Over the last quarter Century and especially
during the last decade, a dramatic `re- experimentalization' of Mathematics has
begun to take place. In this process, fueled by advances in hardware, software and
theory, the computer plays a laboratory role for pure and applied
mathematicians; a role which in the eighteenth and nineteenth centuries the
physical sciences played much more fully than in our century.
Operations previously viewed as non-algorithmic, such as indefinite
integration, may now be performed within powerful symbolic manipulation
packages like Maple, Mathematica, Macsyma, Scratchpad to name a few.
Similarly, calculations previously viewed as ``practically'' non-algorithmic
or certainly not worth the effort, such as large symbolic Taylor
expansions are computable with very little programming effort.
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