Wednesday, May 08, 2013

Errors in mathematics literature

From Errors and Corrections in Mathematics Literature (via Mark Thoma) a quote from Newton:
“There are a number of gray areas in which the experts know that the proofs are not complete or are partly incorrect. Since they are experts they know exactly what you can take; in a sense they are the happy few. This situation is definitely not acceptable, and we have to fight that results are really available (and not by jumping over this statement, which is not true, but you can take the next one, and so on). In recent years,
for many reasons [competition, complexity, and proliferating duties which reduce the time for careful peer review], the gray areas have been growing, and if they reach a certain level, then mathematical development will be injured.”
The most minute errors are not in mathematical matters to be scorned.11
— Isaac Newton [40, pp. 124–125]
referring to fluxions

In conclusion, the article states "In summary, the mathematics literature observably has low correction rates, yet systemic considerations suggest that mathematicians do not have lower error rates than other researchers. This mismatch may stem from a cultural emphasis on perfection that discourages discussing mistakes.The consequences are an absurdly high expectation for peer review to catch all errors and a neglect of policies to correct the literature once published."

In my own case, I and a collaborator are still finding mistakes in a paper published in 2003 and still writing a list of corrections.

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