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21.06.11 · 10:57 Uhr

Rejecta Mathematica

Kategorie: Naturwissenschaften  ·  Kommentare: 5

"minor or traditionally unpublishable results, non-traditional ideas and proof techniques, misunderstood genius, results based on questionable assumptions, and controversial papers and open letters."

Ich habe gerade eine e-Mail bekommen:

The highly anticipated follow up to the inaugural issue of Rejecta Mathematica has been posted at

http://math.rejecta.org/vol2-num1 http://math.rejecta.org/vol2-num1

This issue features articles by Christoph Bauer, Hermann Bauer, Jean-François Burnol, Aran Nayebi, Karin Schnass, Oruganti Shanker, Satish Shirali, and Pierre Vandergheynst.

Topics include subspace classification, distributions of pseudoprimes, a challenge to Gödel's theorem, and more!

If you are excited by the Rejecta Mathematica mission, we welcome your participation in the support required to keep this journal going. In particular, we ask that you be sure to send us your paper submissions and spread the word to your colleagues. We welcome feedback, submissions, and support for the Rejecta Mathematica mission through our website: math.rejecta.org.

Rejecta Mathematica ist eine Open Access-Online-Zeitschrift, die unwichtige, unveröffentlichbare, untraditionelle, unverstandene, auf fragwürdigen Voraussetzungen aufbauende oder kontroverse Arbeiten aus Mathematik, Physik und Ingenieurwissenschaften veröffentlichen will.

Gegründet wurde die Zeitschrift 2007, die erste Ausgabe ("Inaugural Volume") erschien dann im Juli 2009 und seitdem hörte man nichts mehr von dem Projekt. Es ist aber doch noch nicht eingeschlafen und jetzt ist also die zweite Ausgabe erschienen.

Die Artikel sind meist ganz ernsthafte mathematische Arbeiten (allerdings findet sich auch eine Widerlegung des Gödelschen Unvollständigkeitssatzes, immerhin im Stil eines üblichen mathematischen Beweises), die (wie aus den einführenden Erklärungen der Autoren hervorgeht) wohl nicht wegen inhaltlicher Fehler, sondern eher wegen fehlender Relevanz abgelehnt wurden.

Es handelt sich bei Rejecta Mathematica also nicht (wie man vielleicht zunächst hätte erwarten können) um zur allgemeinen Belustigung¹ öffentlich gemachte Crackpot-Artikel, sondern eher im Gegenteil um recht technische Arbeiten, für die man trotz Unveröffentlichbarkeit eine feste referenzierbare Adresse haben will.

¹: Off topic: wer mathematischen Nonsens lustig findet, dem kann ich "The General Science Journal" wärmstens empfehlen.

Den Artikeln ist jeweils ein "Offener Brief" des Autors vorangestellt. Meist drücken die Autoren in diesen offenen Briefen ihr Unverständnis über die mehrmalige Ablehnung ihrer Arbeiten aus, manche der offenen Briefe haben fast schon den Charakter einer Abrechnung mit den verantwortlichen Herausgebern (die immerhin nicht namentlich genannt werden). Ein typisches Beispiel:

I wrote this paper in 2006, and submitted it to a journal specializing in integral equations and operator theory. After circa 14 months I received a report which I reproduce in full here (I allow myself to correct the spelling of a mathematician's name cited in the report):

"In spite of desperate efforts, the referee has failed to understand what the paper is about. Apparently it does not have a definite goal but consists of miscellaneous remarks to the papers by de~Branges and Rovnyak. It is practically impossible to distinguish original results in this jumble. Actually, the text does not look as a mathematical article but rather as some notes for personal use.

In the referee's opinion, the paper should be rewritten according to conventional rules and its volume should be divided by the factor 5-10. The author should try to formulate the results which he considers to be new."

Let me explain why I consider the publication of the paper important. First of all the referee's report only serves to demonstrate that the referee did not read the manuscript. I tried to point this out to the editor in chief, to no avail:

"Dear Professor Burnol,

I read all your letters to us. I am not changing my mind! Your paper is not accepted for publication. This decision is final and the discussions about this paper this time I consider finished.
Sincerely, XXX"

I think this illustrates nicely how dysfunctional the peer-review process may be, at times. Regarding the paper itself, it is well structured, and its goal was to prove new mathematical theorems (!), a goal which was achieved (!). I corrected a typo in 2008 (there was a superfluous imaginary i in some equations, see the footnote on page 1), this is the only change to the 2006 version.

The referee asked me to divide the "volume" by between five and ten, a request which at that time particularly infuriated me. In fact, a more acceptable comment would have been to point out that the paper contained material for between 3 and 5 reasonably sized quasi-independent publications (of reasonable, but obviously not earth-shaking interest!), but I wanted to make a common exposition with in particular a common introduction. What would be the point of repeating 5 times the same introduction? An introduction is made necessary by the fact that my perspective is unique and links together a priori disjoint topics, the reader needs some help in entering this framework.

Another difficulty is that in 2008, during a stay at Institut des Hautes Études Scientifiques (IHES), I made very significant advances (establishing links with domains apparently completely unrelated, and which moreover have been of great interest for the last thirty years to large communities of researchers), on which I have had opportunities to give lectures at IHES, at the European Conference of Mathematics (ECM) at Amsterdam, and at a workshop at the Independent University of Moscow (Conference Zeta functions II). I have circulated a hand-written manuscript of about 80 pages, and prior to publishing this novel material in peer-reviewed journals, I need to make my earlier work available to the mathematical community.

I did sufficiently serious and dedicated work on this in 2006 resulting in a paper of about 65 pages. It would be all too easy, and far more beneficial to my career, to instead divide the paper into at least 3 publications, but I just don't see the point. If one is not sufficiently committed to mathematics to place great importance on the form one gives to one's own contributions, if one is ready to obey arbitrary diktats, if all that matters is adding lines of publications to a CV, then one practices a job and not a passion and one does not care about his/her legacy, one lives amidst superficial illusions and pleasures.

This paper will be necessary reading to get a full understanding of my earlier as well as of my future works.

This article was submitted to Journal of Pure and Applied Algebra on December 15, 1998, and it was rejected with a very short report about eight months later, the cited reason being that it was too long for its content. By the time I received that overdue rejection, I was nearly done writing a sequel,

Ezra Miller, The Alexander duality functors and local duality with monomial support,
Journal of Algebra 231 (2000), 180-234.

which contained more general results. The sequel has been well-cited, but the current article was already on the arXiv (math.AC/9812095), and according to Google Scholar it has also been well-cited. In fact, this article has been cited more than most of my others--as much or more, for example, than my articles in Journal of the American Mathematical Society and Duke Mathematical Journal. It seemed a shame that what is apparently a useful article should languish in eternal semipublication, so I submitted it to Rejecta Mathematica.

Why is this article useful? It is more concrete than its sequel: more examples, more illustrations, and fewer functors. The article contains no known errors and no known uncited rederivations of earlier work; in fact, subsequent work (by other authors as well as in its sequel) has confirmed the results herein by independent methods many times over. The article is unchanged from the version submitted to Journal of Pure and Applied Algebra.

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