History sees this city with two faces. One is modern day – Kaliningrad, a Russian city between Lithuania and Poland. The other is Konigsberg, a Teutonic Knights fort. It became Kaliningrad when the Red Army of the Soviet Union captured it near the end of World War II. Konigsberg was founded in 1255 in place of an Old Prussian town. In 1701 it became the capital of Prussia.
Kaliningrad, or Konigsberg, is perhaps most famous with the luminous citizens that it had bred throughout its history. The most well known of those must be Immanuel Kant.
Kant is crucial in the history of thought, or philosophy, as it is more formally known, for uniting many conflicting views at the time. Briefly, Kant believed that the rift between empirisists and rationalists was illusionary or at best misguided. He, brilliantly, introduced the notions of apriori and aposteriori knowledge.
Kaliningrad, Russia
The apriori knowledge includes our concepts of space, time, cause, effect, continuity and so on. These concepts shape the way we think and the way we perceive the world. These notions cannot be inferred from the world, they must exist independent and antedecent.
However, these notions have no other purpose than perceiving the world. This is aposteriori knowledge – the objects and experiences that are categorized according to the apriori knowledge. The first one is the noumenal world, the second one is the phenomenal world. In a way, he said that we conform the world to ourselves, rather than conforming ourselves to the world.
Away from philosophy, and on to mathematics (which is not that different, really). Konigsberg was the place where a number of prominent and quite important mathematicians lived. One of the more recent ones is David Hilbert.
Hilbert introduced many important ideas in the then rapidly changing world of mathematics. Ideas such as Hilbert spaces, which quickly became excellent and actually indispensable tools in Fourier analysis, quantum mechanics and partial differential equations, to name just a few.
He is also one that brought to acceptance Georg Cantor’s set theories, but what Hilbert will be perhaps most remembered and known for in the non mathematical world is his Hilbert program.
It was his effort to put mathematics on a firm basis, demanding rigorous proof and put forward a number of problems that were to be resolved if mathematics is to go forth. Many of them were resolved, but the whole program was doomed to fail, as Kurt Godel showed later with his Incompleteness Theorem.
Another of the Konigsberg mathematicians was Christian Goldbach, who, in a letter to Leonhard Euler proposed what is now known as the Goldbach conjecture. It simply states that any integer bigger than two can be written as a sum of two primes (another conjecture of his is that any integer bigger than five can be written as a sum of three primes).
Speaking of Leonhard Euler, he has a problem that is actually directly connected to the city of Konigsberg (now Kaliningrad) and is known as the Seven Bridges of Konigsberg. When you are there, you should certainly try to solve it yourself. The problem is to find a way to cross all the bridges of Konigsberg, but going through each one only once.
You are not allowed to reach the islands in any other way and you also have to cross each bridge completely, but without retracing it. It is a simple game, try it. Simple though as it is, this problem prefigured the field of topology and practically kickstarted graph theory.
