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Topic: Recommended reading for WM Mueckenheim and others
Replies: 9   Last Post: Apr 16, 2013 12:37 PM

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trj

Posts: 92
From: Korea
Registered: 2/23/12
Re: Recommended reading for WM Mueckenheim and others
Posted: Apr 8, 2013 5:18 AM
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> "But the messages that Kronecker did communicate
> contained some very important truth; in particular he
> complained that much of set theory was fantasy
> because it was not algorithmic (that is, it contained
> no rule by which one could decide, in a nite number
> of operations, whether a given element did or did not
> belong to a given set). Today, with our computer
> mentalities, this seems such an obvious platitude
> that it is hard to imagine anyone ignoring it, much
> less denying
> it; yet that is just what happened. We think that,
> had mathematicians paid more attention to this
> warning of Kronecker, mathematics might be in a more
> healthy state today."


And likewise "...much of computer science is fantasy
because it is not polynomial (that is, it contains no rule
by which one could decide, in a polynomial number of operations,
whether a given problem is a yes or no instance). Today, with our
computer mentalities, this seems such an obvious platitude
that it is hard to imagine anyone ignoring it, much less denying
it; yet that is just happens. We think that, had computer scientists
paid more attention to this warning, computer science might be
in a more healthy state today."



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