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The proof is in the pudding.

Opening a copy of The Mathematical

Intelligencer you may ask yourself

uneasily, "What is this anyway--a

mathematical journal, or what?" Or

you may ask, "Where am I?" Or even

"Who am I?" This sense of disorienta-

tion is at its most acute when you

open to Colin Adams's column.

Relax. Breathe regularly. It's

mathematical, it's a humor column,

and it may even be harmless.

Column editor's address: Colin Adams, Department of Mathematics, Bronfman Science Center, Williams College, Williamstown, MA 01267 USA e-mail: Colin.C.Adams@williams.edu

Rumpled Stiltskin Colin Adams

O nce upon a time there was a topol- ogist who lived with his daughter

in a tiny office in the Math Building at the University of Chicago. One day the Chairman of the department happened to stop to talk to a colleague just out- side the door of the topologist's office.

"The hiring season looks tough," said the Chairman, a bit discouraged. "I hope we can find someone extraordinary."

The topologist, who was barely known to the Chair, stepped out of his office. "Pardon me," he said timidly. "I hate to interrupt. But I know of an extraordinary mathematician. She can turn coffee into theorems."

"Really?" said the Chair. "And who is this mathematician?"

"She is my daughter," said the topol- ogist.

"Then send her to my office this af- ternoon," said the Chair.

That afternoon, the topologist's daughter went to the Chair's office. She was quite apprehensive, as she had no idea how to turn coffee into theorems. "Follow me," said the Chair as he led her to the department lounge.

"Here you see a coffee maker, and three pots of coffee. I want you to turn the three pots of coffee into theorems by morning. If you do not, then I will see to it that the only job you ever get is at a regional university with high research expectations and a teaching load of four courses per semester."

With that he left the lounge, locking the door behind him.

The poor girl was disconsolate. She fell sobbing on the couch. "Oh, what ever will I do?" she cried. "My career is over before it has even started."

Suddenly, as if by magic, the door to

the lounge swung open, and in walked a squat, disheveled creature, with long matted beard and hair. He was a squat man dressed in a dirty t-shirt, jeans, and an even dirtier red sports coat. He seemed surprised to see her.

"What are you doing here?" he asked.

"Oh, the Chair has said that I must turn this coffee into theorems, or he will destroy my career."

"And you don't know how to turn coffee into theorems?" asked the little man, a smile playing across his lips.

"Oh, no. I have no idea how. My fa- ther just said I could to impress the Chair."

"And what will you give me if I turn this coffee into theorems?" said the un- sanitary fellow.

"Ummm, how about this mint con- dition copy of Stewart's Calculus book?" she suggested, pulling the book from her briefcase.

"Let's see," he replied. "Is it the new edition? I could get 50 bucks for that. You got a deal."

And with that, the strange man gulped down all three pots of coffee. His bloodshot eyes began to glow. His eyebrows started to twitch. Then he sat down before a pad of paper and wrote furiously for three hours. When he was finished, the pages of three pads of pa- per were covered with the most beau- tiful lemmas the girl had ever seen.

"That ought to do the trick," said the little man, and with that, he scooped up the calculus book and was gone.

The next morning the Chair un- locked the door, expecting to find the girl crying or sleeping, with nothing to show for her night. But his jaw dropped when he saw the scribblings on the pad. "This is really quite good," he said.

"Thank you," said the girl timidly. "Can I go now?"

"What, are you kidding? This is the beginning of some really good mathe- matics. But you need to fill in the de- tails. Flesh out the theory. Come back this evening."

2 2 THE MATHEMATICAL INTELLIGENCER �9 2004 SPRINGER-VERLAG NEW YORK

When the girl arrived that night, the Chair pointed to six pots of coffee sit- ting on the table. "If you don't turn this coffee into theorems, I will make sure the only work you get is as a recitation instructor, teaching fifteen problem sessions a week for large calculus lec- tures." And again, he locked her in the lounge.

The girl fell sobbing on the couch. But she said to herself, if the little man can do it, why can't I? With that she went over and poured herself a cup of the steaming brown liquid. She took a sip and spat it out immediately. "Ahhrgh," she said, "This tastes like it has been sitting in the pot for the last 12 hours"--which in fact it had.

But then the door swung open again, and in walked the little man. His jeans were torn at the knee and his teeth ap- peared never to have experienced the friction of a toothbrush.

"Back again, are we?" he said. "Yes, the Chair said I must turn

these six pots of coffee into theorems by morning, or he will turn me into a recitation instructor."

"And what, pray tell, will you give me, if I do it for you?"

The girl thought for a moment and then pointed to her computer brief- e a s e .

"How about my laptop?" she asked hopefully.

She handed it to the man. "Hmmm, looks like a Mac Titanium Power PC Gd, 800 MegaHertz, with one megabyte L3 and 256K L2 cache. You got a deal."

So again, he gulped down the cof- fee, and set to work. Six hours later, he had filled six pads of paper with the- orems and proofs.

"This should do it," he said. And grabbing up the laptop, he disappeared out the door.

When the Chair arrived the next morning, he was flabbergasted by the beauty of the mathematics on the pads.

"This is really good stuff," he said enthusiastically. "These are the germs for a whole new theory. I am really im- pressed."

"Good," said the girl nervously. "Now can I go?"

"Yes, but you must come back tonight," said the Chair. "You have more work to do."

That evening, the Chair sat her down before twelve pots of coffee.

"If you don't turn this coffee into theorems," he threatened, "I will make you into a permanent grader for our remedial algebra course. But, if you do succeed, I will give you a tenure-track position on the faculty here at Chicago." Then he turned and left the lounge, locking the door be- hind him.

The girl fell on the couch sobbing. It was too much to hope the smelly man would be back to help her once more. And besides, she had nothing left to give him.

Suddenly the doorknob turned and in he walked.

"Still trying to turn coffee into the- orems, are we? Haven't learned how to do it yet?"

"Oh, no," she said. "I can't do it. And the Chair is going to make me into a permanent grader. Oh, woe is me."

"And what will you give me if I do it for you?" asked the hair-encumbered individual.

"I don't know," said the girl. "I don't have anything left to give."

The little man grinned mischie- vously. "Oh, I think you do," he said. "I want you to give me your first-born theorem."

"What do you mean?" asked the girl. "The first theorem that you prove

yourself, I want you to give it to me, to claim as my own."

Now the topologist's daughter knew that if she said no, she wouldn't ever have the opportunity to create her own theorems, anyway. So there wouldn't be anything to lose. On the other hand, if she did survive all this nonsense, and had a career as a mathematician, what was one theorem more or less? So she agreed. The little man laughed delight- edly.

"Oh, yes we have a bargain," he laughed as he danced about the room. Then he gulped down all twelve pots of coffee, and worked through the en- tire night, finishing just before day- break.

"Remember our deal," he said as he slipped out the door, leaving twelve pads of paper filled with mathematics on the table.

When the Chair arrived, he was

stunned by the level of work that he s a w .

"You have a job, a tenure-track job," said the chair, shaking her hand en- thusiastically.

So the young woman began her career at Chicago. She was an able teacher, and enjoyed that aspect of her job. But at first she found it difficult to work on her research, as her other du- ties were so numerous.

But one day, she attended a number theory seminar. The speaker gave a dis- cussion of Catalan's Conjecture, which says that the only two consecutive powers of whole numbers are the in- tegers 8 and 9. She found the question quite fascinating. Soon, she was spend- ing all her time working on the prob- lem. She would have worked even more but sometimes exhaustion over- came her. Finally, one evening, want- ing to continue her work but unable to keep her eyes open any longer, she stumbled into the department lounge and quickly swallowed a cup of coffee, before she had a chance to gag.

Suddenly, she felt awake. Within minutes, the caffeine was coursing through her system, and her neurons seemed to be firing every which way. She worked all that night and by morn- ing, she had proved Catalan's Conjec- ture.

Although she was tired and in great need of sleep, she decided to wait un- til the Chair arrived at 8:00 to tell him the good news. At 7:30, just as her eyes were closing with exhaustion, the door to her office swung open, and the little man, whom she had not seen for the last two years, bounded in.

I am here to collect my debt," he said.

"Oh no," pleaded the assistant pro- fessor. "It's too good. You can have my next one."

"I don't want your next one," said the diminutive hairball. "I want this one."

"Please, please, don't take it. It has taken me all this time to learn how to turn coffee into theorems. I can't give it up."

"I'll tell you what," said the little man, an evil grin on his face. "If you can guess my name, I will not take your theorem. And I will give you three days

VOLUME 26, NUMBER 1, 2004 2 3

to guess it." He laughed then and scooted out of the office.

The young woman thought to her- self that this couldn't be so hard. After all, he had made no rules about the guessing. She could guess as many names as she wanted. Eventually she would get it right.

The next morning, the door to her office opened and in popped the minor mutant.

"And what do you guess is my name?" he asked.

"Is it Pythagoras?" she queried. "Is it Zeno? Is it Euclid?"

"No, no, and no." He hopped de- lightedly from one foot to the other.

"Is it Nicomachus? Is it Diophantus? Is it Pappus?"

"Not even close." "Is it Hbonacci? Is it Newton? Is it

Liebniz?" "Ha." "Is it Bernoulli, or Euler, or Lagrange? "No, no, and no again. You will have

to do better than that." And with that he was gone.

That day, the young woman searched for every name she could think of. She asked others around the department for any other names they might know.

When the little man arrived the next morning, she asked, "Is it Gauss? Is it Cauchy? Is it M6bius?"

"No, no, and no," he laughed, hardly able to contain himself.

"Is it Lobachevsky? Dirichlet? Liouville?"

"Be serious." "How about Weierstrass? Cayley?

Hermite? Cantor? Dedekind? Bel- trami?"

"No, no, no, no, no, no." "What about Lie, or Poincar6 or

Peano or Hurwitz or Hilbert or Cartan?" "Give me a break." "Maybe Zermelo, Dickson, or

Lebesgue?" "No, no, and no. Tomorrow is your

last chance." And with that, he disap- peared out the door.

The young professor was crushed. She didn't know what to do.

"Oh, woe is me," she cried. All that day, she wrung her hands. That evening, as she went to get a tissue from the bath- room to dab her tears, she heard a voice singing from within the Men's Room.

"I am so happy. I could sing, as I shower in the sink.

For she doesn't realize who I am, And how with Chicago I link. She doesn't know that I live in the

Lounge, She doesn't know my game. And she doesn't know the most

important part, Rumpled Stiltskin is my name."

She immediately went to her fa- ther's office.

"Pop," she said, "Have you ever heard of someone named Rumpled Stiltskin?"

"Oh sure, everybody knows about Rumpled Stiltskin. One of the most brilliant minds ever to grace this

campus." "Who is he?" "Who was he is the more appropri-

ate question. Bob Stiltskin was a gradu- ate student here thirty years ago. A real star. But he got hooked on Catalan's Conjecture. Spent all his time trying to prove it. Couldn't bring himself to solve an easier problem and get a Ph.D."

"So what happened?" "After eight years, they cut his sup-

port, and threw him out of the program. But he still hung around. Used to sleep in the Math Lounge. Somehow he had gotten hold of a key. About ten years ago, he disappeared entirely. Nobody knows where he went. But there are ru- mors of a sighting every now and then."

"And why is he called Rumpled Stiltskin?"

"Well, he always wore the same red sports coat, and calling it rumpled is being generous."

The next morning, the pungent per- son sprang into her office, and said, "Last chance. What's my name?"

The girl smiled and said, "Is it Ve- blen, or Noether, or Sierpiiiski?"

"No, no, and no again." "Is it Birkhoff, or Lefschetz, Little-

wood, or P61ya?" "No, no, nope, and no." "Maybe Ramanujan or Banach,

Cech, or Bloch?" "No, oh no, oh no, and no." "Klein, Wiener, Nevanlinna, or

Urysohn?" "Not even close." "Artin or Zariski?" "Double no." "Church or Whitehead?" "No and again a big no. Looks like

you are plumb out of luck." He was grinning from ear to ear.

"I guess I don't know," she said pausing for a second. "Unless of course, perhaps, it is Rumpled Stilt- skin."

The odoriferous oddball froze, stunned for an instant. "How could y o u ? . . , how did you?" he spluttered.

"I guess I keep the proof of Catala- nis conjecture after all," she said.

"Arghhh," screamed the minute mis- creant, his face turning as red as his jacket. He stomped his feet and gnashed his teeth, and pulled forcefully on his matted hair. His eyes rolled up in their sockets, and then he stormed out of the office, never to be seen at the University of Chicago again.

Since then, every once in a while reports filter down from the Univer- sity of Illinois at Chicago of coffee pots found empty just minutes after they had been full. And at Northwest- ern, department copies of Stewart's Calculus disappear at an alarming rate.

The young professor went on to a very successful career at Chicago. She and her father wrote some joint papers, on the basis of which her father was promoted to an office of reasonable size. And although she did drink coffee for the next five years, she switched to herbal tea after receiving tenure. And even then, the theorems kept coming.

2 4 THE MATHEMATICAL INTELLIGENCER