Mathematics as a subject has had a much longer and varied history than many other scientific disciplines. The reasons for this are numerous, but the major impetus was its usefulness in calculating assets and probably even taxes for old empires. However, the most important facet for its early history was that it was a thinking game, and was independent of location or individual prejudice. In all of mathematical history, perhaps no other place has exerted a greater influence on its modern development, then a small German town called Goettingen.
Goettingen, was until the World War II (WW II), the absolute centre of all of modern mathematics. People like Hilbert, Klein, Riemann and going back to Gauss can trace their history and lineage to the University of Goettingen, where much of the mathematics one studies in their college education now, could be traced back to. It was an absolute necessity for any young mathematician then, to have made a trip to Goettingen and learn at the feet, nay at the classrooms of the greats.
But, all of this has changed now, and the United States of America has taken over as the new epicentre of world mathematics. The reason for this is simple in some sense, but deeper has a complex socio-political angle. We just focus on the simpler explanation. The World War II, saw the exodus of intellectuals from Europe, which has not been since before or after that period in human history. Persecution of Jews, and several other people was an important factor in shifting the world center of mathematics. Cities like Paris, Berlin and Vienna had such an illustrious list of professors and students prior to WW II that it is impossible now to think about the quality of work that was being done at that point in time. And the top of this intellectual hierarchy was Goettingen.
The first truly great mathematician to have been appointed to the University at Goettingen was Carl Friedrich Gauss, considered universally as one of the greatest in the history of intellectual thought, standing shoulder to shoulder with Newton and Archimedes. But interestingly, Gauss was not a professor of mathematics at the University, but was the Director of the Observatory where he spend all of his later life. The Observatory is now an important landmark in the city.
From the appointment of Gauss, there followed a stream of appointments, each a stalwart in their own fields. Names such as Dirichlet, Riemann, Felix Klein, Schwarz and culminating with David Hilbert, the single most important person to have shaped the history of 20th century mathematics; were all associated with the university. It is just a tiny list of world class mathematicians who made their way through the city. At the height of its hay-day, it was not usual to image a Einstein or a Poincare strolling through the halls of the institute or lecturing for students or engaging in mathematical fistfights.
I made a trip to Goettingen in early September of 2018, it was a pilgrimage for me, in some sense. When I was younger and discovered the amazing oeuvre of mathematical literature that seemed to originate from this city, I had the desire to visit it once in my life. So, without any thought when an opportunity came to visit the city I booked my train tickets and spend two very memorable days in this quaint little German town. The highlight of my trip was the museum-like display that is a fixture at the Mathematics Institute building now. The display contains many calculating devices and geometrical models, which were used by several of the people mentioned earlier for their work. Seeing a model made by Klein in front of your eyes, is perhaps akin to touching the piano which Mozart used to make his music.
It is not only mathematics, that the city has a claim to fame for. In the central cemetery of the city, a unique rotunda is placed, where all of the Nobel Prize winners from the city are buried. There is still some space left in the rotunda for any future Nobel Prize winners to be buried. One could sit in front of grave of Max Planck and think about physics, or in front of the grave of Siegel and think about number theory. The aura of such an atmosphere could hardly be captured with just a few simple words. I sat there for a very long time and talked with a few people over the phone who would appreciate the moment that I was at, then.