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 Professor Kaluza in Göttingen warnte seine Studenten oft vor den Gefahren des doppelten Grenzüberganges und ermahnte sie, damit vorsichtig umzugehen. Er machte dies an folgendem Beispiel klar: Ein Mann kommt mit Magenbeschwerden zum Arzt. Der Arzt untersucht ihn gründlich und sagt dann: Sie müssen öfter essen, aber dabei weniger!
Der Mann wollte es besonders gut machen und führte einen doppelten Grenzübergang aus: Er ass von nun an immer nichts! 



During a lecture, professor Dirac made a mistake in an equation he was writing on the blackboard.
A couragous student raises his finger and says timidly : "Professor Dirac, I do not understand equation 2.".
Dirac continues writing without any reaction. The student supposes Dirac has not heard him and raises his finger again, and says, louder this time: "Professor Dirac, I do not understand equation 2."
No reaction. Somebody on the first row decides to intervene and says: "Professor Dirac, that man is asking a question."
"Oh," Dirac replies, I thought he was making a statement."


While Boltzman gave a lecture on ideal gasses, he casually mentioned complicated calculations, which didn't give him any trouble. His students could not follow the fast mathematics and asked him to do the calculations on the blackboard.
Boltzman apologized and promised to do better next time.
 The next lesson he began: "Gentlemen, if we combine Boyle's law with Charles's law we get the equation
pv= p\sub 0 v\sub 0 (1 + a t).
Now it is clear that \sub a S \sup b = f(x) dx x (a), then is pv=RT and \sub V S f(x,y,z) dV = 0.
It is so simple as one and one is two. At this moment he remembered his promise and dutyfully wrote 1 + 1 = 2.
Then he continued with the complicated calculations from his bare mind. 



Im Jahre 1964 hatte B.L. van der Waerden eine Gastprofessur in Göttingen. Als sein Gastsemester zu Ende ging, lud er alle seine Göttinger Kollegen zu einer Abschiedsgesellschaft ein. Carl Ludwig Siegel, der Göttinger Zahlentheoretiker, hatte aus irgendwelchen Gründen keine Lust, zu dieser Gesellschaft zu kommen. Um sich lange Entschuldigungen zu sparen, schrieb er van der Waerden kurz, er könne leider nicht kommen, da er soeben verstorben sei. Darauf sandte ihm van der Waerden postwendend ein Beileidstelegramm, indem er ihm seine tiefe Anteilnahme über diesen Schicksalsschlag ausdrückte.



 The English mathematician John Wallis (1616-1703) was a friend of Isaac Newton. According to his diary, Newton once bragged to Wallis about his little dog Diamond.
"My dog Diamond knows some mathematics. Today he proved two theorems before lunch."
"Your dog must be a genius," said Wallis.
"Oh I wouldn't go that far," replied Newton. "The first theorem had an error and the second had a pathological exception."



The french scientist Ampere was on his way to an important meeting at the Academy in Paris. In the carriage he got a brilliant idea which he immediately wrote down ... on the wand of the carriage: dH=ipdl/r^2. As he arrived he payed the driver and ran into the building to tell everyone. Then he found out his notes were on the carriage and he had to hunt through the streets of Paris to find his notes on wheels.



Student:  "Er, excuse me, Professor von Neumann, could you please help me with a calculus problem?"
John:     "Okay, sonny, if it's real quick -- I'm a busy man."
Student:  "I'm having trouble with this integral."
John:     "Let's have a look."  (insert brief pause here)
          "Alright, sonny, the answer's two-pi over 5."
Student:  "I know that, sir, the answer's in the back -- I'm having trouble deriving it, though."
John:     "Okay, let me see it again." (another pause)
"The answer's two-pi over 5."
Student (frustrated):  "Uh, sir, I _know_ the answer, I just don't see how to derive it."
John:     "Whaddya want, sonny, I worked the problem in two different ways!"



Norbert Wiener wurde einmal auf dem Campus der Universität von einem Studenten angesprochen, der eine mathematische Frage hatte. Wiener blieb stehen und erörterte mit dem Studenten das Problem. Als sie fertig waren, fragte er: "Bin ich aus dieser Richtung oder aus der entgegengesetzten Richtung gekommen, als Sie mich ansprachen?" Der Student nannte ihm die Richtung, aus der er gekommen war. "Aha", sagte Wiener, "dann habe ich noch nicht gegessen.", und setzte seinen Weg in Richtung der Mensa fort. 



Hilbert hatte abends Gäste im Haus. Als die Abendgesellschaft bagann, kam Hilbert die Treppe herunter, jedoch ohne Krawatte. Seine Frau bemerkte es gerade noch rechtzeitig und schickte ihn sofort wieder ein Stockwerk höher, um sich einen Schlips umzubinden. Sie wartete, die Gäste warteten, doch wer nicht kam, war David Hilbert. Nach einer Dreivirtelstunde ging sie schliesslich ins Obergeschoss und sah ins Schlafzimmer. Da lag Hilbert seelenruhig im Bett und schlief.
Was war geschehen?
Hilbert war die Treppe hinaufgestiegen, ins Schlafzimmer gegangen, und hatte begonnen, sich die Jacke auszuziehen. Ganz in Gedanken hatte er sich dann immer weiter ausgezogen, Pyjama angezogen, und war, nichts natürlicher als das, ins Bett gegangen. Gäste und Abendgesellschaft hatte er vollkommen vergessen. 



Thomas Hobbes:
He was 40 years old before he looked on geometry; which happened accidentally. Being in a gentleman's library, Euclid's Elements lay open, and "twas the 47 El. libri I" [Pythagoras' Theorem]. He read the proposition .
"By God", sayd he, "this is impossible:" So he reads the demonstration of it, which referred him back to such a proposition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that truth. This made him in love with geometry. 



Before they immigrated to the US, the Einsteins endured the severe economic situation in post WWI Germany. Mrs. E saved old letters and other scrap paper for Albert to write on and so continue his work.
Years later, Mrs. Einstein was pressed into a public relations tour of some science research center. Dutifully she plodded through lab after lab filled with gleaming new scientific napery, The American scientists explaining things to her in that peculiarly condescending way we all treat non-native speakers of our own language.
Finally she was ushered into a high-chambered observatory, and came face to face with another, larger, scientific contraption. "Well, what's this one for?" she muttered.
"Mrs. Einstein, we use this equipment to probe the deepest secrets of the universe," cooed the chief scientist.
"Is THAT all!" snorted Mrs. E. "My husband did that on the back of old envelopes!" 



Carl Friedrich Gauss hatte nicht viel Sinn für die Musik, im Gegensatz zu seinem Freunde Pfaff (Pfaffsche Formen), der ein grosser Musikliebhaber war. Er versuchte Gauss immer wieder vergeblich zu einem Konzertbesuch zu bewegen.
     Schliesslich hatte sein Drängen Erfolg, und beide gingen ins Konzert, um sich die Neunte von Beethoven anzuhören.
     Nachdem die Sinfonie geendet hatte und der gewaltige Schlusschor verklungen war, fragte Pfaff seinen Freund Gauss um seine Meinung. Darauf antwortete Gauss: "Und was ist damit bewiesen?"



Mr. Hilbert has accepted an invitation to deliver a keynote address to a large engineering convention. The organizers subsequently learned that Hilbert was known for rather acerbic attitude towards engineering.
Greatly concerned they decided to go back and talk to him.
After beating around the bush for a while they managed to convey to him that they are worried that he may offend some people, and if he could sort of hold back during his speech.
When Hilbert realized what they were asking he grinned broadly and said, "You don't have to worry about that at all. How could I possibly offend anyone for mathematics and engineering have absolutely NOTHING IN COMMON". 



Professor von Neumann supposedly had the habit of simply writing answers to homework assignments on the board (the method of solution being, of course, obvious) when he was asked how to solve problems.  One time one of his students tried to get more helpful information by asking if there was another way to solve the problem. Von Neumann looked blank for a moment, thought, and then answered, "Yes.". 



Professor Norbert Wiener was in fact very absent minded.  The following story is told about him:  When they moved from Cambridge to Newton his wife, knowing that he would be absolutely useless on the move, packed him off to MIT while she directed the move.  Since she was certain that he would forget that they had moved and where they had moved to, she wrote down the new address on a piece of paper, and gave it to him.  Naturally, in the course of the day, an insight occurred to him. He reached in his pocket, found a piece of paper on which he furiously scribbled some notes, thought it over, decided there was a fallacy in his idea, and threw the piece of paper away.  At the end of the day he went home (to the old address in Cambridge, of course).  When he got there he realized that they had moved, that he had no idea where they had moved to, and that the piece of paper with the address was long gone. Fortunately inspiration struck.  There was a young girl on the street
and he conceived the idea of asking her where he had moved to, saying, "Excuse me, perhaps you know me.  I'm Norbert Wiener and we've just moved.  Would you know where we've moved to?"  To which the young girl replied, "Yes daddy, mommy thought you would forget."
The capper to the story is that I asked his daughter (the girl in the story) about the truth of the story, many years later.  She
said that it wasn't quite true -- that he never forgot who his children were!  The rest of it, however, was pretty close to what
actually happened... 



Enrico Fermi, while studying in college, was bored by his math classes. He walked up to the professor and said, "My classes are too easy!" The professor looked at him, and said, "Well, I'm sure you'll find this interesting."
Then the professor copied 9 problems from a book to a paper and gave the paper to Fermi. A month later, the professor ran into Fermi, "So how are you doing with the problems I gave you?"
"Oh, they are very hard. I only managed to solve 6 of them."
The professor was visibly shocked, "What!? But those are unsolved problems!" 



Surely, Professor Bohr, you do not really believe that a horseshoe over the entrance to a home brings good luck?
  No, I certainly do not believe in this superstition. But you know, they say it brings luck even if you don't believe in it.
-- A house visitor and Niels Bohr 



Der Mathematiker David Hilbert war für sein schwaches Kopfrechnen berühmt. Einmal stand er in seiner Vorlesung vor dem Problem, 8 mal 7 ausrechnen zu müssen:
     "Nun meine Herren, wieviel ist wohl 8 mal 7?"
     "55?"
     Ein anderer: "57!"
     Darauf Hilbert: "Aber meine Herren, die Lösung kann doch nur entweder 55 oder 57 sein!"



The following problem can be solved either the easy way or the hard way:

Two trains 200 miles apart are moving toward each other; each one is going at a speed of 50 miles per hour.  A fly starting on the front of one of them flies back and forth between them at a rate of 75 miles per hour.  It does this until the trains collide and crush the fly to death.  What is the total distance the fly has flown?

The fly actually hits each train an infinite number of times before it gets crushed, and one could solve the problem the hard way with pencil and paper by summing an infinite  series of distances.  The easy way is as follows:  Since the trains are 200 miles apart and each train is going 50 miles an hour, it takes 2 hours for the trains to collide. Therefore the fly was flying for two hours.  Since the fly was flying at a rate of 75 miles per hour, the fly must have flown 150 miles.
That's all there is to it.

When this problem was posed to John von Neumann, he immediately replied, "150 miles."
"It is very strange," said the poser, "but nearly everyone tries to sum the infinite series."
"What do you mean, strange?" asked Von Neumann.  "That's how I did it!" 



(I'm not sure if the following one is a true story or not)
The great logician Bertrand Russell (or was it A.N. Whitehead?) once claimed that he could prove anything if given that 1+1=1.
So one day, some smarty-pants asked him, "Ok.  Prove that you're the Pope."
He thought for a while and proclaimed, "I am one.  The Pope is one.  Therefore, the Pope and I are one." 



Hilbert über die Physiker:
     Die Physik ist für die Physiker eigentlich viel zu schwer. 



"Paper or plastic?"
"Not 'Not paper AND not plastic!!'"
(Augustus DeMorgan in a grocery store) 



Hay una anécdota que se cuenta, de cuando Einstein hizo una gira por todas las universidades de los Estados Juntitos, para dar a conocer su trabajo en la Teoría de la Relatividad, a principios del siglo XX.
Einstein tenía un enorme pavor a los aviones, probablemente justificado en aquella época, por lo que se agenció un chófer para que le llevara de ciudad en ciudad.
En uno de aquellos viajes, el conductor vio a Einstein bastante agotado, y le propuso lo siguiente:
    - De tanto escucharle en sus conferencias sobre su Teoría, creo que podría permitirme, señor, que yo la diera en su lugar, si no le importa.
Al fin y al cabo aquí en Louisiana nadie conocerá muy bien su rostro. Albert aceptó con una risilla burlona. Se detuvieron a medio camino en un Motel de mala muerte y se cambiaron sus trajes, y las posiciones dentro del coche. Cuando llegaron a la universidad de esa ciudad, los decanos y altos cargos de la misma recibieron calurosamente al anónimo chófer que, dicho sea de paso, se las arregló con gran finura de modales para con todos los que allí estaban. El chófer científico pre-premio Nobel de Física entró después de que toda la comitiva se acomodara en los asientos del salón de actos de la universidad, y tomó asiento en una butaca lateral, no muy lejos de su colega.
Resultó que la conferencia fue expuesta al pie de la letra por el iletrado chófer, que debía de tener una magnífica memoria. Einstein sonreía satisfecho en su butaca, fumando un cigarrillo de esos americanos. Al llegar al final, sin embargo, el vicedecano en funciones de la universidad de Louisiana se levantó de su mullido asiento y levantó el brazo para formular una pregunta. El émulo del genio mantuvo la expresión sonriente a medida que escuchaba una pregunta que sin duda había sido meditada a conciencia y anotada para que no se olvidara ningún detalle. Einstein se irguió en su asiento, pues estaba convencido de que el
chófer no sabría contestar absolutamente nada, pues se trataba de una cuestión puramente matemática, pero de gran envergadura.
Pero, sorprendido, escuchó lo que dijo el impostor:
- Esa pregunta, señor vicedecano; esa pregunta se la puede responder hasta mi chófer, que ahí se sienta.
La gente aplaudió al chófer, mientras éste subía al escenario y tomaba las riendas de una contestación llena de genialidad y fundamento, que hizo que se elevaran vítores por toda la sala, mientras el señor vicedecano ahuecaba el ala poco después, totalmente enrojecido por la ira y la vergüenza propia.



Prof. Manfred Schneider rechnet einen Beweis.
Die vorletzte Zeile lautet "2 - 7". Er schreibt als letzte Zeile "= -3" hin, der Hörsaal lacht.
Er stutzt, wischt es weg und schreibt "= -1", woraufhin der Saal tobt.
Er wischt es erneut weg und schreibt "< 0", was für den Beweis auch vollkommen ausreichte.