Matthew Moss wrote:

>> Out of interest, any mathmaticians care to enlighten me as to whether
>> happy numbers are in any way "useful"?
> 
> As has been said, "real mathematicians" shudder that their work might be
> useful.
> 
> In actuality, sometimes things like this aren't, and sometimes they
> are years later. Prime numbers never had much use until recent years,
> where they have become very important for encryption.

Another example is non-Euclidean geometry, which was an impractical, exotic
plaything for about 100 years, until general relativity came along and
required it. Without non-Euclidean geometry, Einstein wouldn't have been
able to express GR at all.

Prior to that, few would have guessed that the universe isn't Euclidean.

-- 
Paul Lutus
http://www.arachnoid.com