The irrationality of π was first proven by Johann Heinrich Lambert (1728-1777) in the 1760s and published in 1768.

His proof was given in a long paper whose title is ``Mémoire sur quelques propriétés remarquables des quantités transcendentes circulaires et logarithmiques.''

Partial translations were published in English, for instance by Struik in 1969 (A source book in mathematics, 1200-1800) or by Berggren, Borwein and Borwein in Pi: A source book in 2004 (3rd edition).

However, to my knowledge, no complete English translation had been made available before the one I published in 2020:

D. Roegel: Lambert’s proof of the irrationality of Pi: Context and translation, 30 October 2020, https://hal.science/hal-02984214

I had actually translated Lambert's article in 2010-2012, but only finalized my work in 2020.

In 2023, in their book Irrationality, Transcendence and the Circle-Squaring Problem An Annotated Translation of J. H. Lambert’s Vorläufige Kenntnisse and Mémoire (snapshot available on google books), Eduardo Dorrego López and Elías Fuentes Guillén published a new complete translation of Lambert's article and only mention me on page 77, where they write:

To begin with, there is no complete English translation of this work; this is the first one. The works that are constantly referred to are commentaries or translations of certain parts of the Mémoire.What there is is an annotation in French of the complete work in its original language; it is (Juhel 2009).

After the first sentence, there is the footnote:

During the writing of this book, on which we began work in late 2019, a preliminary draft of an English translation of (Serfati 1992) by Denis Roegel was published online (available at: https://hal.archives-ouvertes.fr/hal-02984214) but, to our knowledge, a final version of it has not yet been published.

This is all what the authors have to say. Not only do they claim that I have translated Serfati's article, which is incorrect, they also claim that Juhel gave an annotation of the complete work in French, which is also false. I find it extraordinary that the authors merely discarded my work, perhaps because it was not peer-reviewed, or more likely, because it was not welcome. Many other works, such as Juhel's, were not peer-reviewed (to my knowledge), and yet they are cited. My complete translation, correction, annotation, and additions, has completely been bypassed by the authors. Was this intentional?

The authors claim that there have been changes by the publisher, but I can't see how the publisher can be made responsible for a sentence such as ``there is no complete English translation of this work.'' I also can't see why I do not appear in the list of references (page 81), and how the authors came to the claim that I translated Serfati's article.

In any case, the first complete English translation of Lambert's article is, unless proven otherwise, the one I made available online on October 30, 2020. It was not a sketch or a draft, although the title page writes so. It suffices to read it to see that it is a near final version of the translation.

My translation was not published in book form, or peer-reviewed, but that doesn't mean that Eduardo Dorrego López and Elías Fuentes Guillén should ignore it. In my translation, I also made reference to several non journal-published articles, because they were relevant. The same is true when someone cites manuscripts or other unpublished archive material.

So, Eduardo Dorrego López and Elías Fuentes Guillén have not been the first ones to translate Lambert's memoir entirely in English and make it available publicly. They were only the first ones, I believe, to publish such a translation as a book.

Now, it will be interesting to compare these two translations, and perhaps derive from them an even better annotated version of Lambert's article.

Last update: D. Roegel, 3 November 2023.

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