David Hilbert

I had one of the best experiences of my entire sabbatical today thanks to David Hilbert and a choice he made just over a hundred years ago! Soon after the turn of the twentieth century, physicist Max Born arrived in Gottingen, and mathematicians David Hilbert and Hermann Minkowski took Born, along with their families, on a walk up to Plesse Castle for a picnic.

After having climbed there yesterday myself I have a great deal of respect for how hardy they were! It's 8 km north of Gottingen. I took a bus the first 6 km and walked the last 2 km, and there were points where the hill was so steep that I wasn't sure if it was possible to make the walk! Once I got to the top, however, I felt it was well worth the effort. The castle itself is fascinating, and the views of the surrounding countryside and the small village below are gorgeous. The vegetation around the area is just beautiful - wooded and filled with wildflowers. The air is so fresh. It was also refreshing to visit such a place and find it more visited by locals than by tourists.

I have no idea how much or how little time Hilbert spent here over the course of his years in Gottingen, but because it was one of my favorite things of the entire sabbatical trip and because I think it gives at least some insight into his life aside from his mathematics I'm going to post many pictures of this site!

Some folks took horses up. That was smart!

Clearly many other people decided this would be a good destination - as did I - as did Hilbert, Minkowski and Born a century ago.

 I enjoyed some time to journal here.

 One can also see Gauss's tower from here - one vertex of his triangle. (See this link for details.)

The afternoon here with Hilbert and Minkowski is one that Max Born never forgot.  What he writes of it later gives some insight into Hilbert and Minkowski:

The conversation of the two friends was an intellectual fireworks display.  Full of wit and humor and still also of deep seriousness.  I myself had grown up in an atmosphere to which spirited discussion and criticism of traditional values was in no way foreign; my father's friends, most of them medical researchers like himself, loved lively free conversation; but doctors are closer to everyday life and as human beings simpler than mathematicians, whose brains work in the sphere of highest abstraction.  In any case, I still had not heard such frank, independent, free-ranging criticism of all possible proceedings of science, art, politics.

I wouldn't be surprised if Hilbert had often hiked to the castle.  He was known to enjoy walking and hiking.  He would often walk with students or colleagues in the Gottingen Forest to the east of town, pictured below.

These woods were only about one kilometer from his house at 29 Wilhelm Weber Strasse.

When Hilbert began teaching at Gottingen in 1895 all classes were held in the same building, the Auditorienhaus, but eventually a plan would be developed to create a separate mathematics institute within the university with a building of its own.

The Auditorienhaus of Gottingen University

Prior to the building of the Mathematical Institute, the third floor of the Auditorienhaus was the center of mathematical life.  Here Felix Klein, who was instrumental in bringing Hilbert to Gottingen, established a mathematical reading room called the Lesezimmer, which was entirely different from any other mathematical library in existence at the time.  Books were readily available to students - on open shelves.  Additionally Klein established a collection of mathematical models that were housed here as well.

The Mathematical Institute began with a dream of Klein's, but he would not live to see it built.  Instead, it would be brought to fruition by Richard Courant and and David Hilbert.  It was opened in 1927.  It is a T-shaped building, and on the second floor at the top of the T, in a space built specially for it, resides the collection of mathematical models and instruments.

Gottingen Mathematical Institute from the back

Gottingen Mathematical Institute from the front

Upon entering the Mathematical Institute, one sees a study area for student use - and if one looks closely, one can see that the students have a sense of humor about their august mathematical heritage.

Bust of Hilbert in the Gottingen Mathematical Institute - as decorated by students

Directly above this study area is the mathematical models collection - of which more at this link.

David Hilbert and French mathematician Henri Poincare were the greatest mathematicians of their time. When Poincare died, Hilbert stood alone as the mathematical giant of his era.  It was during the time of Klein and Hilbert that Gottingen became the most important mathematical center in the world.

David Hilbert truly was a mathematical giant.  He would dominate one branch of mathematics, creating and publishing cutting-edge work in that branch and speaking of no other area of mathematics.  But then he would suddenly enter a new area of mathematics and produce in it immediately great mature work, and before long he would move on to another entirely new area of mathematics.

On August 8, 1900, David Hilbert gave a talk at the International Congress of Mathematics in Paris, which was held at the Sorbonne.  In his talk (and the proceedings) he presented 23 problems that he felt were the most important to be solved in the twentieth century.  This single talk definintely had a powerful influence on the direction of 20th century mathematics.

The opening words of his talk are given below, along with pictures of the Sorbonne.

Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be towards which the leading mathematical spirits of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought will the new centuries disclose?

 In January of 1930, David Hilbert reached the mandatory retirement age of 68.  He delivered a "Farewell to Teaching" speech to a lecture hall crowded with students and other professors.  He was also honored by having a street (strasse) named after him.  Upon finding out about his honor, Hilbert's wife Kathe exclaimed, "A street named after you!  Isn't that a nice idea, David?"  It is reported that David shrugged and said, "The idea, no, the execution, ah -- that is nice, Klein had to wait until he was dead to have a street named after him!"

Sadly, towards the end of Hilbert's life his country entered a very difficult time with the rise of Hitler as chancellor in 1933.  Because of Hitler's policies, many professors, especially those who were Jewish but others as well, lost their positions at universities.  Gottingen had been the mathematical center of the world, and its Mathematisches Institut had only just opened its doors in 1927, but by 1933 when Hilbert was asked how mathematics was in Gottingen now that it had been freed from its Jewish influence, Hilbert, sadly, had to reply: "Mathematics in Gottingen?  There is really none anymore."

Hilbert died in 1943, but before visiting his grave I wish to visit one more topic of importance to him, so important to him that is engraved on his tombstone.  In the mid-to-late nineteenth century there was a widely embraced reaction against the then long-standing positivism of the explanatory power of science, and that reaction was "ignoramus et ignorabimus," that is "we do not know and will not know."  It expressed a position on the limits of scientific knowledge.  Both Hilbert and Minkowski found this idea abhorrent, and in his address at the Mathematical Congress in August of 1900 at the Sorbonne in Paris he expressed that mathematical knowledge is possible with human effort.  He said:

"We must not believe those, who today, with philosophical bearing and deliberative tone, prophesy the fall of culture and accept the ignorabimus.  For there is no ignorabimus, and in my opinion none whatever natural science.  In opposition to the foolish ignorabimus our slogan shall be Wir müssen wissen — wir werden wissen! (Our motive must be to learn -- We shall this way greatly achieve!)"

Wir müssen wissen — wir werden wissen!

We must know -- we will know!

I found the tombstone, and the engraving (though, sadly, I see that it is fading) in Gottingen's Stadtfriedhof Cemetery -

A recording of Hilbert's voice exists and can be heard on this YouTube clip. This is from a radio broadcast he gave later in life in which he reiterated his positive credo, Wir müssen wissen wir werden wissen!, which can be heard at the very end (3:56-4:01)

Wir müssen wissen wir werden wissen!

We must know; we will know!