Background
There is a saying “The shy one shalt not learn”. In my student years this statement was bandied about generously by calculating university professors, who openly encouraged question-asking, while secretly looking for naïve students to subject to public humiliation!
For example in the classic approach to teaching maths, every step of a theorem is first written on the blackboard in rigorous detail and then meticulously copied by every student simultaneously. In Advanced Infinitesimal Calculus, the proof of one of the Bolzano-Weierstass Theorems was expounded over three weeks of lecturing by Professor Saharon Shelah. Due to its length and complexity, apart from occasional explanations the only other sound came from the squeaking of chalk, in the unfolding of lemmas and propositions. In truth most of the students were lost in the first few minutes of the opening lecture, and even the brightest of us had given up by the end of the first half hour. However Rafi Heiman[1], a truly exceptional student, frustrated at having lost track of the proof, finally decided to interrupt our venerable professor with a question. Most of us could not even grasp the subject, but we were glad for a moment of respite in the tireless duet of symbols and chalk. The professor stalled, scowled at Rafi pointing out that the material relevant to his question had not only been explained but also erased two weeks before. He then asked why on earth had Rafi waited so long to ask his question?
One of those interminable silences followed while Rafi and the professor locked gazes. Eventually Rafi dropped his head in defeat. The reality was that in spite of the saying, you had to be extremely courageous to ask a question in a maths lecture.
One distinguished exception to this adage was Professor Aumann[2], with whom I was keen to study because he taught in English. It has been remarked that a mathematician is a “machine for turning coffee into theorems” and true to form Professor Aumann would show up at lectures holding a small glass of “BOTZ” (literally mud), fresh coffee that is stirred in as if it were instant.
The Story
In his opening lecture on Set Theory at the outset of the Spring Term of 1982, Professor Aumann started out by saying we were not required to copy any of the proofs demonstrated during his lectures. This was a complete break from the classic approach. Professor Aumann went even further by telling us that we did not have to take any notes whatsoever at his lectures, we simply needed “to look and to listen”. He assured us that if we did just that we would sail through his class easily.
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Seeing our bewilderment Professor Aumann amicably decided to illustrate his message with a story. He told us of another professor who was initiating another group of students on their very first day in the faculty of medicine. He too told them they simply needed to “look and listen”. However in their case one more thing was required to become a doctor: and this was the “courage” to behold blood and organs and so forth. He picked up a glass beaker containing a brown substance and told the students it was human excrement. Professor Aumann illustrated using his own almost empty glass of “BOTZ”. Holding up the glass of excrement the professor of medicine looked round his audience, (as did Aumann), saying that if they wanted to be doctors, they would have to be courageous enough to dip a finger into the glass, place their finger in their mouth and suck it. The professor, again illustrated by Aumann, immediately did so himself. Nausea and disgust swept across the room, as the professor of medicine looked around for a guinea-pig. His eyes called on a girl in the second row, “Do you want to be a doctor?” he smiled, “ugh yes …” she replied and went up front nervously.
“Do you want to be a doctor?” the professor repeated politely, again the girl nodded. “Then show me you have the courage”, and he held out the glass beaker. The poor girl dipped her trembling index finger into the substance, and gagging placed the same finger into her mouth.
“Thank-you,” said the professor, “you, my dear, are a most courageous person, but I fear you may not become a doctor.” The girl looked back bewildered as he continued, “Because you did not follow my instructions. I said that you must look and listen. You listened well. However you did not look closely enough, for while I put my index finger into the beaker, I put my middle finger into my mouth.”
“And so”, said Professor Aumann, “you people are lucky - all you have to do here is to look and listen – but remember it isn’t always as easy as it sounds”.
Conclusion
No one asked but everyone hoped the girl had learned her lesson, and that so had we. Professor Aumann turned out to be one of those rare teachers capable of both inspiring and caring.
Later that year Professor Aumann’s son, a reserve officer, was called up and tragically killed in action, in South Lebanon. The Professor’s eyes dimmed, and from then on only rarely did a sparkle surface. He grew a very long beard, and was often seen wondering around the campus, in a world of his own. More than twenty years later he was recognized with a Nobel Prize for his mathematical contributions in the field of economics.
[1] I looked up Rafi and found his Ph.D. Dissertation "Randomized Decision Tree Complexity For Read-Once Boolean Functions".
[2] An internationally known researcher in the area of game theory, Robert J. Aumann is a professor emeritus in the Institute of Mathematics at the Hebrew University of Jerusalem and a member of the University's Centre for the Study of Rationality.
There is a saying “The shy one shalt not learn”. In my student years this statement was bandied about generously by calculating university professors, who openly encouraged question-asking, while secretly looking for naïve students to subject to public humiliation!
One of those interminable silences followed while Rafi and the professor locked gazes. Eventually Rafi dropped his head in defeat. The reality was that in spite of the saying, you had to be extremely courageous to ask a question in a maths lecture.
One distinguished exception to this adage was Professor Aumann[2], with whom I was keen to study because he taught in English. It has been remarked that a mathematician is a “machine for turning coffee into theorems” and true to form Professor Aumann would show up at lectures holding a small glass of “BOTZ” (literally mud), fresh coffee that is stirred in as if it were instant.
The Story
In his opening lecture on Set Theory at the outset of the Spring Term of 1982, Professor Aumann started out by saying we were not required to copy any of the proofs demonstrated during his lectures. This was a complete break from the classic approach. Professor Aumann went even further by telling us that we did not have to take any notes whatsoever at his lectures, we simply needed “to look and to listen”. He assured us that if we did just that we would sail through his class easily.
-the-anatomy-lecture-of-dr-nicolaes-tulp.jpg)
“Thank-you,” said the professor, “you, my dear, are a most courageous person, but I fear you may not become a doctor.” The girl looked back bewildered as he continued, “Because you did not follow my instructions. I said that you must look and listen. You listened well. However you did not look closely enough, for while I put my index finger into the beaker, I put my middle finger into my mouth.”
“And so”, said Professor Aumann, “you people are lucky - all you have to do here is to look and listen – but remember it isn’t always as easy as it sounds”.
Conclusion
No one asked but everyone hoped the girl had learned her lesson, and that so had we. Professor Aumann turned out to be one of those rare teachers capable of both inspiring and caring.
Later that year Professor Aumann’s son, a reserve officer, was called up and tragically killed in action, in South Lebanon. The Professor’s eyes dimmed, and from then on only rarely did a sparkle surface. He grew a very long beard, and was often seen wondering around the campus, in a world of his own. More than twenty years later he was recognized with a Nobel Prize for his mathematical contributions in the field of economics.
[1] I looked up Rafi and found his Ph.D. Dissertation "Randomized Decision Tree Complexity For Read-Once Boolean Functions".
[2] An internationally known researcher in the area of game theory, Robert J. Aumann is a professor emeritus in the Institute of Mathematics at the Hebrew University of Jerusalem and a member of the University's Centre for the Study of Rationality.