Re: mathematicians and longhand arithmetic

From: Herman Rubin (hrubin_at_odds.stat.purdue.edu)
Date: 07/06/04 

Date: 6 Jul 2004 12:27:31 -0500

In article <20040705131834.23777.00001118@mb-m28.aol.com>,
R3769 <r3769@aol.com> wrote:
>Andrzej Kolowski writes:

>>Tim923 <tws0923@verizon.net> wrote in message
>>news:<3cdde0hbokr2kof4sk0oe1lnfq9dcb55bg@4ax.com>...
>>> Lots of people think that because I have a math degree I should be
>>> outstanding at longhand arithmetic, but I thought that being forced to
>>> do longhand arithmetic only interferred with doing the more important
>>> math, such as algebra and calculus. So I'm not that fast or quick
>>> with longhand arithmetic. Where do the other mathematicians stand?
>>> Does being poor at arithmetic make a person any less of a
>>> mathematician?

I doubt that being forced to do longhand arithmetic would
interfere with learning how to carry out algebra and
calculus manipulations, which are still unimportant.

However, not being sufficiently proficient at longhand
arithmetic has been used, and is still being used, to deter
people with mathematical ability from proceeding, even to
the other manipulative stages. The worse aspect is that
mathematical concepts, and the use of the language part of
mathematics, is at best made somewhat more difficult, and
at worst even destroyed, by the emphasis on manipulation.

As for doing real mathematics, possibly a small amount of
longhand arithmetic may be useful. Unless there is a
problem of calculating numbers in which small details are
important, it is unclear that any proficiency in arithmetic
had that much value.

>> Gauss and Euler were prodigious at arithmetic and it was
>>useful to them especially in doing astronomical computations.

Is "doing astronomical calculations" mathematics? I read
that Gauss memorized logarithm tables for sufficiently many
small integers, going a little above 100, and mentally did
7 point interpolation to compute them for other values. He
used these logarithms for astronomical calculations; in
fact, he considered his profession to be an astronomer.
What mathematician uses base 10 logarithms today?

Was any of this in his mathematical papers? I know of none.
Was it useful to him? Yes, it saved time, and in his days,
least squares and other calculations could only be done by
longhand arithmetic. The only other assistance came from
such things as Napier's Rods, tables of logarithms and other
functions, and the slide rule after that came into being.

                                G. D.
>>Birkhoff was also a great calculator. Such skills are much less
>>relevant now with computers and pocket calculators.

Where are these calculations found in Birkhoff's works?

>I am curious: What skills have become *more* relevant to the mathematician,
>given the power of modern computers?

I have pointed out that these skills have never been relevant
to the mathematician for the purpose of mathematics, except
possibly for a few situations where accurate numerical values
were needed. What is needed is an understanding of logic and
proofs, and of mathematical concepts. Euclid's _Elements_,
which have little arithmetic even in the parts on numbers, is
a far better beginning. 

-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558

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