MadSci Network: Physics
Query:

Re: albert einsteins contribution to mathematics and how it affects us today

Date: Fri Mar 5 16:59:30 1999
Posted By: Raymond Nelson, Grad student, Physics, University of New Mexico
Area of science: Physics
ID: 920557129.Ph
Message:

This is a peculiar question, but I'll give it a shot.  Einstein, unlike 
other great physicists struggled with mathematics a great deal.  One of my 
favorite quotations by him is from a letter he wrote on 3 January 1943 to a 
schoolgirl in Washington, D.C. who had written him and mentioned that she 
was having trouble in mathematics in school.  He said, "Do not worry about 
your difficulties in mathematics; I can assure you mine are still greater."

Physicists often make great contributions to the fields of mathematics by 
demonstrating the physical importance of unusual mathematical techniques.  
The most famous example of this is not due to Einstein at all, but due to 
one of the greatest Russian physicists, named Lev Landau.  He brought a 
mathematical theory called complex variable analysis into importance by 
using it to correctly predict a particular phenomenon.  

Einstein's contributions were a little different.  When he first published 
his special theory of relativity there was nothing mathematically startling 
about it.  In fact, one could call it pretty standard mathematical fare, 
since he began his derivations with two statements called postulates.  This 
is a fancy mathematical term for something you start with but don't have to 
prove.  It was only understood by a few physicists, however, until a 
mathematician named Minkowski reformulated the theory in a very satisfying 
mathematical way.  Einstein himself said that Minkowski had transformed 
physics from "a happening in three dimensional space to an existence in a 
four dimensional world."  This change is very important and parallels a 
theme of modern physics; the equation is the most important thing, not a 
personal ability to visualize the thing you are studying.  All of the 
advancements in early 20th century physics came from men who were willing 
to trust the equations rather than their intuition.  Einstein started this 
trend.  

The General theory of relativity is another matter.  To express it 
effectively Einstein knew that he would have to master a very difficult 
form of mathematics called tensor analysis.  It took him nearly ten years.

Einstein helped to usher in the age of mathematical physics.  To become a 
physicist you have to master a lot of techniques in math.  Other physicists 
have done things differently.  One of the most gifted mathematical 
physicists of this century, Richard Feynman, was always looking for simpler 
ways to understand things and to express his understanding.  

Einstein's contribution, though it was not his alone, was to create among 
other scientists an appreciation that mathematical results should be 
trusted until they are proven wrong by experiment.  

Ray Nelson


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