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A_BEAUTY_COLD_AND_AUSTERE

                                             September 15, 2020

 Picking over a passage by Bertrand Russell in which
 he talks up the joys of doing mathematics solely for
 the sake of appreciating it's beauty.

                        This is a slightly odd opinion here in the year
                        2020-- maybe it was an odd idea back in 1907--
                        but I keep puzzling over what exactly Russell
                        thought he was doing with projects like
                        "Principia Mathematica", and I'm beginning to
                        think this point is his all purpose fall back:
                        Even if it looks like a crazed project by any
                        other standard, at least it's *beautiful*.


Bertrand Russell, "The Study of Mathematics", (1907)
collected in "Mysticism And Logic And Other Essays", (1917):

  "To those who inquire as to the purpose of mathematics,
   the usual answer will be that it facilitates the
   making of machines, the travelling from place to
   place, and the victory over foreign nations, whether
   in war or commerce."

   "If it be objected that these ends-- all of which are
   of doubtful value-- are not furthered by the merely
   elementary study imposed upon those who do not become
   expert mathematicians, [--] "

That seems like a dubious claim-- you can do a hell of
a lot with a little arithmetic and trig, and differential
equations are nifty and all but that approach becomes rough
going once you've used it to solve the simpler problems...

   "[--] the reply, it is true, will probably be that
   mathematics trains the reasoning faculties."

Turn of the century England
was a simpler time, eh?

A little in this piece,
Russell complains:              "And the reasoning faculty itself is generally
                                conceived, by those who urge its cultivation,
                                as merely a means for the avoidance of pitfalls
                                and a help in the discovery of rules for the
                                guidance of practical life."

                                    I think young Russell was being a bit of an
                                    upper class Romantic here, sneering at the
                                    "practical life".

Then this following passage might seem like
gibble-gabble, because here Russell seems to be
riding some of his hobby horses, and ending up
making convoluted, obscure remarks:

    "Yet the very men who make this reply are, for the most
    part, unwilling to abandon the teaching of definite
    fallacies, known to be such,  ..."

Russell had a bug about the focus on Euclid in British
schools.  I'm pretty sure that's what he was talking            CROOKED_EUCLID
about there.
                                                                    MATHISM
    "... and instinctively rejected by the
    unsophisticated mind of every intelligent
    learner."

There, I think, Russell is falling into the trap of
projecting his own reactions on "every intelligent
learner".

           <A HREF="SUCH_A_THING_AS_KNOWLEDGE.html">SUCH_A_THING_AS_KNOWLEDGE</A>



    "All these are undeniably important achievements
    to the credit of mathematics [--]"

Okay, that's a nice concession, however
condescending...  and you know it's
introducing a "but", right?  It's
"undeniably important", and yet we are       The way rhetorical flourishes
about to deny it's importance, aren't we?    like this work in English makes
                                             one despair of using language as
    "[--] yet it is none of these that       a tool of thought.
    entitles mathematics to a place in
    every liberal education."                               "One" meaning "me",
                                                            of course.  I count
Here in the modern day world, some might even ask           as one, don't I?
why Russell is convinced what he's calling a
"liberal education" is worth all that much...

    "Plato, we know, regarded the contemplation of
    mathematical truths as worthy of the Deity; and
    Plato realized, more perhaps than any other
    single man, what those elements arc in human
    life which merit a place in heaven."

I sometimes wonder if there's *anything* in Plato that's
not pernicious nonsense presented with literary flair.
When someone invokes Plato, you're about to hear some
bad craziness.

    "Mathematics, rightly viewed, possesses not only
    truth, but supreme beauty-- a beauty cold and
    austere, like that of sculpture, without appeal to
    any part of our weaker nature, without the gorgeous
    trappings of painting or music, yet sublimely pure,
    and capable of a stem perfection such as only the
    greatest art can show.  The true spirit of delight,
    the exaltation, the sense of being more than man,
    which is the touchstone of the highest excellence, is
    to be found in mathematics as surely as in poetry."



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