[Avodah] O(n^2) algorithm for matrix multiplication

[David Cohen]

I disagree with  R' David Riceman's assertion that his search for an O(n^2)
algorithm for matrix multiplication is "na'arishkeit" that would wouldn't
be engaged in by a "total oveid Hashem."

I see this activity as having inherent value, aside from the potential
parnasah value and the value of having recreation activities, which have
already been mentioned.  First off, such an algorithm could be implemented
and used in software that would be significantly more efficient (when n is
very large) than what is currently available.  This could enable the
solving of problems that can't be efficiently solved by computer today, and
that could have a direct positive impact on people's lives.  Just like
scientific research, abstract mathematical research can contribute to
yishuvo shel olam.  Even outside of research, I believe that most
professions contribute something positive to society, even when the
"contribution" seems indirect.  If you are take any part in a system that
enables society and the economy to function properly, which in turn enables
people to live respectably, it seems self-evident that this has positive
spiritual value.  This is my kavanah in avodat Hashem as I go to work each
day, in addition to the kavanah of providing for my family.

Yishuvo shel olam aside, I also see inherent value in learning math: it is
truth.  We learn Torah because it is revealed truth, and some of us study
science because it is another reflection of the ways of Hashem, who is
truth.  The laws of math are objectively true, independent of their mapping
onto the physical world.  I remember that I once shocked a friend when I
said that Hashem, notwithstanding His omnipotence and ability to change any
of the laws of physics, cannot change the value of Pi.  I don't mean
changing the semantics -- anybody could say that a circle means something
else, or that 3.14159 means something else -- but the value of Pi is
objectively true, independent of the physical existence of the universe.  I
can't think offhand of a pasuk or maamar Chazal that makes this point
explicitly, but it seems self-evident to me that studying such truths can
help us to perfect the brains with which Hashem created us, and this has
spiritual value.

-- D.C.
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