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Date: Around 1993


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?



Replies:
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


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


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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