Ask A Scientist Mathematics Archive

Question: As I understand it, the mathematics used in physics today is not 
the sort of mathematics that interests mathematicians.  Yet, Newton was 
somewhat of both.  Is this division real, and if so, are there any books or 
articles that discuss the history of this division? 
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Yes there is a real division!!  You should be able to find some 
information if you look in your library under science history or math history.  
I recently read a story that illustrates the division as you have outlined it.  
There were 3 men/women, an engineer, a physicist, and a mathematician who were 
sharing a room while attending a conference.  In the middle of the night a 
fire broke out.  The engineer woke up, grabbed a bucket, filled it with water 
and put the fire out.  A little later the fire started again.  This time the 
physicist woke up, calculated the correct amount of water needed to extinguish 
the blaze, filled the bucket with just that amount of water, and put the fire 
out.  Still later the fire started again. This time the mathematician woke up, 
calculated the amount of water needed to put out the fire, worked out the 
proof that it would work, then went back to bed.
Michael Rosing
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Certainly, in the past, pure and applied mathematicians have 
argued at length over which endeavor is nobler.  I think that there is not so 
much conflict along those lines today.  It certainly is the case that 
mathematics is much broader in scope than the portion of it which is 
traditionally of highest interests to physicists.  Physics is only one area of 
applications.  There are lots of significant applications of mathematics to 
fields such as economics, business, biology, computer science, the social 
sciences, etc.  There seems to be both an old and a new meaning to the term 
"applied mathematics".  The Mathematical Experience by Philip J. Davis and 
Reuben Hersh.  Check the table of contents for the appropriate section.  This 
book also contains a bibliography with additional references.
Robert Allan Chaffer
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However, it should be noted that there really is considerable 
interplay between physics and mathematics - mathematicians often become 
interested in problems raised by physicists (variational calculus is an old 
one, but there are newer examples, particularly in calculus extended to "bad" 
functions like distributions), and sometimes physicists even invent new ideas 
in mathematics (Dirac's spinors, or more recently wavelets (invented by a 
geophysicist, I think)).  Mathematicians have of course been greatly inspired 
by Einstein's successful use of non-Euclidean geometry (although they hate to
admit that they might be doing anything practical, I doubt differential 
topology and its extensions would be as fruitful a field today without this 
implication of usefulness).  Physicists are often discovering that areas of 
mathematics previously deemed useless (various things in advanced number 
theory, for instance) actually have implications in the real world.  And, I am 
speaking only from the physicist's perspective, of course.  It is true that 
most of modern mathematics is pretty far removed from anything the average 
physicist would enjoy using in real work, and sometimes it seems that we 
physicists should be able to tell mathematicians, "Hey, I really need to 
understand this particular aspect of geometry a little better could you work 
on it please?"...but communication between fields is always difficult, and 
getting somebody else to work on your problem is too...
Arthur Smith
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