FOM: General intellectrual interest

Michael Thayer mthayer at
Thu Dec 18 15:54:29 EST 1997

Lou van den Dries responds to Harvey as follows:
>Otherwise I am not conceding anything. Sure, "suspect" is vague, so is
>"general intellectual interest", and perhaps even more, the significance
>of "general intellectual interest".
I will go farther: it is blatant nonsense as used by Harvey and Steve.  What
"general intellectual interest" do most of Harvey's "interesting technical
results"  (to quote Anand) actually have.  How many people even understand
large cardinals, much less care about them?  Far fewer than are interested
in number theory, be it abc or FLT.
I suspect that the folks who partake of the botanicals that grow in Doctor
Cantor's garden have OD on them: we know since Goedel that number theory is
incomplete, indeed incompleteable.  So details as to what large cardinal
hypotheses are required to prove the graph minor theorem, or
Paris-Harrington are about as exciting as improving the exponent on
logloglogloglog(n) in the error term for some number theoretic function.
The real "general interest" stuff has been mostly discussed by Tennant and
Pratt in their discussion about mathematics on Quasar 1036, and Shipman et
al in the recent discussion of "convincing proof".
The two biggest foundational questions in mathematics are:
1. What is the origin of the certainty that many (but NOT all) people feel
when presented with a mathematical proof?
2. When, and why is this feeling of certainty justified?
as Machover says, he can recognise a proof when he sees one, although he may
not be able to describe what is required.  He also mentions evolution etc as
a reasonable explanation for the justification.  (Neil T. made similar
remarks on the necessity of arithmetical notions for sufficiently advance
Next to this sort of discussion (which may be too vague for Harvey) details
of which uninteresting set theory statement follows from the existence of
which implausible infinite entity seems remarkably like medieval theology -
which is probably not of much intellectual interest to most people.


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