# The Mathematical Universe

## William Dunham

Following is an excerpt from

William Dunham,*The Mathematical Universe*

Fortunately, there is a higher form of mathematical humor that goes beyond mere puns. This commonly involves distortions of logic. The humor arises, after a moment's thought, from some sort of logical inconsistency. Mathematicians, whose scholarship is logic-driven, find it especially funny when the wheels come off.

We begin with an example from Polya. Looking back from late in his career, he reminisced about his lifelong affection for the discipline of philosophy and wrote: "Who is a philosopher? The answer is: A philosopher is one who knows everything and nothing else." This quip has the sort of logical convolution mathematicians find amusing.

Along similar lines is a comment made by the physicist Wolfgang Pauli. Pauli, who displayed brilliance and arrogance in roughly equal proportions, once disparaged a new colleague with the wonderfully twisted comment, "He's so young and already so unknown." Or consider Stephen Bock's Description of a sheltered man and his dreams: "Reading was something Jay knew about only from books, yet he was quite anxious to experience it for himself."

The use - or misuse - of logic also figures in the story of mathematician Henry Mann who, it is told, drove himself and a group of colleagues to scientific meetings in Cincinnati. Unfamiliar with Cincinnati streets, Mann became ever more lost. His colleagues, although uneasy, remained silent until they realized he had turned the wrong way onto a one-way street. But Mann dismissed their warnings. This street could not possibly be one-way, he pointed out, since their car was heading in one direction and any number of vehicles were coming toward them in the other."

These are examples of logic turned on its head. The following story finds humor in the illogic of English pronunciation. The Polish mathematician Mark Kac immigrated to the United States and tried to master the sometimes inexplicable English language. Particularly vexing were those words that, although spelled with identical endings, were pronounced differently. For instance, the "ow" ending might be pronounced with a long 0, as in *grow* or* know*, yet the same ending is said very differently when it appears in *cow* or* how*. Of course, the word bow, with two different pronunciations, incorporates the worst of both worlds.

In any case, Professor Kac, in grappling with this phenomenon, came to realize that the word *snowplow* was doubly bizarre, because the same "ow" is pronounced in two different ways *within the same word.* Mindful of this, he took special care to recall its illogical pronunciation. Unfortunately, he interchanged the variants, so that instead of rhyming *snowplow with grow-cow*, he rhymed it with *cow-grow. *

Finally, there is this story with its own surprise twist. During an informal moment at a mathematical conference, a young admirer asked the noted mathematician R. H. Bing for his autograph. With this in hand, she asked Paul Halmos, another celebrated mathematician, to sign on the same sheet. Thus she held in her hand what was the mathematical equivalent of a page jointly autographed by Gilbert and Sullivan, or Ruth and Gehrig, or Siskel and Ebert.

When she showed this prize to a colleague, he immediately said, "I'll give you $25 for that page." But another, wittier mathematician jumped in with the clincher: "Yes, but I'll give you $50 if you let me sign my name below theirs."

These examples indicate the sort of humor popular among mathematicians. A moment's thought is required, and the typical response is not necessarily to laugh at the humor but to appreciate it. Neither ribald nor slapstick, mathematical humor tends to be cerebral. One suspects that very few mathematicians are numbered among the Three Stooges Fan Club.

If attire and humor, eccentricity and absentmindedness set mathematicians apart, their shared identity may be viewed as something of a defense mechanism. They truly find strength in numbers.

For instance, there is the widespread impression that mathematicians are merely accountants who spend their days adding up columns of numbers. Mathematician/poet JoAnne Growney, in confronting this perception, was moved to verse:

## Misunderstanding

Ah, you are a mathematician, they say with admiration or scorn. Then, they say, I could use you to balance my checkbook. I think about checkbooks. Once in a while I balance mine, just like sometimes I dust high shelves.

Are mathematicians misunderstood? Certainly. Are they scorned? Without a doubt. The two comments most often heard when someone is introduced to a mathematician are, "I hate mathematics," or "I fear mathematics," although these may be combined into the incomparable, "I hate *and* fear mathematics."

Why should mathematicians constantly be bombarded with such remarks? Why do so many people regard the subject as the academic equivalent of eye surgery without anesthetic? Were they, as children, bitten by a mathematician? Upon inquiry, one discovers two common sources of mathophobia: Either the respondent once had a terrible math teacher or the respondent perceives a terminal inadequacy in his or her mathematical abilities.

The former excuse, that of the bad instructor, is quite widespread and quite remarkable. People who forget things such as their wedding anniversary or the name of the president can nonetheless remember with absolute clarity an offending algebra teacher from decades ago. Whether Mr. Jones or Ms. Smith really was as awful as claimed or whether the bad memories have some deeper, darker origin is always a matter of speculation.

But if the math teacher from hell is one excuse shared by millions, even more common is the explanation, "I never could do math and I never will." This is a confession every teacher of mathematics has heard hundreds of times. It suggests that mathematical success is genetic. Just as some people are born with blue eyes, so others are bom with the ability to do math. If you were not so bom, you are destined to be a mathematical basket case, and nothing can change the prognosis.

It is not easy to disabuse people of this attitude. Many who encounter difficulty with mathematics quickly conclude that the fault lies in their stars and not in themselves. All too few draw the opposite inference, that a little more study might help.

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