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I would like to know sources, articles, books or other, that provide information on ethical aspects in the research of mathematics, I wondered what is the literature that this community knows about ethical issues and proposals that were proposed in the context of mathematical research.

Question. What is the literature about ethical aspects in the context of the mathematical research? Many thanks.

I'm asking about it as a reference request, thus only is required to add the reference of such remarks, articles or books. From your answer to this reference request I can to contrast with the information that I know.


I think that my question is legitimate. I think that this site MathOverflow should be a safe site to ask good questions, and I think that my Question as reference request can be useful for more users.

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    $\begingroup$ Not so much for OP as for those voting to close, I note that questions concerning math and ethics have come up here before, and while some have been closed, many have been well-received. Especially considering that OP is asking for references and not for opinions, I don't see any reason to close this question. Here are some previous questions/answers where ethics was an issue: mathoverflow.net/questions/345049/… and mathoverflow.net/questions/41719/… (continued...) $\endgroup$ Nov 26, 2019 at 1:46
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    $\begingroup$ There is a book "Weapons of Math Destruction" by Cathy O'Neil of mathbabe.org, about various societal hazards of machine learning. Not so much about pure math research, but maybe of interest. $\endgroup$
    – none
    Nov 27, 2019 at 6:36
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    $\begingroup$ I think that this is a question about research-level ethics, not research-level mathematics. $\endgroup$ Nov 27, 2019 at 9:33
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    $\begingroup$ @YCor the question is a reference request. Polemical discussions and "questionable statements" would be non-answers, liable to be voted down and deleted. Do you see any polemics or questionable statements in the three answers that were posted before the question got closed? $\endgroup$ Nov 27, 2019 at 12:05
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    $\begingroup$ @Sergei, we're not discussing questions of ethics of mathematics here, we're just collecting them. $\endgroup$ Nov 27, 2019 at 22:30

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Maurice Chiodo is someone I am aware of regularly writing on ethics. Here's one starting point: https://ethics.maths.cam.ac.uk/pub

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  • $\begingroup$ Many thanks for your reference. $\endgroup$
    – user142929
    Nov 25, 2019 at 16:09
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    $\begingroup$ Further to my website above, you can find two recent pieces written by me in the LMS Newsletter about ethics in mathematics, both of which make some specific reference to mathematics research: The Importance of Ethics in Mathematics, Newsletter of the London Mathematical Society, Issue 48, p22-26, September 2019. Teaching Ethics in Mathematics, Newsletter of the London Mathematical Society, Issue 49, p22-26, November 2019. Unfortunately I cannot list these as an answer, as the question is currently on-hold. $\endgroup$
    – MCC
    Nov 27, 2019 at 11:17
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    $\begingroup$ @MCC you can now add them as an answer, as the question is re-opened $\endgroup$ Dec 2, 2019 at 8:19
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Michael Harris has written some blog posts on ethical aspects of mathematics.

There is also an opinion piece by Tom Leinster about ethical questions arising for mathematicians working for intelligence agencies. More on mathematics and mass surveillance can be found here.

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  • $\begingroup$ Many thanks I'm going to read your references. $\endgroup$
    – user142929
    Nov 26, 2019 at 21:09
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Here's an article from the 1980's on the AMS voting to turn down Reagan-era Star Wars funding in math:

https://www.the-scientist.com/news/math-society-votes-down-funding-by-sdi-military-62998

Bill Thurston was instrumental in getting the AMS to vote on this. He also wrote an article "Military funding in mathematics" that I can't find online, but a shortened version was in the Notices: https://www.ams.org/journals/notices/198701/198701FullIssue.pdf (p. 39). Thurston's AMS obituary also mentions that: https://www.ams.org/journals/notices/198701/198701FullIssue.pdf

Allyn Jackson discussed the AMS motion in a 2008 article: https://www.ams.org/notices/200804/tx080400445p.pdf

Alexander Grothendieck also famously resigned from IHÉS, ostensibly over similar issues.

Is that the kind of thing you were askng about?

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  • $\begingroup$ Many thanks for your answer, the only source that I've seen before posting this question was a video on YouTube about the ethic aspects consider by Alexander Grothendieck (also refers Bourbaki). This (Mooc course) video (in Spanish) on YouTube from the official channel ULLmedia - Universidad de La Laguna and title 3.2 La financiación de la ciencia y la tecnología: Alexander Grothendieck (the date is 22nd March, 2019). Your references also are very good. $\endgroup$
    – user142929
    Nov 27, 2019 at 8:31
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    $\begingroup$ You might like Terry Winograd (computer scientist)'s article on a similar topic to Thurston's: cpsr.org/prevsite/publications/newsletters/issues/2001/Summer/… $\endgroup$
    – none
    Nov 27, 2019 at 9:09
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The Just Mathematics Collective maintains a list of resources related to ethics in mathematics.

One of those resources is itself a list of resources, an Ethics in Mathematics reading list by Allison N Miller at Swarthmore. This reading list alone is 12 pages long - food for thought for those who think there's nothing to be said.

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  • $\begingroup$ Many thanks, good day. $\endgroup$
    – user142929
    Oct 1, 2021 at 14:14
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At the upcoming Joint Mathematics Meeting in Denver, January 2020, there will be an AMS Committee on the Profession Panel Discussion: Mathematics and Ethics, Wednesday 15th. It might be worthwhile contacting the moderator and/or panelists of this discussion to see what references they know about.

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  • $\begingroup$ Yes, it is a good idea. $\endgroup$
    – user142929
    Dec 2, 2019 at 7:52
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In November, the American Mathematical Society will publish A Conversation on Professional Norms in Mathematics. Here is some information from the AMS website:

Edited by Mathilde Gerbelli-Gauthier: Institute for Advanced Study, Princeton, NJ,
Pamela E. Harris: Williams College, Williamstown, MA,
Michael A. Hill: University of California, Los Angeles, Los Angeles, CA,
Dagan Karp: Harvey Mudd College, Claremont, CA,
Emily Riehl: Johns Hopkins University, Baltimore, MD

The articles in this volume grew out of a 2019 workshop, held at Johns Hopkins University, that was inspired by a belief that when mathematicians take time to reflect on the social forces involved in the production of mathematics, actionable insights result. Topics range from mechanisms that lead to an inclusion-exclusion dichotomy within mathematics to common pitfalls and better alternatives to how mathematicians approach teaching, mentoring and communicating mathematical ideas.

This collection will be of interest to students, faculty and administrators wishing to gain a snapshot of the current state of professional norms within mathematics and possible steps toward improvements.

Readership

Undergraduate and graduate students and researchers interested in mathematical culture and society.

Table of Contents for MBK/140
• Introduction by Emily Riehl
• The time for miracles is over by William Yslas Vélez; Ana Christina Velez
• On toxic mentorship and the academic savior complex by Pamela E. Harris
• Todxs cuentan: Building community and welcoming humanity from the first day of class by Federico Ardila-Mantilla
• Congressive question time by Eugenia Cheng
• Mathematics, we have a problem by Michelle Manes
• Fiber bundles and intersectional feminism by Dagan Karp
• On parameters for communicating mathematics by Oliver Knill
• Turning coffee into unions: Mathematicians and collective bargaining by Denis R. Hirschfeldt
• Universities in the time of climate change by Izabella Laba

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    $\begingroup$ Many thanks I hope to read all answers, Many thanks again for your attention, and nice answer. The best day. $\endgroup$
    – user142929
    Oct 1, 2021 at 14:18
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Alexandre Grothendieck talked a lot about ethics when a member of the group Survivre et Vivre. He also made a famous speech at CERN , entitled "allons nous continuer la recherche scientifique", for which there exists both audio recordings and written translations.

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  • $\begingroup$ Many thanks, also for refer to the professor Alexandre Grothendieck $\endgroup$
    – user142929
    Oct 1, 2021 at 14:16
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Ethics in the practice or use of mathematics is often addressed indirectly by mathematicians. Below I give three examples that come to mind, the first expounded in more detail than the others (because it is less obvious).

In a not always direct way V. I. Arnold often wrote about ethics in mathematics. By way of illustration, I quote a bit from the beginning of his article Topological problems of the theory of wave propagation:

The difference between pure and applied mathematics is not scientific but only social. A pure mathematician is paid for uncovering new mathematical facts. An applied mathematician is paid for the solution of quite specific problems.

Example. Columbus began by making a purely applied study, trying to find the way to China, and he was being paid for this.

The end of his voyage is reminiscent of a fact of pure mathematics. Note that the immediate direct benefit to the Spanish economy of the discoveries of Columbus was far less than that from the coastal navigation of ordinary captains.

Mayakovsky has well described the difference between pure and applied mathematics in "How to make poetry". "The man who found that twice two is four was a great mathematician even if he found it out by counting cigarette stubs. Those who now calculate by the same formula much greater things, for example locomotives, are not mathematicians at all."

The theory of algebraic curves over finite fields has now become applied mathematics, financed by the CIA, the KGB and other similar organizations. Fermat's problem would also be applied if its solution were of monetary value. Many mathematicians of the twentieth century have warned of the dangers of dividing mathematics into parts. Hermann Weyl has written: "In our time the angel of topology and the devil of abstract algebra are fighting for every mathematical domain" 1.

...

Generations of mathematicians were taught by this method, not having any contact at all with any other kind of mathematics. As a result they cannot understand any other science and enthusiastically busy themselves with tedious details of generalizations of achievements of their teachers of little interest.

Although, as is apparent from the cited text, Arnold's affirmations about history and culture were frequently questionable, when not outright wrong, to focus on this is to miss the point of the cited text, which is to use the history as a cartoon to illustrate an ethical/social claim about the practice of mathematics. I do not here try to summarize what I think the claim is, in part because the cited text is taken out of its context in a larger text, and in part because Arnold's intentionally polemical and ironical writing style was well adapted to expressing his ideas succinctly, if not always transparently. (I recommend reading the article to see what his point was and whether one agrees with it.)

This sort of passage is by no means isolated in Arnold's writing. Many of his essays, particularly in his later years, contain similar commentaries. So does the introduction to his book on geometrical methods in ordinary differential equations, whose statement

The axiomatization and algebraization of mathematics, after more than 50 years, has lead to the illegibility of such a large number of mathematical texts that the threat of complete loss of contact with physics and the natural sciences has been realized.

is well known. That this statement is part of a basically ethical commentary seems to me clear, as it self-evidently is in the following passage from the above cited article:

It is clear, however, that the writer does not understand anything, but only knows how to prove. The absurdity and even the criminality of a system of education, leading clearly intelligent people to such a state, seems to me to be obvious. For 'applied' work such 'knowledge' is useless and even dangerous (the consequences may take on the character of a Chernobyl disaster).

The aim of a mathematical lecture should be not the logical derivation of some incomprehensible assertions from others (equally incomprehensible): it is necessary to explain to the audience what the discussion is about and to teach them to use not only the results presented, but—and this is major—the methods and the ideas.

Arnold's writings of this style are often (partly unfairly) considered merely a (misguided) attack on Bourbaki (although there is some of this in them) and this can distract from what was a coherent point of view enunciated repeatedly over many years. It would be interesting for someone interested in such matters to try to distill in nonpolemical terms the essential ethical content of that commentary. I have my own idea, but it's not scholarly, and I don't feel able to express it well in a forum like this, although I will comment that I think my own learning process suffered from precisely what Arnold criticizes and as the years have gone by I have adjusted how I try to research and teach accordingly, although often unsuccessfully.

I think examples of similar writings by other mathematicians can be found, particularly among those who came of age during the cold war in the countries it most afflicted (e.g. USA and USSR) and had direct contact with the use of mathematics in contexts related to defense, warfare, and spying.

Doron Zeilberger posts on his webpage "Opinions", many of which have an ethical character, in particular with respect to the questions of how to do mathematics and what constitutes good mathematics.

The "Bible codes" episode generated writings by mathematicians having an ethical character.

If one broadens the context from "mathematics" to the "mathematical sciences" then there is much more written, often of a more explicitly ethical character. I have in mind something like Andrew Gelman's blog, which frequently, as do Gelman's articles, addresses ethical questions related to the use and practice of statistics. There are many more examples.

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    $\begingroup$ Many thanks, good day. $\endgroup$
    – user142929
    Oct 1, 2021 at 14:14
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Oliver Rosten published a paper On functional representations of the conformal algebra in the European Physical Journal in 2017. In the acknowledgements section he included the following in reference to the death by suicide of a friend of his, Francis Dolan, in 2011.

I am firmly of the conviction that the psychological brutality of the post-doctoral system played a strong underlying role in Francis’ death. I would like to take this opportunity, should anyone be listening, to urge those within academia in roles of leadership to do far more to protect members of the community suffering from mental health problems, particularly during the most vulnerable stages of their careers.

There was resistance to having these lines included in the published article with at least two journals refusing to publish them. See this article for more details.

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  • $\begingroup$ Many thanks, good day. $\endgroup$
    – user142929
    Oct 5, 2021 at 7:43
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Jonathan Korman (a mathematician) and Wing-Yee Tong (an artist) coauthored The NSA and the Social Responsibility of Mathematicians in the December 2016 issue of The Mathematical Intelligencer. It argues that "mathematicians have a moral obligation to make sure the power of mathematics is developed and used responsibly and not against public interest", in contrast to the general lack of involvement as evidenced e.g. by the observation that

... in the period January 2014 to February 2015, only 33 individuals with affiliations to mathematics departments have signed the declaration Academics Against Mass Surveillance. In contrast, a petition in support of continued funding for the Institute for Mathematics and Its Applications accumulated more than 2000 signatures over the one month period January 16 to February 16, 2015.

This cites another article Declining Mathematics Funding at the DoD, by Allyn Jackson in the January 2000 issue of the Notices of the AMS, which also discusses the AMS referendum referred to in the other answers. Here are a few relevant paragraphs:

It was almost twelve years ago that the AMS membership passed a referendum concerning support for mathematics from the DoD agencies. Motion 2 of the referendum expressed concern about the “tendency to distribute this support through narrowly focused (mission-oriented) programs and to circumvent peer review procedures.” The motion warned that this tendency “may skew and ultimately injure mathematics in the United States,” and ended by saying, “Therefore those representing the AMS are requested to direct their efforts towards increasing the fraction of non-military funding for mathematics research, as well as towards increasing total research support.” The referendum also included motions about the Strategic Defense Initiative and other, less controversial, matters of funding policy. The referendum drew about 7,000 votes, and motion 2 passed by a wide margin, with about 74% in favor and about 19% against (there were some abstentions).

At AMS meetings and in the pages of the Notices, passions flowed so hot that it is surprising to see how cool they are today. In retrospect the referendum seems like a quaint reminder of a less practical, more idealistic time that has since passed. The referendum’s main effect seems to have been to alienate, at least temporarily, certain segments of the mathematical community from the AMS. Some mathematicians were deeply offended by the referendum; one was James Crowley, who at the time was the head of the mathematics program at AFOSR and is now the executive director of SIAM. Today AMS representatives do not seem constrained to focus their attention only on “increasing the fraction of non-military funding for mathematics research.” As one observer put it, the AMS referendum is “not on the radar screen” of anyone concerned with funding for mathematics or science.

Indeed, the AMS has been active on a variety of fronts to try to boost funding for science and mathematics by all federal agencies, including those in the DoD. The AMS Committee on Science Policy, chaired by Arthur Jaffe, has invited to its meetings a number of key people from the DoD, including Robert J. Trew, director of research in the office of the secretary of defense. The AMS is active in the CNSR (Coalition for National Security Research), a group of sixteen scientific societies, university groups, and industry representatives who are advocates for increased support for research by the DoD. Perhaps their voices are being heard: The fiscal year 2000 defense appropriations bill, signed into law by President Clinton in October 1999, contains a 7.3% increase for DoD research. Consistent advocacy for all of science and mathematics, bolstered by alliances with other scientific groups, is what is likely to improve the funding picture for mathematics at the DoD agencies. As Rankin put it, “It is in the interest of mathematics to have all agencies that fund science be healthy.”

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