The Living Culture of Learning: The Gottingen Mathematical School

The University of Gottingen

  "What a great book! I wish I could read a little more but it is time to sleep. After all I need to get up early to make it to the exam tomorrow." The student reluctantly kept the book aside on the table and closed his eyes. He was a student of Electrical Engineering. But Theoretical Physics was his real calling. Unfortunately, the Bachelors Degree programs in Science to which he had hoped to join had been infamous for their total lack of meaningful subjects. True, he could have ignored them and studied Theoretical Physics on his own. But his parents had been somewhat apprehensive and anyway he felt that it did not really matter what he took.

Physics was more of an inner need and he would do it irrespective of his formal studies. Therefore he found himself enrolled in the Electrical Engineering Degree program in one of the prestigious engineering colleges in his city. And now it was exam time and he needed to get some sleep. His eyes still closed he tried to slip into sleep. But he could not take his mind off the book he had been reading. What a fascinating book it was. It was by Robert Jungk's "Brighter than a Thousand Suns." The book itself had been out of print but thanks to the internet, one of his friends across the Atlantic had mailed an ebook to him.  

One glance inside the book and he was hooked. It was difficult to keep it aside and concentrate on his exam preparation. Fortunately, he had actually learnt the topics of the very same exam at a far deeper level. After all the exam was on "Strength of Elastic Materials," and he had studied the subject of Elasticity from the fountainhead itself, from the fabulous Landau and Lifshitz's Course of Theoretical Physics. In addition he had mastered Marsden and Hughes "Mathematical Foundations of Elasticity". Compared with these his exam demanded a tiny modicum of learning in the subject. he could easily maintain his distinction level scores in the exam. Having comforted himself thus, he had continued to read Robert Jungk's book. 

What was it that was so captivating about the book? He himself wondered on the secret of the gripping flow of the writing in the book. And then he remembered that he needed to sleep. He tried to slip into sleep. But again his mind drifted to the events described in the book. Slowly, after a while it appeared that he had indeed slid into sleep. He felt he was somehow awake and in a different space and time. "Perhaps I am dreaming," he had a faint thought. But his awareness was not enough to probe the thought further. He let himself dream on. 

It seemed that he was in the quaint little town of Gottingen, Konigsberg, in prewar Germany. He was walking along a street observing the people around. He found another visitor like himself knocking on the door of a house.
"Could you please tell me where Mr. Bach's home is?" He enquired. "Bach, you mean Sebastian Bach, the musician? Well, his home is over there." the man who opened the door replied. The student who was peering closely at the face of the man was surprised. "Richard Courant!" He gasped. Just then a horse carriage stopped in front of that same house. And who could he see but…he could only gasp in wonder once again, "David Hilbert." Curious he continued to watch. David Hilbert got down from the carriage and was warmly welcomed by Richard Courant. "Weyl and Runge are already here, and so is Caratheodory. But Hurwitz is yet to come," he told Hilbert. "Well, let's wait for him. Meanwhile, did you manage to get my lecture notes typed out? I plan to take them with me to Paris when I am meeting Hadamard." Hilbert replied. "Yes, here it is," Courant handed it to Hilbert. "Well, is the new Copernicus arriving soon?" Hilbert asked. "We have invited him. It remains to be seen if he will actually turn up." Courant replied. "I wish Minkowski were here," Hilbert spoke, "He told me that this new Copernicus had been his student at the Ecole Polytechnic. Only, he was an erratic one, always missing classes, sitting in the last bench and talking. It looked that he would never amount to something. But now…Minkowski has it that his work is revolutionary, not only for physics but also for mathematics. It promises to revitalise the whole of the theory of invariants. He has given new meaning to the work of Gauss, Riemann, Levi Civita, Ricci and Christoffel." 

 "What an honor for Courant that the great David Hilbert is visiting him, not to speak of all those luminaries of mathematics," thought the student. Just then he was attracted by a noise in the street. A man had fallen on the street and a younger man was rushing to help him. And instead of being thankful to the young man, the older man appeared to be angry. "What did you do? You spoiled the insight Why did you disturb me by trying to help me. I had fallen so what? I had fallen because I could not see anything but that insight. But now…I wonder if will come again…"

Across the street the student found a young man running to and fro. In a moment he was at the front of a house. He knocked furiously on the door. Shortly the door opened and an older man asked, "what is it? what is it?" "I have found the proof, we had missed an important point and that was why it was not matching," the young man answered. "Well, than, come in, we must settle it immediately," the older man ushered the young man inside.

"Oh, I seem to be experiencing what I was reading a while ago…" the student felt somewhere a thought stirring.
He continued to walk along the street. Soon he came across a restaurant. "I am a little hungry, maybe I forgot to have my dinner, so absorbed I was in the happy discovery of the analogy between elasticity and the gauge theory of gravity. But can I eat in my dream…" Thus wondering the student went up to the restaurant. He saw a strange sight. He found most of the tables empty. But in a corner on a single round table were to be found around ten to fifteen young men. They appeared bent over the table and one or two of them were scribbling furiously on the table cloth. The student managed to get close and looked at the table cloth. It was filled with equations and writing. As he watched fascinated, the number of equations increased without limit. "Perhaps they want to take the limit of the number of equations possible on the table cloth," he thought humorously. Slowly, dusk began to wrap the surroundings and it became more and more difficult to perceive the writing on the table cloth. One by one the young men got up and left the restaurant. It was when all of the young men had left that the waiters who were apparently waiting respectfully in a corner made their appearance. Three of them came to the table with great gravity and with great care folded the table cloth. And then with equal care they respectfully carried the table cloth to a corner of the room and gently deposited it on a shelf. They performed the whole act as if it was part of a sacred ritual.  

 "Ah, what respect, what reverence for learning!" The student exclaimed. "The waiters are going to bring that table cloth back when those young men came tomorrow, so that they can continue their research discussions and work..." It seemed it was becoming difficult to think. Perhaps the dream was drifting into dreamless sleep. "I better see what else is there in this town, before I am unable to do so" the student thought and hurried through the street. He was soon at the outskirts of the town and saw a sign on a certain statue. "Extra Gottingam non est vita", that means, "Outside Gottingen there is no Life." "Wait a minute, who is that person? Well…he is…Einstein…Albert Einstein…oh, he is the person, the new Copernicus, they were all talking about at Richard Courant's home!" He felt a thrill passing through him. "No wonder the author called those times the beautiful years…I must continue reading the book…now…maybe…tomorrow…in the exam…no…later..." Perhaps that was the last thought he had before he slipped into deep slumber.

Schools that Learn: A Fifth Discipline Handbook


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Sunday, 21 April 2019