[FOM] pathology

[Martin Davis]

Harvey asks me to define "mathematically interesting". I could in turn ask
him to define "general intellectual interest", but I won't.

All one can reasonably say is that something in mathematically interesting
if mathematicians, generally, find it interesting. As a definition this has
the obvious flaw that, being part of human culture, the concept is subject
to changes of fashion.

I am told that at some point in the mid 19th century, work on invariants,
much of it based on long intricate calculations, was interesting and
important. Of course the concept of invariance is still regarded as
interesting, but the detailed earlier work is regarded as rather boring.

My mathematical friends and I found fascinating the existence of solutions
of f(x+y)=f(x)+f(y) based on a Hamel basis together with the fact that any
assumption of regularity, however weak, brought one back to the trivial
linear solution. Evidently so did the editors of Fundamenta.

Martin
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