darker turn.
There is a story of a student by the name of Teichmuller who was after Landau. Landau was eventually dismissed from this students efforts. Teichmuller was described by the faculty as being insane. He was an absolute Nazi loyalities joining their paramilitary branch very early on. Landau, being Jewish, naturally wound up in Teichmuller's cross hairs and Teichmuller eventually won out. The interesting part of the letters that Reid dug up was that even though many described Teichmuller as being insane, they also noted he was a genius. There is a branch of mathematics called Teichmuller theory that still exists today and it is based on only five papers written by Teichmuller. Teichmuller would eventually meet his end fighting on the Eastern front, which he volunteered to do. However, I like to think he would have eventually been executed at the Nuremburg trials even if he had survived the warfare. When I was talking with another graduate student on the history of Teichmuller we both marvelled how someone could be so gifted in a subject like mathematics, which is based on incredible logic, and then be so out of their mind as to think their faculty needs to be purged of the teachers that taught them! We can both see why the faculty often referred to him as an insane person.
Despite the hardships imposed, Courant wound up being very lucky and managed to escape to the United States along with many other German scientists during the 30's as they sought to escape the turn in politics. Most of the faculty at places like Gottingen were not at all prejudiced, so things became more dangerous for those who even supported their colleagues. Luckily a large portion were able to escape to other areas before war would really break out.
Courant came here and founded an institute with the help of New York University at the time. It was a major player in bridging the gap between Pure Mathematics and Physics. Courant always pushed for an Applied Mathematics styled school and he eventually built one. Once again, the famous names that he surrounded himself with were quite incredible. Aside from his efforts to help the U.S. government fight the war with research, he also used his influence to save quite a few people from the Nazis after he left. He would pay for whoever he could to come over to the U.S. and reading about this effort to save others when he could was an amazing thing. It really showed the character of Courant and one hopes they can live up to such greatness in similarly trying times.
While I have paraphrased the overall story and offered some opinion of the tales where I found it interesting, I highly recommend reading these books. These are more than stories of mathematicians. These are stories that tell of a trying time in history. It gives us special insight into how the changes of political winds would affect others. How it wasn't just a sudden turn of events, but instead of a subtle threat at first turning into something much more dire as time went on. It was a rather incredible thing to see who was choosing to leave before the new regimes policies truly got out of hand. In sum... pay attention who is leaving your nation if you live to see such times.
Through it all was some wonderful mathematics. Tying together a joy that brought people together through one of the most creative disciplines one could devote themselves to. A truly wonderful story and it makes me want to track down and read more of Reid's books.
November 4, 2013
Reading the book gave me a never before insight into the lives of famous mathematicians. It was fascinating to read about those people whom I may know only by their work or equation or theory..Do read it if you want to catch a glimpse of a life of a mathematician!! You will wonder how vulnerable they are..how human they are..
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