Mathematically Bent Colin Adams, Editor

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 disorientation 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

CSI: MSRICOLIN ADAMS

IIwas in Berkeley, having just given a seminar on fluxionsat the university. Only a handful of people had shownup, including one calculus student who had stumbled

into the wrong room and didn’t seem to know the difference,and an emeritus professor who kept raising his hand to ask ifanyone had seen his underwear. The seminar organizerhadn’t even come, claiming in an e-mail he had to clean hisgutters. After finishing my talk, I asked for questions. Therewas a long silence and then the emeritus professor leaptup and ran for the door. The rest of the group filteredout without giving me even a desultory applause. Feelingdejected, I wandered over to Telegraph Avenue. Pickingfrom among the dozens of coffee houses, I ordered acappuccino latte, and settled into a chair opposite a studentreading Hungerford’s Algebra.

‘‘That’s a big book,’’ I said, hoping for a little intellectualbanter. ‘‘I’ll show you my theorem if you’ll show me yours.’’

She sighed, slapping closed the book.‘‘This I don’t need,’’ she said, as she got up and walked

away. I sipped nonchalantly on my latte. A postdoc satdown at the next table with a copy of Russell’s PrincipiaMathematica. I kept my mouth shut.

Suddenly, my cell phone buzzed. It was Schmishschmitt,an old grad-school friend who had washed out of gradschool, but ended up on the police force. He had the mathbeat.

‘‘Hello, Mangum,’’ he said. That’s me, Dirk Mangum, P.I.That’s right. I’m a principal investigator on an NSF grant.

‘‘I thought I would find you here.’’‘‘You called me on my cell phone, Schmishschmitt, so

you shouldn’t be too proud of the fact you found me.’’‘‘True,’’ said Schmishschmitt. ‘‘Nevertheless, I have an

interesting case for you.’’‘‘What makes you think I would find it interesting?’’ I

replied.‘‘It involves MSRI.’’MSRI. Math lingo for the Mathematical Sciences Research

Institute, way up in the hills overlooking Berkeley. Thegolden citadel of mathematics. A building dedicated to onething and one thing only. Math all day, every day.

The founders of MSRI had had a simple dream. Plunk abunch of mathematicians down all by themselves amongthe eucalyptus trees, without any distractions but a beau-tiful view of the bay. Then they would have nothing betterto do than create great mathematics. Unfortunately, theyhad that view. It might have been smarter to plunk them in

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DOI 10.1007/s00283-010-9183-2

a basement somewhere. But, it was a view I wanted to see.And Schmishschmitt knew it.

‘‘How soon can you get here?’’ he asked, assuming hehad reached me in my office at UCLA.

I checked my pocket to see if I had the dollar inchange I needed for the bus. ‘‘I’ll be there in 20 minutes,’’I replied.

The bus dropped me off in front of the MSRI building onGauss Way. As I entered, a police officer waved me up thestairs, and another pointed me to an open door. I could seethe victim’s legs sticking out from behind the desk. Policehad cordoned off the area, and were taking photos.Schmishschmitt waved me over.

As I joined him, I couldn’t help but catch a glimpse outthe window over the bay. A fog was rolling in. It wasmagnificent.

‘‘Okay, Mangum. You got your view. Now quit yourrubbernecking. We have a case to crack.’’

I sighed, turning away from that amazing panorama tothe sordid reality of the crime scene before me.

‘‘Give me the lowdown,’’ I said.‘‘She’s a tenured professor at Cornell, name of Kate

Witherspoon.’’I knew Witherspoon. She had started her career at Five

Mile Island Community College. Then she knocked off theLittle Armandhamer conjecture and got a job at SouthernMiami State. She followed that with the Big ArmandhamerConjecture and moved to University of Miami. When sheproved the Strong Big Armandhamer Conjecture, Cornellcame knocking. I mean that literally. Armandhamer, whowas the math chair at Cornell, flew down to Miami, knockedon her office door, and made her the offer. He had a fewmore conjectures he was hoping she would solve.

‘‘She was here at MSRI for a special semester on Com-binatorial Counting,’’ said Schmishschmitt. ‘‘She was a verygood counter.’’

‘‘Probably didn’t count on this,’’ I said dryly, motioningto the scene before me. Papers were strewn about herprone body.

‘‘She had been here for three weeks,’’ continuedSchmishschmitt. ‘‘By all accounts, she was quiet, unas-suming. Kept her nose to the mathematical grindstone.Didn’t get in any trouble with residents of the neighboringoffices. Then, suddenly, at 3:27 this afternoon, the inhab-itants of the next office heard a scream. They rushed in andfound her lying there.’’

‘‘Can I talk to them?’’‘‘No. None of them speak English. Mostly Lithuanians,

with a Rumanian or two mixed in. But they’re goodwith hand signals. I would want them on my team forcharades.’’

‘‘This isn’t a good time for games, Schmishschmitt.Maybe we can play later. What exactly happened to her?’’

‘‘Why don’t you ask?’’She was sobbing, as she lay on the floor.‘‘Excuse me,’’ I said, ‘‘Professor Witherspoon? Can I

interrupt your blubbering for a moment? I have a fewquestions.’’

‘‘Who are you?’’ she asked as she sat up, pushing away apoliceman dusting her for prints.

‘‘Name’s Mangum, Mangum P.I. I’m a principal investi-gator on a National Science Foundation grant. I’m also theguy the police call when there is a crime involving math.’’

‘‘Well, you’re in the right place,’’ she said, as she slowlypulled herself to her feet.

She was taller than she looked when she was lyingdown. Seems to be a pretty common phenomenon.

‘‘Can you tell me what happened?’’She pointed to her computer screen. I leaned forward to

read an e-mail message.

‘‘Dear Dr. Witherspoon,

I regret to inform you there is a counterexample to yourproof of the Strong Big Armandhamer Conjecture. Take forinstance the collection of integers {7, 41, 321, 6,432}. Sorryabout that.

T. Boone Picky’’

‘‘Is he right?’’ I asked.She started bawling.‘‘Well, that is unfortunate,’’ I said. ‘‘Nobody wants to see

a good theorem go down. But if it’s wrong, it’s wrong.These things happen. It’s hardly a criminal matter.’’

Schmishschmitt looked confused.‘‘If the theorem was wrong, wouldn’t the referee catch it

before it was published?’’I laughed out loud. Then I pounded the desk a few

times and laughed some more. Nobody was taking the bait,so I slapped Schmishschmitt between the shoulders, andlaughed some more.

‘‘What’s so funny?’’ asked Schmishschmitt.‘‘Referees are like people,’’ I said. ‘‘In fact, come to think

of it, they are people. And just like people, they come in avariety of types. There are good referees and bad referees.There are referees who will hit you up for not capitalizingthe first word of every sentence. There are referees who getupset when you say 1 and you mean 2. There are refereeswho will reject a paper because their name doesn’t appearin the list of references. And there are referees who couldgive a flying flype, referees who agreed to referee yourpaper for no better reason than some dean at their schoolcounts that as service. And they’d rather be watching TheBachelorette on TV than poring over your paper trying tofigure out if A implies B. So they do a quick skim, tenminutes glancing over dense, detailed mathematics. Andthen they flip a coin, and send in a two-sentence report.’’

‘‘But you don’t understand,’’ said Witherspoon, havingstifled her tears. ‘‘It’s not a mistake on my part or on thereferee’s part. The paper is correct.’’

‘‘Listen, Witherspoon,’’ I replied. ‘‘If there is a counterex-ample, a counterexample consisting of only four integers, thennoconclusion ispossibleother than that the theorem iswrong.’’

‘‘I know,’’ she said. ‘‘That is what is so strange. I knowmy paper is right.’’

‘‘Can I see it?’’ I asked.She handed me a reprint. It was from the Annals of

Analytic Computational Counting, Series B. Very impres-sive. It came in at a hefty 27 pages.

� 2011 Springer Science+Business Media, LLC, Volume 33, Number 2, 2011 19

I glanced the intro over.‘‘So you use some other results in your proof.’’‘‘Yes, just a few. I use the Proper Premise Proposition.

And I use the Leminscate Lemma.’’‘‘And how long has the Proper Premise Proposition been

around?’’‘‘Since 1943. It appeared in a paper by Peter Proper.’’‘‘And the Leminscate Lemma?’’‘‘That was published in 2009.’’‘‘Who did it?’’She looked confused.‘‘Who proved the Leminscate Lemma?’’ I repeated.‘‘Vito Leminscate,’’ she replied.The name rang a bell.‘‘Not the Vito Leminscate who used to be at NYU?’’‘‘No. The Vito Leminscate who used to be at Brown.’’That brought up some memories, some very unpleasant

memories.Manyof themwereof the times I hadconfused thetwo Vito Leminscates. But a few of them were unpleasantmemories about the Brown Vito Leminscate.

‘‘I had heard he disappeared off the mathematical map,’’I said. ‘‘Went into i-banking.’’

‘‘That’s right,’’ confirmed Witherspoon, ‘‘But he didn’tlast long in the real world. He came back to math when thebottom fell out of the market. A lot of quants did.’’

‘‘And where is he now?’’‘‘Actually,’’ she answered, ‘‘he’s two doors down. He’s

here for the semester in Combinatorial Counting.’’‘‘Excuse me,’’ I said, as I stepped out of the office.I saw a head pop back into the office two doors down.As I headed down the hall, a crowd of Lithuanians and

Rumanians popped out of the next office. They were alljabbering at once, and I knew immediately I would have toplay some charades after all. I pantomimed my gratitude fortheir having phoned in the emergency, and explained byway of hand signals that it was essential I get past them tothe open door beyond. They expressed their immensegratitude for the invitation to visit at MSRI and explainedhow much they enjoy the quarter pounder at MacDonald’s.

Schmishschmitt was right. They were good. With acouple of swift hand gestures, I managed to convince themthat MSRI would be providing them with bacon-wrappedscallops but they would need to be in their office to receivethem, and then I walked up to the open door beyond.Leminscate was pretending to be hard at work, chewing ona pencil and staring off at the view of the bay.

‘‘You can get lead poisoning that way,’’ I said.‘‘There is no lead in the lead of a pencil. It’s made of

graphite,’’ he replied, spitting some pencil shards in to thewastebasket.

‘‘Doesn’t mean you should chew on ‘em. Have youconsidered the splinters?’’

Leminscate looked uncomfortable, as he ran his tonguearound the inside of his mouth.

‘‘You know, Leminscate, I think the last time I saw youwas at a bar in Providence in ‘05 after the number fieldsseminar at Brown. You were passing out preprints like theywere cupcakes. Trying to convince naı̈ve grad students youwere hotter than Heegaard Floer homology.’’

‘‘Mangum, I don’t have to listen to your guff. I actuallyhave an office in this building. Do you?’’

‘‘I’m here on business,’’ I said. ‘‘I’m here to talk about theso-called Leminscate Lemma.’’

Leminscate almost choked on his pencil shards.‘‘You got nothing on me,’’ he said, spitting into the

wastebasket.‘‘You know, Leminscate, let me tell you about my plans

for this evening. I’m thinking I’ll be sitting down with aglass of wine and a copy of the proof of the LeminscateLemma. Just the two of us. It’ll be very cozy. Some romanticmusic in the background, the lights down low. We’ll get toknow each other real personal. I’ll start with a slow perusal,just a skim up and down. But eventually, that lemma willopen up to me. And by the time I’m done I will haveexamined every inch of that lemma, from top to bottom, I’llhave checked under the hood. There will be no bit of thatlemma that was not exposed to my scrutiny. I’ll get to knowit better than I know my own…..’’

‘‘I don’t know how you did it, Mangum. But you madereading a theorem sound dirty.’’

‘‘If the theorem’s dirty, then reading it’s dirty, too.’’‘‘All right,’’ said Leminscate. ‘‘You caught me. It’s a fake.’’‘‘What?’’‘‘The proof is a fake. I admit it.’’‘‘What do you mean, it’s a fake?’’‘‘The proof is wrong. I have been dying to tell someone.

It’s so good. You see, in the Leminscate Lemma, I use aninductive argument. I prove the base case, which corre-sponds to one leminscate. And I prove the inductive step,that if there are n leminscates, then there are n+1.’’

‘‘That sounds like the whole proof.’’‘‘But guess what, Mangum. The proof of the inductive

step implicitly assumes there are already at least two lem-inscates. So you never get past the base case. You actuallynever have more than one leminscate. Nobody thinks tocheck that.’’

‘‘Clever,’’ I acknowledged. ‘‘But why? Why would youwant to plant false results in mathematics?’’

‘‘I’m a mathematical terrorist.’’‘‘A what?’’ I asked.‘‘A mathematical terrorist. Those results, once they

appear, get used by other mathematicians in their results,and those results get used by others. Given enough time,the seeds that I have planted will blossom into the diseasedtrees that will bring mathematics to its knees.’’

‘‘But why would you want to destroy mathematics?’’‘‘I spent a few years in the financial world.’’‘‘I heard that. So?’’‘‘So, I built an algorithm designed to milk the market. It

was based on algebraic combinatorial counting. It utilizedthe differential between the current rate of pork bellyfutures and the diminishing return on lateral derivativeindices. It made me a pile of money. A pile so high that Ineeded oxygen when I sat on it.’’

‘‘So what’s so bad about that?’’‘‘It didn’t predict the pork belly run of 2008. Before you

knew it, there wasn’t a pork belly to be had on the entireisland of Manhattan. Who knew pork bellies would become

20 THE MATHEMATICAL INTELLIGENCER

the biggest thing since supersubindices? I lost everything.And all thanks to that algorithm.’’

‘‘So?’’‘‘So, mathematics destroyed my life. It’s only fair I return

the favor.’’‘‘But math isn’t a person. You can’t exact revenge on a

logical system.’’‘‘Oh yeah?’’ he said, ‘‘You just watch me.’’ With that he

leapt up, spitting shards of pencil in my face. As I coveredmy eyes with my arm, he plowed into me, knocking me flaton my keister.

‘‘There’s nothing you can do to stop me,’’ he screamed,as he ran to the top of the stairs, and then leapt over thebanister, landing on the floor below. Hearing the ruckus,the Lithuanians and Rumanians poured out of their office,gesticulating wildly, wanting to know where the bacon-wrapped scallops had gotten to. As I tried to disentanglemyself from them, he shot out the front door of thebuilding. I sprinted after him as he headed up the path intothe woods. I knew that if I lost sight of him I wouldprobably never see him again. But as he turned a corner inthe trail, he almost tripped over a yoga class practicing inthe woods. As he swerved to avoid them, I caught up.Diving forward, I wrapped my arms around him, andtackled him hard to the ground.

‘‘What the hell are you doing?’’ he screamed.It was a good question. There wasn’t anything criminal

he could be charged with.

‘‘Hmm,’’ I replied, as we lay in a tangle of limbs, someours, some the nearby trees’.

‘‘I will have you up on charges of assault and battery,’’he cried, as he stood up, brushing himself off. ‘‘I havewitnesses.’’ Luckily, the yoga class was meditating, and allof them still had their eyes closed.

‘‘Listen, Leminscate,’’ I said. ‘‘You’re right. There’s nothingI can do to you in a court of law. But the truth is that you’llnever work in this business again. You try to publish any-thing ever again and I’ll make sure the editors of the journalhave eight referees going over every +, -, epsilon, anddelta.Your tawdry plan has been exposed.’’

It would have been a great way to end the story, as Iwalked away, leaving him to ponder his fate. But unfortu-nately, we both needed to take the bus down to Berkeley, sothere was a very awkward 20 minute wait at the bus stop.

When we climbed on the bus, we made a point of sittingapart. As the bus finally stopped to let him off he turned tome and said with a sneer, ‘‘There are more like me outthere. This isn’t finished. Hahaha!’’ The others waiting toget off pushed him out the door.

Andmaybe what he said is true. Maybe there are more likehim, intentionally hiding bogus results in the structure ofmath, with the long-term goal the utter destruction of math aswe know it. But he is awfully weird. I kind of doubt it.

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