In the latest Notices of the AMS three researchers describe their frustrations getting plainly incorrect... As the systems we use to manipulate data become more complicated it becomes more difficult to determine their validity... Robert Jacobson originally shared: In the latest Notices of the AMS three researchers describe their frustrations getting plainly incorrect results from Wolfram Mathematica. The computation is quite elementary: compute the determinant of a matrix with integer entries. They give a few other examples of clearly wrong answers that Mathematica reports. They are careful to say that every major software system contains errors, and examples of incorrect results can be found in any major computer algebra system. But in a proprietary block box system like Maple or Mathematica, researchers have no way of checking that the algorithms it contains are correct, and the vendor has every motivation to be less than forthcoming with the list of known errors in the software. Whats more, reporting errors to the vendor is difficult or impossible, and you may never get feedback from the vendor regarding your reported bug. This is in sharp contrast to open source mathematical software like +Sage Mathematical Software System and the many OSS packages it contains. There are trade-offs: convenience, coverage, speed (in some cases), nice UI or IDE… The authors suggest researchers provide evidence in their papers that a computer algebra systems output is accurate, such as performing the computation with more than one computer algebra system. Is this sufficient? It seems to me that despite leveraging computers in our research for decades, mathematicians still have not figured out what status computations done by computer should have. Proofs and computations performed by human beings undergo rigorous peer review, at least in theory. I think computations done by computer should be subject to the same level of review. But Im not sure what that would look like. The article is The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems. Can We Trust in Them?, by Antonio J. Durán, Mario Pérez, and Juan L. Varona.ift.tt/1qTrTUi
Posted on: Sat, 25 Oct 2014 20:49:43 +0000
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