MadSci Network: Physics |
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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