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Can you commit fraud in a mathematics publication? Or is this a privilege of empirical sciences?

If a mathematician jumps from one bit of information to another that does not follow logically, from more basic principles, then, that's not fraud, but a logical fallacy, akin to saying 1+1=3.

If an empirical scientist gets a results of 3.3341, but claims it was 3.7341 that's fraud.

1 Answer 1

As an example, a review by Almgren of a book by Fomenko comes quite close to an accusation of what, with some stretch, could be considered a fraud:

The reviewer has known Fomenko personally for more than two decades and still is at a loss to understand why he is not more responsible in his mathematical claims. The following are two particular examples of concern.

The book cover states "In this volume, the solution of the Plateau problem in the class of all manifolds with fixed boundary is given in detail ... " Fomenko made a similar claim in a lecture at and in the proceedings of the 1974 International Congress in Vancouver, in the introduction to a major paper (in Russian), and in an interview published in the Mathematical Intelligencer. His preface in the volume under review is ambiguous about this issue. In any case, the claim is not proved, as he acknowledges privately <...> The only significant contributions to this representation problem are due to B. White.