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Short Summaries of Articles about Mathematics in the Popular Press

"Computer Experiments Are Transforming Mathematics," by Erica Klarreich. Science News, 24 April 2004, pages 266-268.

Besides using logic and formal proof, mathematicians have often experimented with numbers as a means for determining new results. For example, Gauss made many discoveries empirically, although at least one of his conjectures waited over a century for formal proof. Now, mathematicians have a new tool for running experiments and obtaining answers: computers. Klarreich describes two recent examples: a simple formula for the number π found using a computer program that searched for relationships between π and numbers with known formulas, and certain exciting discoveries made in the field of hyperbolic geometry using software known as "SnapPea."

Some mathematicians believe that experimental results should be considered as another means, beside formal proof, of determining mathematical truth. But the more mainstream view seems to remain that formal proof is necessary, in part because things that may look true based upon experimentation could actually be false. And, in AMS President David Eisenbud's words, "Proof is the path to understanding."