Gauss's Day of Reckoning
A famous story about the boy wonder of mathematics has taken on a life of its own
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.