Mikhail Katz

The article "Leibniz's laws of continuity and homogeneity" was submitted to the periodical "American Mathematical Monthly" on 19 sep '11. The pdf version of the submitted article may be found here. The article argues that Leibniz's system for infinitesimal calculus was consistent, contrary to a widely held view. The article was rejected on the basis of two referee reports. The first referee report is reproduced here.

The article consisted of 4 pages of text and 1 page of bibliography. The referee report was 12 pages, i.e. three times as long as the article itself. The historian most quoted in the report (namely, three times) was the French historian Michel Serfati. At the top of page 11 of the report, the referee refers to non-standard analysis as ANS, the French acronym for "analyse non-standard". The report is in broken English suggestive of French authorship. Serfati was not cited in the submitted article.

The report's "final conclusion : as far as I know, since the XVIIth century, no serious mathematician has claimed that the system of Leibniz was consistent. And here's a text in 2011 which claims it's true ... Will there soon be an article claiming the possibility of squaring the circle?"

The article has since been published in the Notices of the American Mathematical Society http://www.ams.org/notices/201211/ A more detailed technical study is in Erkenntnis http://dx.doi.org/10.1007/s10670-012-9370-y









More on infinitesimals
Return to homepage