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To complement the recent post on Euler's errors, I would pose the following question: what common errors of Euler interpetation appear in the literature? What errors are attributed to Euler's work in infinitesimal analysis even though he never made them? In addition, what cultural attitudes tend to contribute to the persistence of a desire to seek to attribute errors to Euler (sometimes without bothering to study his works firsthand)? As an example, I would cite Jeremy Gray's comment to the effect that

At some point it should be admitted that Euler's attempts at explaining the foundations of calculus in terms of differentials, which are and are not zero, are dreadfully weak,

while providing no evidence whatsoever for such a claim. See page 6 here.

Another example is the thread Euler and infinity whether both the question and the accepted answer assume that Euler cavalierly assumed that sine equals the infinite product merely because they have the same zeros. Over 300 visitors to the page didn't disagree and apparently nobody bothered actually to look at what Euler wrote.

Note 1. Qualified editors are invited to click on the "reopen" button below to permit an exploration of specific issues of objectivity or lack thereof in Euler interpretation.

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Mikhail Katz
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    The only desire to seek errors is the truth, i.e., to find out whether a proof is really "correct". It may be difficult to say what this means, but it has nothing to do with Euler. – Dietrich Burde Apr 22 '14 at 09:18
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    An example of the kind of attitude I am referring to is found in the currently fourth answer at the "Euler's errors" post. I responded to the answer there; see here – Mikhail Katz Apr 22 '14 at 09:22
  • Yes, you are right. But this is also the problem I mentioned, i.e., the discussion whether a given proof is correct or not. – Dietrich Burde Apr 22 '14 at 11:34
  • @DietrichBurde, I agree with you in principle about seeking the truth, but in practice the truth desperately sought turns out, mysteriously but unavoidably, to be a Weierstrassian one rather than an Eulerian. That's part of my question. – Mikhail Katz Apr 22 '14 at 18:00
  • I'd think one "cultural attitude" that contributes is that it's comforting to know that "even the giants blundered" from time to time. Makes one feel less stupid if one is in good company making mistakes. – Daniel Fischer Apr 23 '14 at 12:03
  • @DanielFischer, thanks for your insight. But somehow I don't recall anybody looking for errors in Grothendieck, Deligne, and hardly ever in Gauss, Dirichlet, etc. (with some notable exceptions). What seems to fascinate the public is that it was the great infinitesimalists that were at fault for committing logical errors. This is consistent with the cultural attitude that Cantor, Dedekind, and Weierstrass saved mathematics from the dustbin of perpetual error by eliminating infinitesimals. – Mikhail Katz Apr 23 '14 at 12:07
  • Does anyone look for errors in Euler? As far as I know, people know about Euler's mistakes simply because they read his works and go "oh, a mistake". I haven't heard of any deliberate efforts to seek out errors in his works. – Jack M Apr 23 '14 at 12:10
  • @JackM, Which mistakes are you referring to? Often what is going on is that his valid infinitesimal techniques are misinterpreted and vilified without a valid reason. See the article I cited. – Mikhail Katz Apr 23 '14 at 12:12
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    @user72694 I don't see how that addresses my comment. I was simply questioning your apparant claim that people go out of their way to dig up errors in Euler's works. – Jack M Apr 23 '14 at 12:14
  • @JackM, few mathematicians actually go to the trouble of reading historical texts. What I was referring to is a tendency to assume such mistakes because Euler and other greats used infinitesimals, which are often viewed as suspect at best and possibly even inconsistent; see here. Those mathematicians that do go to the trouble of reading Euler's work with an unprejudiced eye usually come away impressed by its consistency; see e.g., McKinzie. – Mikhail Katz Apr 23 '14 at 12:16
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    I think it's clear OP has an agenda and is more interested in pushing a point than in enquiring about mathematics. Voting to close. – Gerry Myerson Apr 23 '14 at 13:10
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    @GerryMyerson has distinguished himself in this kind of narrow-minded interpretation of SE rules before. I invite other editors to distance themselves from this kind of practice of suppressing viewpoints deviating from the received wisdom. – Mikhail Katz Apr 23 '14 at 15:20
  • @GerryMyerson, on the contrary I am very interested precisely in understanding Euler's mathematics and have studied Euler firsthand. Moreover I have already published some articles on this subject. Your actions here indicate that you seem more interested in suppressing certain points of view than in having an open discussion. I urge you to reconsider and revert your "closing" vote. – Mikhail Katz Apr 23 '14 at 15:50
  • Discussion, open or otherwise, is not what this website is for. Get yourself a blog. – Gerry Myerson Apr 24 '14 at 00:30
  • @Gerry, my question looks specifically for instances of tendentious reading of Euler. If everybody you disagreed with had to move out of SE this would be a much less interesting place. – Mikhail Katz Apr 24 '14 at 09:32
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    @Gerry If you follow the homepage link in user72694's profile you will learn that he is a mathematician who has published much on these historical matters. I think that we should welcome his contributions here (as we should all serious historical contributions). As such, I've voted to reopen, and I encourage others to also do so. – Bill Dubuque Apr 25 '14 at 13:38
  • @Bill, thanks for your comment. – Mikhail Katz Apr 26 '14 at 18:39

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A possible reason for holding Euler to be suspect has to do with the fact that Euler was an infinitesimalist par excellence. Starting around 1870, Prussian mathematicians launched a program of rigorizing mathematics that was inextricably linked in their minds with a desire to extirpate infinitesimals. This contributed to a widespread attitude of suspicion toward infinitesimals which was perpetuated in numerous writings by historians who sought to embellish the significance of the Prussian effort. Thus, C. Boyer in his influential text goes so far as describing Cantor, Dedenkind, and Weierstrass as "the great triumvirate". Such historians also repeatedly painted a picture of rigor and infinitesimals as being antonyms. By association, the great infinitesimalists of the past also became suspect. More details can be found in this article.

Mikhail Katz
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