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Mathematics and science

An example of the controversial impact of computers on math is the 4 color map problem. This problem deals with how many colors are necessary for a map on which no two adjacent areas have the same color. Example: How many colors would it take to color a map of the US? This problem has been worked on for at least one hundred years. The conjecture was four, however, no one was able to offer a proof until some mathematicians an the University of Illinois programmed their parallel processor. After using 1000 hours of computer time to examine all possible cases, they were able to state four colors were enough. This computer approach to proofs represents a fundamentally new approach to math. The computer methodology fundamentally challenges the ideal that the goal in proving theorems is simple proofs which can be checked by other mathematicians. Examining the proof for the 4 color map problem requires understanding the software which is anything but simple. There are many phenomenon in science which simply can not be studied without supercomputers. To analyze models of the weather requires computing tens of thousands of equations. Until the invention of supercomputers, these equations could not be computed in a reasonable time frame. Numerous physics problems exist which push the limits of computing. Chemists have programs which simulate chemical reactions and thus enable the chemist to tell the outcome without experiment. Complex molecules are studied with computer graphics. Economist have developed several types of world models with up to 15,000 equations; however these models can be simulated on a workstation.


norman@eco.utexas.edu
Thu Jun 8 16:37:44 CDT 1995