**Richard Bellman**

The book Dynamic Programming by Richard Bellman is an important, pioneering work in which a group of problems is collected together at the end of some chapters under the heading “Exercises and Research Problems,” with extremely trivial questions appearing in the midst of deep, unsolved problems. It is rumored that someone once asked Dr. Bellman how to tell the exercises apart from the research problems, and he replied: “If you can solve it, it is an exercise; otherwise it’s a research problem.”

At parties, when asked what he did for a living, Bellman would always reply “I am a tennis coach.” When asked why he invariable did this, he remarked, “I get tired of the automatic response to the statement that I am a mathematician.”

**Abram Besicovitch**

In 1950, on his fifty-ninth birthday, Besicovitch was elected to the Rouse Ball Chair of Mathematics, succeeding the first holder J. E. Littlewood. Twenty-three years earlier, on his thirty-sixth birthday, thinking that the years of greatest intensity of life were passing, he had said “I have had four-fifths of my life.”

When J. C. Burkill reminded him of this in 1950, he received a postcard which read “Numerator was correct.”

*Told by S. J. Taylor in “Abram Samoliovitch Besicovith,” Bull. of the London Math. Soc. 7 (July 1975) 194.*

**George Dantzig**

George Dantzig, while studying in college, arrived late to one of Neyman’s graduate math classes. On the blackboard there were two problems, clearly the homework problems assigned for the week. Dantzig copied them down, and worked on them for days and days. Fully a month later, Dantzig finally turned the problems into Neyman, remarking that they had been a little harder to do than usual.

About six weeks later, at 8 am on a Sunday morning, Dantzig and his wife were awaken by the sound of Professor Neyman banging loudly on their apartment door. Bleary-eyed, Dantzig opened the door, through which Neyman rushed in carrying papers, clearly excited: “I’ve just written an introduction to one of your papers. Read it so I can send it out right away for publication.”

“What are you talking about?”

“Those problems on the board weren’t homework problems. They were famous unsolved problems in statistics!”

George Dantzig went on to become the “Father of Linear Programming.”

*Various versions of this story circulate around, usually with better known mathematicians and physicists as the protagonists, with 6 or 8 as the usual number of unsolved problems. I think this — the real story — is just as cool; you can find it in “An Interview with George. B. Dantzig: the Father of Linear Programming,” by Donald J. Albers, Coll. Math. J. 17 (September 1986) 301.*

**Paul Adrien Maurice Dirac**

Dirac had a horse shoe over his desk. One day a student asked if he really believed that a horse shoe brought luck. Professor Dirac replied, “I understand that it brings you luck if you believe in it or not.”

Dirac, while still a student, attended a mathematical congress where the following problem was proposed:

Three fisherman were fishing on a secluded island. The fish briskly gobbled the bait; the fisherman were so absorbed that they did not notice that night had come and did not realize till too late what a mountain of fish they had hooked. So they had to spend the night on the island. Two fisherman quickly fell asleep, each nestled down under his boat, but the third had insomnia and decided to go home. He did not wake his comrades, but divided all the fish into three parts. There proved to be one extra fish. After a moment’s thought, he threw it into the water, took his hare, and went home.

In the middle of the night, the second fisherman woke up. He did not know that the first fisherman had already left and also divided all the fish into three and, as before, there was one fish left over. As before, the fisherman threw the extra fish in the water, took his share, and went home.

By early morning, the third fisherman awoke. He did not notice that the other two fisherman had left, so he too divided all the fish into three and, as before, there was one fish left over. As did his comrades before him, the fisherman threw the extra fish in the water, took his share, and went home.

The problem was to determine the least number of fish that the fisherman could have caught. Dirac thought about the problem for a moment before coming to an answer: there were (-2) fishes.

His reasoning? After the first fisherman carried out the antisocial action of throwing a fish into the water there were -2-1 = -3 fish. The he went, carrying in his bag -1 fish, and there were -3-(-1) = -2 fish left behind. The other two fisherman merely repeated this procedure.

*Related by V. Berezinsky in his article “How a theoretical physicist works,” from Paths into the Unknown No. 2, 1968.*

**Albert Einstein**

Albert Einstein, who fancied himself as a violinist, was rehearsing a Haydn string quartet. When he failed for the fourth time to get his entry in the second movement, the cellist looked up and said, “The problem with you, Albert, is that you simply can’t count.”

**Ia I Frankel**

It is said that in the Physical Theoretical Institute in the 30s, a certain experimenter caught up with him in a corridor and showed him a curve obtained from an experiment. After a minute’s thought Ia I gave an explanation for the form of this curve. However, it was explained that the curve had accidentally been turned upside down. The curve was put into place and having thought it over he explained this behavior too.

*Related by V. Berezinsky in his article “How a theoretical physicist works,” from Paths into the Unknown No. 2, 1968.*

**Evereste Galois**

Evariste Galois was not only a mathematical genius but also a dedicated revolutionary. Ironically, he proved that many problems cannot be solved by radicals.

**Jacques Hadamard**

At the Bologna Congress, the meetings started in Bologna and ended in Florence. That’s about a three-hour train ride and for this there was a special train. Hadamard was placed in a compartment of particularly noisy mathematicians, but he himself was tired and wanted to have some peace. Rather than simply try and ask the group to settle down (and since they were easily excitable mathe,aticians, this would likely be ineffective anyway), he instead posed aloud in the compartment a puzzle — a rather difficult problem.

Very quickly, everyone started working on the puzzle, and it suddenly became quiet so Hadamard could sleep.

*Polya was one of the mathematicians in the compartment, and he tells this story in A Polya Picture Album, Boston: Birkhauser, 1987, p. 87.*

**Godfrey H. Hardy**

Hardy once said that he could prove anything if it given a contradiction to begin with. McTaggart denied the consequence: “if 2+2=5, how can you prove that I am the pope?” Hardy replied: “if 2+2=5, 4=5; subtract 3; then 1=2; but McTaggart and the pope are two; therefore McTaggart and the pope are one.”

A famous mathematician (I don’t know who) was to give a keynote speech at a conference. Asked for an advance summary, he said he would present a proof of Fermat’s Last Theorem — but they should keep it under their hats. When he arrived, though, he spoke on a much more prosaic topic. Afterwards the conference organizers asked why he said he’d talk about the theorem and then didn’t. He replied this was his standard practice, just in case he was killed on the way to the conference.

Actually, the previous story is true, although for prosaic reasons, Fermat’s Last Theorem is better known and hence delivers the punchline better. But the real story is just as amusing.

In fact, the story is actually about Hardy and the Riemann Hypothesis.

Hardy had a running feud with God. In Hardy’s view, God had nothing more important to do than to frustrate Hardy. This lead to an insurance policy for Hardy one time when he was trying to get back to Cambridge after a visit to Bohr in Denmark. The weather was bad and there was only a small boat available. Hardy thought there was the real possibility the boat would sink.

So he sent a postcard to Bohr saying: I proved the Riemann Hypothesis. –G. H. Hardy. That way, if the boat sank, everyone would think that Hardy had proved the Riemann Hypothesis. God could not allow so much glory for Hardy, and so he could not allow the boat to sink.

And lo and behold, it did not. Hardy was saved.

*This version of the story is told by George Poyla; c.f. A Polya Picture Album, G. L. Alexanderson (ed.), Boston: Birkhauser, 1987, p. 89.*

Hardy was also highly opinionated. In his workings with Hardy, Polya once had an idea of which Hardy approved. But afterwards, Polya did not work it out sufficiently hard to carry out the idea, and Hardy disapproved. Of course, he did not say so, at least not directly.

However, soon afterwards, he, Polya, and Riesz went to a zoological garden in Sweden. While they were at the bear cage, the bear sniffled the lock of the cage, hit it with his paw, growled a little, and finally turned around and walked away.

At this point, Hardy elbowed Riesz and replied, “He is like Polya! He has excellent ideas, but does not carry them out!”

*Told by George Poyla in “Some Mathematicians I Have Known,” Amer. Math. Monthly 76 (August-September 1969) 752.*

**David Hilbert**

Hilbert was very absent-minded (what famous mathematician isn’t?). During one of tha parties he held at his house with his wife, Frau Hilbert noticed that her husband forgot to put on a fresh shirt. “David,” she said sternly, “go upstairs and put on another shirt.” David, as befitting a married man, meekly obeyed and went upstairs.

However, he did not come back. Five minutes pass… ten minutes pass… and yet David failed to reappear downstairs to greet his guests. Finally, Frau Hilbert went upstairs to see what was taking her husband so long. She entered the room and found him tucked in bed, quietly asleep. You see, it was the natural sequence of things: take off the coat, take off the tie, take off the shirt, and so on, and then go to bed.

*Told by George Poyla in “Some Mathematicians I Have Known,” Amer. Math. Monthly 76 (August-September 1969) 752.*

**Mark Kac**

During an oral examination by the Polish mathematician Mark Kac, a student was asked the behaviour of the Rieman zeta function zeta(s) at s=1. When the student had no idea, Kac gave the hint, “Think of me.”

The anser came immediately. “Aah, it has a simple pole!”

**Paul Levy**

Alfred Errera was a Belgian and a student of Landau’s. He was also a multimillionaire (but then again, so was Landau). To be invited to his house for dinner was quite something: the dinner was always very elaborate, with many courses and different wines, footmen and waiters were there to answer upon each guest, and so one.

Anyway, Errera hosted a part in honor of Levy, who was (of course) notoriously absent-minded. The next day, Levy and Errera met on the street, and Errera (who was very polite) said: “I had great pleasure last evening.”

“Ah, really?” said Levy. “And where were you last evening?”

*Another story told by Polya in the Polya Picture Album.*

**Lev Loytiansky**

Lev Loytiansky was a mathematician in the Soviet Union in the 30s and 40s. Loytiansky organized the seminar in hydrodynamics in his University. Among the regular attendees there were two men in the uniform, obviously military engineers. They never discussed the problems they were working on.

Then one day they ask Loytiansky to help with a math problem. They explained that the solution of a certain equation oscillated and asked how they should change the coefficients to make it monotonic. Loytiansky looked on the equation and said “Make the wings longer!”

**H. A. Rowland**

It seems that Rowland was called on to testify as a science expert in a court case. In exploring his competetnce an attorney asked him who was the foremost American physicist. Unhesitatingly, Rowland answered, “I am.” Later a friend reproached him gently for his immodesty. Rowland’s response was, “Well, you have to remember, I was under oath.”

*Told by Paul Kirkpatrick in A Random Walk in Science, (New York) 1973.*

**Bertrand Russel**

Russell to Whitehead: “My Godel is killing me!”

Russell was once asked if he believed in God. He replied “Yes. Up to isomorphism.”

Around the time when Cold War started, Bertrand Russell was giving a lecture on politics in England. Being a leftist in a conservative women’s club, he was not received well at all: the ladies came up to him and started attacking him with whatever they could get their hands on. The guard, being an English gentleman, did not want to be rough to the ladies and yet needed to save Russell from them.

He said, “But he is a great mathematician!” The ladies ignored him.

The guard said again, “But he is a great philosopher!” The ladies ignored him again.

In desperation, finally, he said, “But his brother is an earl!” Bert was saved.

**Allen Shields**

Shields like to play with words. His letters were spiced with all sorts of intentional and outrageous distortions. A Banache spave was sometimes called a Bone Ache space. He referred to Chubby Chef’s inequality. A proposed course in measure theory with modest prerequisites became a course on the LaVague integral. One page of a manuscript sent to Peter Duren contained a sentence that read “Without loss of genitalia, we may assume…”

When asked why he wrote such things, Shields said that he was just checking if anyone was reading them.

*Told by Peter Dureh in “In Remembrance of Allen Shields,” Math. Intell. 12 (Spring 1990) 12.*

**Waclaw Sierpinkski**

Sierpinski was always rather absent-minded. On one occasion, we had to move into a new residence.. His wife wife didn’t trust him very much, so when they stood down on the street with all their things, she said “Now, you stand here and watch our ten trunks, while I go and get a taxi.”

She left and left him there, gazing off into space and humming absently. Some minutes later she returned, presumably having called for a taxi.

Said Sierpinski (possibly with a glint in his eye): “I thought you said there were ten trunks, but I’ve only counted to nine.”

Panicked that some of their possessions might have been stolen from under their noses, his wife demanded “No, they were TEN!”

“No, no, no! Just count them. 0, 1, 2, …”

**Hugo Steinhaus**

When Steinhaus failed to attend an important meeting of the Committee of the Polish Academy of Sciences in 1960, he received a letter chiding him for “not having justified his absence.” He immediately wired the President of the Academy that “as long as there are members who have not yet justified their presence, I do not need to justify my absence.”

*Told by Mark Kac in “Hugo Steinhaus — A Remembrance and a Tribute,” Amer. Math. Monthly 81 (June-July 1974) 578.*

Steinhaus’ seminar course had a small attendance and one day only two students were present. Steinhaus went through the lecture without so much as a glance at the depleted audience, and at the end, one of the students asked him what was the minimal number of listeners to whom he would feel compelled to lecture.

“*Tres facit collegium*,” said he. “Three make a college.”

The very next day, the other student failed to attend, leaving just the one student present with Steinhaus. Again, Steinhaus went through the lecture as before, untile the student interrupted him and asked jokingly, “What about the *tres facit collegium*?”

“God,” said Steinhaus, “is always present,” and continued to lecture.

Steinhaus was, of course, an avowed atheist.

*The student is question was Mark Kac, the story is related in Enigmas of Chance, New York: Harper and Row, 1985, p. 38.*

**Norbert Wiener**

One day, a student saw Wiener in the post office and wanted to introduce himself to the famous professor. After all, how many M.I.T. students could say that they had actually shaken the hand of Norbert Wiener? However, the student wasn’t sure how to approach the man. The problem was aggravated by the fact that Wiener was pacing back and forth, deeply lost in thought. Were the student to interrupt Wiener, who knows what profound idea might be lost? Still, the student screwed up his courage and approached the great man. “Good morning, Professor Wiener,” he said.

The professor looked up, struck his forehead, and said “That’s it: Wiener!”

Norbert Wiener was lecturing to a class of students. As he wrote something on the board, he said to the class “Of course, this is immediately obvious.”

Upon seeing the blank stares of the students, Wiener turned back to contemplate what he had just written. He began to pace back and forth, deep in thought.

After about 10 minutes, just as the silence was beginning to become uncomfortable, he brightened, turned to the class and said, “Yes, it IS obvious,” and continued with the lecture.

Norbert Wiener bumped into a student on the street one day, and proceeded to engage him in a theoretical discussion. At the end of the interaction, the student was startled to hear the professor ask, “Which way was I headed when we met?”

The student points, saying, “You were going that way, sir.”

“Good,” said Wiener, “That means I’ve had my lunch.”

When Wiener 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?”

“Yes daddy. Mommy thought you would forget.”

*This story was originally told by Steven G. Krantz in “Mathematical Anecdotes,” Math. Intell. 12 (Fall 1990) 38. However, the version above is my personal favorite variation of it.*

**Theodore von Karman**

Karman held a double position: professor at Aachen in Germany and lecturer at Cal tech in Pasadena. As an important aeronautical engineer, he was consulted to several airlines, and so he got free transportation whenever he found an unoccupied seat on the plane of one of these airlines. So he commuted more or less regularly between Aachen and Pasadena, and gave similar lectures at both places.

Once, he was somewhat tired when he arrived in Pasadena, but being a trooper, started lecturing. That was not so difficult anyway: he had the notes which he also used in Aachen. He talked, but as he looked around he had the impression that the faces in the audience looked more blank than usual.

And then he caught himself: he had been speaking in German! He became very upset. “You should have told me — why did you not tell me?”

At length, one student spoke: “Don’t be upset, Professor. You may speak German, you may speak English; we will understand just as much.”

*Karman himself liked to tell this story.*

**John von Neumann**

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!”

*Told by Paul Halmos, in “The Legend of John von Neumann,” Amer. Math. Monthly 80 (April 1973) 386.*

Von Neumann had the habit of simply writing answers to homework assignments on the board when he was asked how to solve problems. (The method of solution was, of course, obvious.)

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”.

Von Neumann is quoted as saying the following to a grduate student. “Young man, in mathematics you don’t understand things, you just get used to them.”

**Antoni Zygmund**

Once, when walking past a loungue in the University of Chicago that was filled with a loud crowd watching TV, Zygmund asked one of his students what was going on. The student told him that the crowd was watching the World Series, and explained to him some of the features of this baseball phenomenon.

Zygmund thought about it all for a few minutes an commented, “I think it should be called the World Sequence.”

*From A Century of Mathematics in America, Part III, Peter Duren (ed.), Providence, RI: AMS 1989, p. 348.*

**Other legends**

The Stanford Linear Accelerator Center was known as SLAC, until the big earthquake, when it became known as SPLAC.

SPLAC? The Stanford Piecewise-Linear Accelerator.

There exists a Harvard student organization called PCC (Peer Contraceptive Counselors) who hand out free prophylactics to students …and go into freshman dorms, armed with bananas, to demonstrate their proper use. Some joker posted one of their flyers in the math department computer lab. The flyer read, “Do You Dream About Latex?”

[ If you have to ask, you don’t understand. ]

This appeared in the euology of a certain mathematician: “He made a lot of mistakes, but he made them in a good direction. I tried to copy this, but I found out that it is very difficult to make good mistakes.”