[FOM] Pure mathematics and humanity's collective curiosity

[Bill Taylor]

Thomas Forster wrote:

->My favourite examples of this is the way in which the Greeks worked out 
->huge amounts of stuff concerning conic sections more than a millenium 
->before Kepler & co discovered that objects under gravity moved in conic 
->sections. 

Yes, that's very telling.  Another one with an even larger time scale is
the study of Egyptian fractions.  These were no use to anyone outside Egypt
nor even there for the last 2.5 millenia.  Yet recently I hear that they
may turn out to be useful in certain types of knapsack problems.

Tim Chow noted:

> ...*all* mathematics/science deserves to be 
> praised as "recreational."  Even mathematics/science that seems not to 
> have any direct recreational value usually has indirect value, because
> it often indirectly contributes to the recreation of *others*

Even the term recreational falls well short - fulfilling humanity's
curiosity about non-mundane subjects is surely one of an individual's
greatest tasks.

Andrei Rodin:

> Lobachevsky had in mind the
> possibility that physical space could be non-euclidean to begin with.

Gauss also, it is said.  I have read that he went to the trouble of
triangulating from three mountain peaks to see if there was significant
deviation from Euclidean angles.  Alas, I cannot find a reference;
can anyone help out on this?

Alasdair Urquhart:

> I think all mathematics is potentially applicable.

Applicable to other math, yes.    But maybe not "directly" applicable
to the physical world, whatever that may mean.  I am thinking of things
like non-measurable sets, CH, and large cardinals....  none of these seems
to have any conceivable physical application in view.

Bill Taylor