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Gauss's Day of Reckoning

A famous story about the boy wonder of mathematics has taken on a life of its own

Brian Hayes

The Narrative Urge

It's a challenge to sort out patterns of influence and transmission in such a collection of stories. When a later author mentions the series 81297 + 81495 + ..., we can be pretty sure those numbers came from Bell. When the example given is 1-100, however, it's not so easy to trace the line of inheritance—if there is one. And the dozen or so other sequences that appear in the literature argue for a high rate of mutation; every one of those examples had to be invented at least once.

Tellers of a tale like this one seem to work under a special dispensation from the usual rules of history-writing. Authors who would not dare to alter a fact such as Gauss's place of birth or details of his mathematical proofs don't hesitate to embellish this anecdote, just to make it a better story. They pick and choose from the materials available to them, taking what they need and leaving the rest—and if nothing at hand suits the purpose, then they invent! For example, several authors show a familiarity with Bell's version of the story, quoting or borrowing distinctive phrases from it, but they decline to go along with Bell's choice of a series beginning 81297, falling back instead on the old reliable 1-100 or inserting something else entirely. Thus it appears that what is driving the evolution of this story is not just the accumulation of errors of transmission, as in the children's game "whisper down the lane"; authors are deliberately choosing to "improve" the story, to make it a better narrative.

For the most part, I would not criticize this practice. Effective storytelling is surely a legitimate goal, and outside of formal scholarly works, a bit of embroidery on the bare fabric of the plot does no harm. A case in point is the theme of "busywork" found in most recent tellings of the story (including mine). It seems we feel a need to explain why Büttner would give his pupils such a long and dreary exercise. But Sartorius says nothing at all about Büttner's motivation, nor do any of the other 19th-century works I've consulted. The idea that he wanted to keep the kids quiet while he took a break is entirely a modern inference. It's probably wrong—at best it's unattested—and yet it answers a need of readers today.

In the same spirit, many authors confront the question that got me started on this quest: How did Büttner do the math? Bell is adamant that Büttner knew the formula beforehand; others say he learned the trick only when Gauss explained it to him. An example of the latter position is the following account written in 2001 by three fifth-grade students, Ryan, Jordan and Matthew:

When Gauss was in elementary school his teacher Master Büttner did not really like math so he did not spend a lot of time on the subject. One of the problems his teacher gave the class was "add all the whole numbers from 1 to 100". His teacher Master Büttner was amazed that Gauss could add all the whole numbers 1 to 100 in his head. Master Büttner didn't believe Gauss could do it, so he made him show the class how he did it. Gauss showed Master Büttner how to do it and Master Büttner was amazed at what Gauss just did.

Am I being unfair in matching up Eric Temple Bell against three fifth-graders? Unfair to which party? Both offer interpretations that can't be supported by historical evidence, but Ryan, Jordan and Matthew are closer to the experience of classroom life.

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Related Internet Resources

A collection of versions of the Gauss anecdote

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