LETTERS TO THE EDITORS
Guessing About Gauss
To the Editors:
I enjoyed Brian Hayes's column "Gauss' Day of Reckoning"
(Computing Science, May-June), but I was surprised that
he didn't consider the very reasonable possibility that the
instructor not only knew the answer but was, in fact, trying to
teach the mathematics of series computation. The task might not have
been to compute a series summing problem, but rather to find an
efficient algorithm to do the computation.
This may be a teacher's embellishment, just as the schoolboys might
embellish the story by having Gauss outsmart his teacher. But the
original version has support for this interpretation since the
eulogy clearly states that the class was busy performing
multiplications and additions. My bet is that every one of those
schoolboys could find some algorithm more efficient than serial
addition, but Gauss was proud of being able to find a very efficient
algorithm very quickly.
The seeds of Gauss's genius may have been there, but this hard
taskmaster may have helped them grow with the kind of mathematical
thinking he taught. Gauss may have been justifiably proud of being
the brightest student of such a teacher, rather than someone
boasting that he outsmarted his teacher.
Robert F. Rakowski
Ohio University
Athens, OH
To the Editors:
Concerning Gauss's quick summation of a series of numbers as a
schoolboy, a likelier explanation occurs to me. If Gauss was as
curious as he was good with numbers, he had probably worked out this
problem ahead of time just from playing around on his own. Many of
us did this sort of thing in the days before calculators (let alone
computers), as such activity provided us with enrichment and
enjoyment that was unavailable to us in the classroom.
John D. Leggett
Canterbury, NH
To the Editors:
Brian Hayes's well-researched essay brings back fond memories. While
Mr. Hayes surmised that only those with a computer or a programmable
calculator would add successively from 1 through 100, I, together
with thousands if not millions of other Chinese students in the
1930s, had done just that with a non-programmable
calculator—the abacus.
After my mother introduced me to the use of the abacus, she
instructed me to get the sum of 1 through 100. I would drill until I
got 5,050 every time, probably at a rate of about one minute per
iteration—not a long enough respite for Gauss's teacher.
Marshall Chao
Midland, MI