From: mccolm@darwin.math.usf.edu. (Gregory McColm)
Newsgroups: sci.math
Subject: Re: Alleged shortage of mathematicians
Date: 8 Dec 92 21:44:40 GMT
Organization: Univ. of South Florida, Math Department

In article <1frs19INNlgc@iskut.ucs.ubc.ca> ramsay@math.ubc.ca (Keith Ramsay) writes:
>In article <1387@kepler1.rentec.com> andrew@rentec.com 
>(Andrew Mullhaupt) writes:
>
>|If we're going to start dividing the birthright into pure vs. applied,
>|then remember that the applied side gets all the big names except
>|maybe Galois until Weierstrass. Then the applied side gets the vast
>|majority of the big names (including Noether and Cartan) until
>|somewhere around the middle of the twentieth century. So although
>|_mathematics_ is a proud tradition going back to prehistory, _pure
>|mathematics_ is a nouveau riche upstart _and it seems to act like one,
>|too_.
>

Huh???

Pythagoras had "philosophical" motivations probably unstained 
by any "logistical" considerations.  Certainly that is also the 
view of Pythagoras's great communicator, Plato.  Hellenistic 
mathematics has obscure motivations:  those of Euclid and 
Diophantus (both rather pure) are unknown.  Eudoxus and 
Apollonius did both "pure" and applied work, and they were 
probably mathematicians in the best sense of the word.  
According to Plutarch (not the best source, admittedly), 
Archimedes was a pure mathematician who occasionally helped 
his friends by solving applied problems (note:  despite 
Mullhaupt's (and Morris Kline's) claim that pure mathe-
matics is a recent aberration, Plutarch shows a very 
"modern" prejudice against applied mathematics).

Need I go on?  Much of ancient Hindu mathematics seems rather 
non-applied, full of cute puzzles (rather like the ancient 
Egyptian Rhind papyrus).  During the last thousand years, 
we have seen a range of people.  Fibonacci was interested in 
business mathematics, but also did some very pure work on 
perfect squares.  Fermat was about as pure as a mathematician 
of that caliber gets.  Liebniz was a lot purer than Newton, 
and actually seemed to have some philosophical motivations 
for his work.  Newton, on the other hand, went out of his 
way to say that he was NOT interested in mathematics in 
itself, but in its scientific application:  obviously someone 
Newton didn't like (eg, Liebniz) was interested pure mathe-
matics.  Anyway, the brickbats have been flying for more 
than a century or so.

>I suggest that it is more accurate to say that these people did things
>which could be counted as applied math as well as things which could
>be counted as pure math. There was much less specialization long ago,
>so one did not have as many people who were narrowly enough
>specialized to be tagged as "pure" mathematicians.

It might also be accurate to say that the split 
between pure and applied mathematics is ancient (and possibly 
all Plato's fault) and will probably be around forever.

-----Greg mcColm



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