Communications of the ACM
Experimental Mathematics: Computing Power Leads to Insights
Credit: Courtesy of Eastern Illinois University
In a forthcoming article, "Exploratory Experimentation and Computation," American Mathematical Society (AMS) researchers will describe how modern computer technology has expanded society's ability to discover new mathematical results.
"By computing mathematical expressions to very high precision, the computer can discover completely unexpected relationships and formulas," says AMS researcher David H. Bailey. "The computer can be seen as a perfect complement to humans---we can intuit but not reliably calculate or manipulate; computers are not yet very good at intuition, but are great at calculations and manipulations."
The article notes that the inductive aspect of mathematics now includes the use of computers, which have increased the amount of exploration that can be completed. The article also discusses the need to redesign mathematics education to include experimental mathematics tools.
"The students of today live, as we do, in an information-rich, judgment-poor world in which the explosion of information, and of tools, is not going to diminish," says AMS researcher Jonathan M. Borwein. "We have to teach judgment [not just concern with plagiarism] when it comes to using what is already possible digitally."
From American Mathematical Society
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