Hippocratic Oaths for Mathematicians?

In this paper I ask whether mathematicians should swear an oath similar to the Hippocratic oath sworn by some medical professionals as a means to foster morally praiseworthy engagement with the ethical dimensions of mathematics. I individuate four dimensions in which mathematics is ethically charged: (1) applying mathematical knowledge to the world can cause harm, (2) participation of mathematicians in morally contentious practices is an ethical issue, (3) mathematics as a social activity faces relevant ethical concerns, (4) mathematical knowledge itself may be ethically charged. I present a conceptual framework for oaths and discuss some empirical results on the effectiveness of oath-taking to foster morally praiseworthy behaviour. My findings suggest that enforcing oath-taking practices in mathematics is not currently a suitable means to foster ethically praiseworthy behaviour amongst mathematicians. Oaths can, however, provide needed edifying narratives about how to act ethically when acting as a mathematician.

. Today, some mathematicians have formed groups and societies that are pushing for an ethical agenda in mathematics, 1,2 have organised special sessions of the American Mathematical Society, 3 argue publicly that mathematicians ought to be aware of the ethical implications of their practices (Müller et al. 2022;Fry 2019;Lott 2004;Shulman, 2002;Hersh, 1990;Davis, 1988), and encourage their students to think about how to do mathematics ethically (Ardila, 2021;Pinch, 2021;Su, 2020;Franklin, 2005). They are joined by mathematics education theorists (Ernest, 2018(Ernest, , 2021Dubbs, 2020;Vale et al., 2016;Adu-Gyamfi & Okech, 2010), philosophers (Hunsicker & Rittberg, 2022;Rittberg et al., 2020;Mittelstadt et al., 2016), and sociologists of mathematics (Barany, 2018;MacKenzie, 2009). These various thinkers reveal and discuss numerous ethical issues that mathematicians may encounter in their work as mathematicians. These issues are thus issues in the ethics of mathematics because they are ethical issues faced by mathematicians. It is in this sense that I say that mathematical knowledge-making is ethically charged. 4 Ethical reflections about one's practices have become standard academic procedure. Research funding organisations routinely ask applicants to reflect on the ethics of their proposals. Researchers in various natural sciences, from stem cell researchers to nuclear physicists, have long since realised the ethical dimensions of their activities. Efforts to engage with the ethical dimensions of mathematical practices, however, have come late. As late as 1988 Davis wrote: I would like to tell you today about an international campaign for a special kind of ethical statement, a pledge for mathematicians analogous to the Hippocratic Oath in medicine. I would like to tell you about it, but I cannot: I do not know that there is any such campaign. (Davis 1988) The American Mathematical Society (AMS) only adopted their code of ethics in 1995 (Hersh, 2008). The UK based Royal Statistical Society (RSS) adopted their code in 1993 and revised it in 2014, 5 and the UK based Institute for Mathematics and its Applications (IMA) formally approved its code as late as 2018. 6 Even today many mathematicians think that their activities are largely ethics-free (Ernest, 2018(Ernest, , 2021Shulman, 2002); cf. also Sect. 1. This raises the question how to effectively encourage mathematicians to engage with the ethical dimensions of mathematical knowledge-making.
Some mathematicians have proposed that mathematicians swear a Hippocratic oath to raise awareness amongst mathematicians of the ethical dimensions of their practices (Sample, 2019;Lott, 2004;Davis, 1988). The Hippocratic oath is sworn by some medical professionals; it's the one in which they swear to "do no harm". In the original version it is also sworn not to carry out abortions using a pessary. This line is missing in modern versions of the oath, e.g. the Declaration of Geneva or the Oath of Lasagna. 7 Interestingly, the line "do no harm" is also missing from many modern versions of the oath, thereby accommodating medical practices such as euthanasia. Perhaps unsurprisingly, there is a debate amongst medical professionals about the timeliness of their practice to swear oaths: should any oath be sworn, and if so which one (Hajar, 2017;Sulmasy, 1999;Pellegrino, 2006)? Medical practices differ; medical students in the US swear modern versions of the Hippocratic oath, students in Pakistan swear the original version, and German students of medicine swear no oath at all (Oxtoby, 2016).
The debate amongst medical professionals notwithstanding, the term "Hippocratic oath" has taken on a life of its own; when mathematician Hannah Fry calls for a Hippocratic oath for mathematicians in an interview with The Guardian (Sample, 2019), she is not calling on mathematicians not to carry out abortions using pessaries. Rather, she is calling for mathematicians to take an oath to engage with the ethical dimensions of their practices. That is, she focusses on the intent of the Hippocratic oath, rather than its specific content. This has become common practice -e.g. there are Hippocratic oaths for bankers (de Bruin, 2016), geologists (Matteucci et al., 2012), or technologists (Abbas, 2019) -and I will adopt it in this paper: a call for a Hippocratic oath is a call for an oath to engage with the ethical dimensions of one's practice (and not a call to swear the original Hippocratic oath).
Calls for Hippocratic oaths for scientists have also been put forward (Bettridge et al., 2018;Matteucci et al., 2012;Rotblat, 1999). The Pugwash group of scientists has proposed an oath for scientists 8 to uphold the Russell-Einstein manifesto for peace in a world with nuclear weapons, 9 and Abbas et al., (2019) propose an oath for users and developers of technologies. Philosopher of science Popper, (1971, 281) voiced his modest hopes that "discussions centering on a revision of the Hippocratic Oath [for scientists] may lead to reflection on such fundamental moral problems as the priority of the alleviation of suffering".
Similarly, the banking crisis of 2007-2008 has led to the proposal of oaths for bankers and business, such as the Dutch Banker's Oath, the MBA Oath of the Harvard Business School, or the Economist's Oath by DeMartino, (2011), and a discussion about their effectiveness (de Bruin, 2016;Boatright, 2013).
This raises questions about what can reasonably be expected from such Hippocratic oaths and how effective they are in satisfying these expectations. This paper explores these questions with a particular focus on the call for a Hippocratic oath for mathematics.
I phrase my argument in terms of individual and structural interventions. To get at what I mean by these two types of interventions, consider the example of a police agent who does not give deserved credit to the testimony of a speaker due to irrelevant social identifiers, such as colour of skin. One remedy, put forward for example in (Fricker, 2007), is to call on the police agent to "behave better": the police agent who does not give sufficient credit to the testimony of a person of colour because of the police agent's bias should stop being biased. There is a focus on the individual here, but in a game that is broken we should not only ask the players not to abuse the broken parts, we should adjust the game. 10 Adjusting the game is what I call a structural intervention. On the other hand, even in the best designed game we still need virtuous players (Cohen, 2019); even in chess one can try to cheat, as the viral video of a chess hustler trying to cheat chess Grandmaster Maurice Ashley shows. 11 But how to be an ethically virtuous player is rarely obvious. That is, we need edifying accounts of how to be such a player. Besides structural interventions we also need individual level interventions. 12 In this paper I propose to learn from the ethical reflections of other practices (most notably: medicine and economics) about relevant conceptual distinctions that help to advance the debate about the ethics of mathematics. I argue that a Hippocratic oath for mathematicians is suitable as an individual but unsuited as a structural intervention for current mathematical practices. This refines the calls for such oaths (Sample, 2019;Lott, 2004;Davis, 1988) and the doubt about their efficacy expressed in (Müller et al. 2022).
In Sect. 1 I present some of the mathematicians' arguments for why mathematicians need to become more aware of the ethical implications of their practices. I individuate four dimensions in which mathematics may be said to be ethically charged; (1) applying mathematical knowledge to the world can cause harm (as well as being a force for good), (2) participation of mathematicians in morally contentious practices is an ethical issue, (3) mathematics as a social activity faces relevant ethical concerns, (4) mathematical knowledge itself may be ethically charged. These four dimensions feature to differing degrees in the calls for a Hippocratic oath for mathematicians (Sample, 2019;Lott, 2004;Davis, 1988).
In Sect. 2 I introduce a conceptual framework for oaths based on work by de Bruin (2016) and Sulmasy (1999). This framework casts promissory oaths, such as the Hippocratic Oath, as publicly witnessed and externally validated ritualistic acts through which the oath-taker encumbers herself with commitments which jeopardise her entire moral standing in case of non-compliance.
In Sect. 3 I discuss how effective oaths are at promoting ethically praiseworthy behaviour. The literature is divided on this point, with numerous social scientists arguing that they are effective and a number of philosophers arguing that they are not. I seek to explain this discordance by pointing to the different conceptualisations of oaths at play. The effectiveness of oaths in the sense of Sulmasy and de Bruin (Sect. 2), I submit in the section, is nearly impossible to test empirically. 10 Obviously policing practices are no game; the metaphor has its limits. 11 https://www.youtube.com/watch?v=U5vnpOp0U_g. 12 "Level" is a filler-word here (and throughout) included to avoid the ambiguity of "individual intervention" as "one particular intervention" and "intervention aimed at an individual". In Sect. 4 I argue for the principal claim of this paper: given the state of contemporary mathematical cultures, a Hippocratic oath for mathematicians is a promising individual level intervention, but as a structural intervention such an oath is unsuited.
In Sect. 5 I conclude by summing up the salient points of this piece.

Ethically Charged Mathematics
In this section I report on mathematicians' arguments why mathematicians need to become aware of the ethical dimensions of their practices. ZIP codes are thus potentially relevant pieces of information to the mortgage-seller, but asking for them brings in the ethical concerns connected to asking for the colour of skin through the backdoor. Fry's argument is that ethical concerns such as these are faced by "young inexperienced white boys" whose mathematical training did not raise their awareness of the ethical issues at stake. Fry is getting at the ethics of digital technologies, which has attracted sustained interest from philosophers (e.g. Noble 2018; Mittelstadt et al., 2016) and computer scientists (e.g. Strümke et al., 2021). Fry's point is that many mathematicians still seem largely unaware of the ethical implications of their activities. Other mathematicians report similar concerns (Müller et al. 2022;Pinch, 2021;Chiodo & Clifton, 2019;Korman & Tong, 2016;O'Neil 2016;Franklin, 2005). Some cases of such ethical unawareness have even made it into the media, such as the case of Andrew Pole, a mathematician working for the US supermarket chain Target, whose customer consumption prediction models were so effective/invasive that they managed to spot pregnancies even before close family members were aware (Duhigg, 2012).
The claim of Fry and the other mathematicians is that, in general, mathematicians do not practise due diligence about ethical matters when applying their mathematical expertise in non-academic settings. This is coupled with the recognition that relevant training about the ethical issues at stake is largely missing. Fry's call for a Hippocratic oath for mathematicians (Sample, 2019) is a proposal to counteract these problems. 13 Applying mathematical expertise to non-academic practices, such as writing algorithms for companies, is not in itself a moral issue. The ethical dimension comes in when we consider how this mathematical expertise is applied. This is the first dimension of the ethically charged nature of mathematical knowledge-making I individuate in this section.
Another aspect of the ethically charged application of mathematical knowledge is engagement in morally contentious practices, such as mathematicians working for the military-industrial complex. Wiener, in (Green & Wiener, 1947), for example makes clear that he does not wish his mathematical achievements be used for militaristic purposes (whilst acknowledging that he is powerless to actually stop such use). Hersh (1990) reminds us that the American Mathematical Society adopted an anti-Star Wars SDI stance: members of the society would not help in the development of this military project. And the Just Mathematics Collective calls on the mathematical community to sever its ties to police states and re-evaluate its connections to the financial sector. 14 Application of mathematical knowledge to morally contentious practices is the second dimension of the ethically charged nature of mathematical knowledge-making I individuate in this section.
The above episodes principally focus on mathematicians who no longer work in an academic setting. Hersh (1990) treats such mathematicians as applied mathematicians and submits that it is obvious that once mathematicians leave the ivory tower of pure academic mathematical activity, ethical concerns arise. He instead focusses on the ethical concerns of what he calls "pure" mathematical activity. He considers briefly whether we might say that proving an ugly theorem is unethical, but remarks that the word "ethical" is laughable in this case (p. 22). Instead, he submits that: In pure mathematics, when restricted to research and not considering the rest of our [the mathematicians'] professional life, the ethical component is very small. Not zero, but so small that it's hard to take very seriously… My conclusion: If our research work is almost entirely devoid of ethical content, then it becomes all the more important to heed our ethical obligations as citizens, teachers and colleagues, lest the temptation of the ivory tower rob us of our human nature (Hersh, 1990, 22-23) 13 Other proposals to raise ethical awareness amongst mathematicians include, e.g., ethics courses, reported on in (Franklin, 2005) and argued for in (Müller et al. 2022). 14 https://www.justmathematicscollective.net/.
Hersh gets at my third dimension of the ethically charged nature of mathematical knowledge-making: mathematics is a human activity and thus ethically charged. Mathematics education theorists have long been aware of this and engaged with the ethical aspects of mathematics teaching; Hunter et al. (2016) gets at ethical concerns connected to cultural differences when she shows how the value of the collective in Pāsifika cultures is starkly opposed to the individualistic reasoning styles of traditional mathematics; Jorgensen et al. (2014) highlight how social class impacts perceived mathematical ability through use of language; Brown (2018a;2018b) points out that the different experiences of racial backgrounds are rarely accounted for in the classroom; considerations of gender in the mathematics classroom fill special issues (Leder & Forgasz 2008); mathematics anxiety is just one disability that affects student's mathematical performance (Luo et al. 2009). That mathematics is a human activity and hence faces social justice concerns is a fundamental insight of the DEI (Diversity, Equity, Inclusion) literature on mathematics. Topics include engagement with the barriers to participation in mathematical practices (Murray, 2000;Hunsicker et al. N.D.), elaborations of the political motivations for awarding prizes (Barany, 2018) and the elitism they foster (Chang & Fu, 2021), as well as arguments aiming to justify the predominance of white males in mathematics through arguments of innate superiority (Herrnstein & Murray 1996). Some mathematicians are aware of these findings and call for engagement (Pinch, 2021;Su, 2020;Lott, 2004;Davis, 1988). Philosophers of mathematics have thus far largely ignored this ethical dimension of mathematics, with a few notable exceptions (Hunsicker & Rittberg, 2022;Ernest, 2016Ernest, , 2018Ernest, , 2021Rittberg et al. 2020;Burton, 1995).
Hersh points out that, because mathematics is a social activity, in the interactions between colleagues ethical concerns arise. There are codes of conduct of various mathematical societies, 15 which largely focus on issues of plagiarism with only minor attention to diversity and equality concerns. Diversity and equality issues find advocates, for example, in the London Mathematical Society Women in Mathematics Committee, 16 the above-mentioned DEI literature, as well as in recent work by the former president of the Mathematical Association of America Su (2020).
Importantly, the social interactions between mathematicians impact on the production of mathematical knowledge. Hersh (1990) does not stress this point; he seems to think primarily about how mathematical colleagues should treat each other rather than about the impact these social relations have on the epistemology of mathematics (Hunsicker & Rittberg, 2022). It thus bears highlighting that interactions between mathematical colleagues are subject to relations of power and in-and-out groups that impact on what makes it into the common body of mathematical knowledge; e.g. for a mathematics paper to be published it needs to be sufficiently new and interesting (Geist et al. 2010) but because such matters depend on who one asks, reviewers of mathematics papers are in positions of power with the potential for abuse .
Besides the application of mathematics to the world (dimensions 1 &2) and the social dimensions of mathematical knowledge-making (dimension 3), Hersh (1990) contends that the ethical component of "merely proving theorems" is very small. This conflicts with Burnyeat's (2000) argument that according to Plato, mathematics and ethics are two sides of the same coin, the study of unity, which makes mathematical knowledge inherently ethical. Ernest (2018) argues that mathematical knowledge has ethical components, in part because styles of mathematical thinking can be harmful when applied outside of academic mathematical contexts. "Mathematical knowledge is ethical" Ernest (2016) argues because "pure mathematical knowledge has ethical implications". Chiodo & Clifton (2019) give the example of a pure mathematician working on the development of an algorithm for fast factorisation. They highlight that such an algorithm would break contemporary cryptographic standards which, they submit, would lead to the collapse of internet commerce. Nonetheless, a typical mathematician would consider finding such an algorithm as an intellectual achievement worthy of publication, regardless of the potential consequences, Chiodo & Clifton (2019, 24) claim. Theirs is an example of how ivory tower research, "just proving a theorem", may have consequences beyond the confines of the tower, in this case a threat to online security. In this sense mathematical knowledge may be said to be ethically charged.
At this point I have individuated four dimensions in which mathematics is ethically charged: (1) Applying mathematical knowledge to the world can have ethical implications.
(2) Participation in morally contentious practices is an ethical issue.
(3) The generation of mathematical knowledge is a social activity which faces relevant ethical concerns. (4) Mathematical knowledge itself may be ethically charged.
Ernest (2016) provides a slightly different conceptualisation: (i) the ethics of applications of mathematics; (ii) the ethics of teaching mathematics; (iii) the ethics of mathematical knowledge itself; (iv) the professional ethics of mathematicians. That is, I divide Ernest's (i) into (1) and (2), whereas he splits my (3) into his (ii) and iv). My (4) is his iii). This is a mere question of focus rather than any disagreement between us. I divided his i) for two reasons. First, I report on the arguments by Fry, Chiodo and others, and they focus on (1) and say little about (2). Second, I believe it bears stressing that the application of mathematics not only raises ethical concerns when its aim is itself morally contentious, such as the development of weapons, but also when its aim is prima facie not a moral issue, such as writing algorithms.
The unquestioned suggestion in the papers by mathematicians such as Fry, Chiodo, or Clifton is that mathematicians should be more aware of the ethical implications of their practices. The question is what to do about this.
One answer to these challenges are codes of ethics; for a contemporary argument for such codes, see (Müller et a. 2022). As mentioned, mathematical societies were comparatively late to develop such codes (Introduction). Today many mathematical societies have codes of ethics. Hersh (2008) questions how successful the AMS code is. He points to Linda Keen, chair of the committee that developed the code, who was doubtful about how successful the code has been, e.g. has it been read by anyone? Does it impact refereeing practices? Is confidence kept when having access to privileged information? Hersh (2008) contends that developing the code was "a good thing to do" (p.2) but the code does not cover the ethical conflicts he encountered in his mathematical career. Hersh has in mind here, e.g., hiring-and-firing procedures not covered by the AMS code. Pinch (2021) makes the additional point that the language used in codes of conduct can be terse and its meaning unclear to the working mathematicians. Furthermore, even successful codes of ethics only govern academic practices. What Fry, O'Neil and others are pointing to is mathematicians who employ their mathematical expertise outside of academia. Codes such as that put forth by the AMS have little hold on such mathematicians.
As a remedy, Fry (in Sample 2018) proposes that mathematicians should swear a Hippocratic oath. She does not go into much detail, but in the context of the interview it becomes clear that she envisions such an oath to raise awareness amongst mathematicians about the ethical dimensions of their practices. 17 Lott (2004) proposes an oath for mathematics teachers. In his proposal various ethical concerns of mathematics teaching are flagged, such as students with differing abilities and respect for those who may be unable to make their needs known. In doing so, Fry and Lott answer to Davis' (1988) call quoted in the introduction of this paper.
The idea then is that swearing an oath raises the awareness of the swearer of the ethical concerns at stake. "At least they have heard about them once" may be a slogan. Not every swearer will always behave ethically -who does? -but by swearing an oath the epistemic status of the swearer is assumed to be impacted in such a way that acting in discord with the oath becomes visible as unethical behaviour.
The intention behind Fry's, Lott's, and Davis' calls for oaths is praiseworthy and the literature reviewed in this section shows that it is timely and much needed. The question is whether oath-swearing is a suitable means to bring about the envisioned impact. Müller et al. (2022) argue that oaths are not suitable for this because mathematical practices lack the ability to suitably sanction those who would break such an oath. I will come back to this in Sect. 4, where I will argue that whilst oaths may not be suitable as structural interventions (i.e. as a form of policy), they can serve as individual level interventions (i.e. as edifying accounts of virtuous behaviour). To make my argument, I first need to outline what oaths are and what they can achieve, which is the topic of the following two sections respectively.

A Conceptual Framework for Oaths
An oath is a particular sort of promise. In this section I provide a conceptual framework for oaths that spells out the particulars that make a promise an oath. This will be helpful for what follows, yet we should not forget that oath is a folk concept. As such it lacks the conceptual sharpness the conceptual framework provides. We should thus read the conceptual framework as providing helpful insights about oaths, rather than as a definition of the concept.
Writing just before the turn of the millennium, Sulmasy (1999) lamented that the debate about the role of oaths in medical ethics lacks conceptual clarity about what an oath is. His paper seeks to supply this lack by providing a conceptual framework for oaths. His framework has been further developed by de Bruin (2016), who employed it to study various oaths for bankers. In this section I present this framework, which will inform the debate in the following sections.
The original Hippocratic Oath is a promissory oath: the oath-taker promises to do no harm to her patients. This is unlike assertory oaths, in which the oath-taker swears to the truth of something, such as a witness swearing to say the truth in court. Sulmasy and de Bruin make this distinction to then focus exclusively on promissory oaths. I follow their lead; in this paper when I speak of oaths, I mean promissory oaths.
Some promises are merely statements of intent, such as the promise to bring back a gift from a trip. Not living up to this promise has only trivial moral consequences. Other promises voluntarily encumber the speaker (Parry, 1976), 18 such as the promise of an alcohol afficionado to act as designated driver and hence not to drink tonight. Breaking such a promise impacts on the trustworthiness of the speaker. Oaths also encumber those who swear them (Sulmasy, 1999), but breaking an oath not only impacts on the trustworthiness but on the entire moral standing of the oathtaker. We might say that oaths deeply encumber those who swear them. Sulmasy's (1999) framework and its further development by de Bruin (2016) cash out how. They present oaths as publicly made promises that are sworn at solemn ceremonies. Oath-takers commit to certain generally described courses of action in regards to particular beneficiaries based on the function the oath-takers play in society, such as doctors swearing to make the well-being of their patient their primary concern. The great moral weight of oaths comes from an element of transcendence; classically, oaths were validated by deities (unlike promises, which are made to men). Furthermore, there are sanctions in case of non-compliance with an oath, even though these sanctions need not be explicitly mentioned in the oath itself. In this section I work out these points in detail.
Sulmasy lamented a lack of conceptual clarity in the debate about the role of oaths in medical ethics. One of his points was that oaths are too often conflated with codes. Cotemporary debates about Hippocratic oaths for mathematics or related practices suffer the same weakness (Müller et al. 2022;Strümke et al. 2022;Abbas et al. 2020); cf. Section 4. As Sulmasy (1999, 337) makes clear, codes are sets of rules, stating "Do this. Do not do that". They are very specific, can include fairly trivial rules, and may offer possibilities for exemptions. Oaths on the other hand commit the oath-taker to future intentions in ways that puts their entire moral standing on the line.
The seven points through which oaths put the entire moral standing of the oathtaker on the line (publicly; ceremonially; general commitments; particular beneficiaries; state function of oath-taker; transcendental validation; sanctions) form what de Bruin calls the form of an oath. This he distinguishes from the content of an oath, which lists the beneficiaries (e.g. patients), core principles (e.g. virtue ethical) and norms and values (e.g. do no harm) the oath puts forward. My focus is on the form of oaths, and I work out de Bruin's seven points in detail in the next subsection. I then briefly turn to the content of oaths in the subsection that follows. After that I briefly outline what de Bruin sees as the virtues of oath-taking, which will lead me to a discussion of the effectiveness of oath-taking in the next section.

Form
In this subsection I discuss the seven points of de Bruin's conceptual framework: publicly; ceremonially; general commitments; particular beneficiaries; state function of oath-taker; transcendental validation; sanctions. 19 First, oaths are sworn publicly. Where promises are private affairs given to individuals or groups, in de Bruin's framework oaths are acknowledged in the public sphere. Interested individuals are generally able to attend the oath-taking ceremony or otherwise witness the oath-taking through publicly available sources (e.g. recordings, reports, cultural traditions). 20 For instance, the US president usually swears an oath of office which can be attended, and which is televised and reported upon. 21 Second, oaths are sworn ceremonially. This point is closely connected to the first. Our alcohol afficionado may promise not to drink tonight wherever they happens to be, but oaths are sworn at solemn ceremonies, often accompanied by ritualistic gestures. Taking an oath means attending the relevant ceremony and hence not doing anything else at the time (whereas the alcohol afficionado may well utter their promise whilst driving to a party). As de Bruin (2016, 24) highlights, Sulmasy's (1999) does not explicitly mention the ceremonial aspect of oath taking but his framework is consistent with it.
Third, oaths are general commitments according to the conceptual framework developed here. I already pointed out that promises and oaths both encumber the 19 Sulmasy (1999) carves up the conceptual space slightly differently, listing nine points: "[1] oaths have greater moral weight than promises… [2] an oath has a public context… [3] an oath is validated by something that transcends both the swearer and the public… [4] an oath seems to involve the person of the swearer more deeply than a promise involves the person of the promisor… [5] oaths often invite or prescribe consequences for failure to carry out the content of the oath… [6] oaths are typically characterised by the generality of the scope of what is sworn compared to the relative specificity of a promise… [7] oaths are also characterised by the generality of the time frame… [8] oaths are 'contractual' in nature and can lose their binding moral power with changes in circumstances… [9] oaths are generally commitments to persons that involve, in a fundamental way, a commitment to the personhood of those to whom the swearer is making a commitment." 20 The knightly vows of the Middle Ages were usually sworn in banquet halls (Boyce, 2012). Not everybody could attend, nor was there any serious reporting about these vows to the general public. Such vows may thus be different from the kind of oaths Sulmasy (1999) and de Bruin (2016) discuss. 21 Usually, but not always. For example, Lyndon B. Johnson was sworn in on Air Force One after the assassination of John F. Kennedy. speaker: they generate a moral commitment of the speaker to a certain course of action. The scope of the commitment of a promise is narrow; not drink tonight, or even not drink ever again. The scope of commitment generated by oaths is much broader; the aggressive drunk swearing (whilst sober) to "do no harm" also swears not to get drunkenly aggressive again, but they swears much more than this. In this sense oath swearing involves the whole person whereas promises involve merely a single action (e.g. drinking alcohol -tonight or otherwise). 22 Fourth, oaths have particular beneficiaries. Whilst the scope of commitment generated by an oath is broad, those who benefit from the oaths are usually clearly delineated. In medical oaths, this is the patient. Who the beneficiary of a Hippocratic oath of mathematics could be will be a problem in Sect. 4. As Sulmasy (1999, 333) points out, this feature of oaths commits the swearer to the personhood of the beneficiary; to break one's oath is also an act of infidelity. One aspect of this is that I cannot swear an oath to myself, even though I can promise myself something.
Fifth, oaths typically state the function of the oath-taker in society. That is, oaths make clear what the oath-taker is supposed to do; medical oath-takers are supposed to make the health care of their patients their primary task, oaths of office make primary certain tasks that come with the office in question, and so on. This feature is not mentioned by Sulmasy (1999). What the function of a mathematician in society could be will be addressed in Sect. 4.
Sixth, oaths are validated by something that transcends both the swearer and the public. This "something" can be religious deities; the US vice president swears an oath of office ending in "so help me God". Failing to comply thus means not merely failing oneself or the public that bore witness to one's oath-taking but failing the religious deity in question. This increases the moral weight and binding force of the oath. Sulmasy makes this aspect of transcendence part of his analysis of oaths. De Bruin points out that today many oaths no longer refer to religious deities; in the Netherlands civil servants are allowed to swear secular oaths of office. In these cases, de Bruin (2016, 25) argues, phrases such as swear, pledge, or solemnly declare generate similar morally binding force by referring to the swearer's honour, dignity, or conscience. The key take-away from this is that when we fail to live up to a promise, we fail whomever we made that promise to, whereas when we fail to live up to our oaths we do not fail the public, they were only witnesses to us taking the oath, but "something bigger". What this "something bigger" could be in a secular world, and if it could be anything at all, is a matter of discussion. I submit that the ethical orders Larvor (2020) teases out of Max Weber's work may be suitable stand-ins. I leave it at this short remark not to derail the focus of this piece.
Seventh, there are sanctions for not complying with one's oath. For Sulmasy (1999, 332), conditions for non-compliance are often part of oaths; he offers the example "may I suffer a painful and ignominious death if I fail to carry out my solemn oath". De Bruin (2016, 25) remarks that the wording of contemporary oaths often no longer 22 Sulmasy (1999, 333) views promises as invoking a limited time frame whereas oaths do not; I promise to do this by Friday, but I swear to be true to you forever. De Bruin (2016) ignores this point and I am inclined to agree; I have promised myself already many times to never smoke again, but this promise was no oath. contains non-compliance conditions. Instead, these are embedded in the laws, regulations, and codes of ethics that govern the context in which the oath was taken; failing to live up to one's medical oath does not invite "ignominious death" but may well lead to disbarment from the medical profession. Non-compliance to oaths thus invites punishment, whether stated explicitly in the content of the oath or not.
At the outset, I remarked that breaking a promise jeopardises the trustworthiness of an agent, but breaking an oath jeopardises their entire moral standing. Here is my take on how Sulmasy's and de Bruin's framework makes clear why. The broad scope commitments (point 3) an oath-taker has subjected themselves to form a narrative for clear moral assessment of the oath-taker's future actions. To see this, consider euthanasia. In the absence of an oath, it is a morally contentious issue. But in the context of (standard interpretations of) the original version of the Hippocratic oath, there is nothing contentious about it: it is just plain wrong for a swearer of the original Hippocratic oath to provide euthanasia in virtue of the fact that they have committed to an oath that forbids it. In this sense oaths give meaning to the future of the oathtaker; oaths frame narratives through which the actions of the swearer can be morally assessed. Obviously, not all actions can be so assessed; medical oaths say nothing about stealing out of hunger, for example. The specificity of the beneficiary of the oath (point 4) as well as the oath-taker's function in society (point 5) ensure a focus and hence a limit to the encumberment the oath-taker takes upon herself by swearing the oath. The meaning-giving narratives of oaths are anchored through rituals (point 2), witnessed by the public (point 1), and transcendentally validated (point 6). This gives gravity to oath breaking. Failing to live in accordance with the meaning-giving narrative of an oath means to fail whatever transcendental force (religious, secular, else) one has publicly and ritualistically committed to. In light of all this, taking an oath means to commit to a meaning-giving narrative about what is morally right and wrong. Oath breaking, i.e. failing to align one's life with this narrative, is to fail to live up to the moral standards one has submitted oneself to. That is, not only is the trustworthiness of the swearer at stake but their entire moral standing.
To summarise, the conceptual framework developed in this subsection presents oaths as publicly witnessed and transcendentally validated ritualistic acts through which the oath-taker encumbers herself with commitments which jeopardise their entire moral standing in case of non-compliance.

Content
So much for the form of oaths. De Bruin (2016) also discusses the content of oaths. He identifies three characteristic elements: beneficiaries, core principles, and norms and values. I briefly outline them here but remark that these characteristics will play little role in what follows.
Beneficiaries. Oaths need to state their beneficiaries. In the above detailed form of an oath, oaths merely need to state some beneficiaries according to de Bruin's (2016, 26) framework. The beneficiary characteristic of the content of the oath demands, according to de Bruin, that the right kind of beneficiaries are mentioned; the beneficiary of medical oaths are patients, not kings for example. Thus, the beneficiary condition of the form of an oath is violated if no beneficiaries are mentioned, whereas the beneficiary condition of the content of an oath is violated if the oath does not individuate the relevant beneficiaries.
Core Principles. This characteristic captures which moral principles frame the oath. De Bruin adopts what he calls a 'traditional view' (de Bruin, 2016, 26), borrowed from Boatright (2012), according to which these principles can be either deontologically normative, virtue ethical, or consequentialist. Nothing much depends on the choice for de Bruin.
Norms and values. Oaths encumber the swearer. The form of an oath discussed above demands general commitments. Yet these commitments should also not be so general that they become a vacuous demand to "behave ethically". They need some specificity to provide the meaning-giving narrative; should they contain the line "do no harm"? Should they forbid abortions? And oaths for medical professionals will include different norms and values than oaths sworn by bankers or mathematicians. In de Bruin's framework, this specificity is collected as the norms and values characteristic of the content of oaths.

Virtues of Oath-taking
Drawing on his form-and-content framework of oaths, de Bruin argues for three virtues of oath-taking: they facilitate moral deliberation; they foster professionalism; they enhance compliance. Notice how these three facets resonate with the mathematicians' call for raising awareness of relevant ethical issues explored in Sect. 1.
That oaths facilitate moral deliberation has become clear by now. They frame a meaning-giving narrative which guides ethical assessment of future actions. For example, working on algorithms that break contemporary cryptography standards may be a morally contentious issue in the absence of an oath (Chiodo & Clifton, 2019), but once you swore to protect online privacy it is morally wrong to develop such algorithms in virtue of the fact that you swore not to do so. That is, oaths provide clear stances on what (within the scope of the oath) is ethically right or wrong, they provide shared narratives about ethical issues. Furthermore, in the absence of such an oath a mathematician may not even be aware that there is any need for moral deliberation about their actions. Oaths can force these issues upon us and provide a stance on the relevant issues. 23 Oaths foster professionalism. For de Bruin the oath-taking ceremony functions as a rite of passage through which students and apprentices demonstrate the completion of their education; de Bruin gives (Parkan, 2008;Gillon, 2000;Exton, 1982) as references. This establishes who is part of the profession and who is not. It also ensures that those who are part of the profession have come into contact with reflections about the social role they perform and the responsibilities that come with it. This allows the public to place justified trust in members of the profession. For de Bruin taking an oath thus means to become part of a group, being informed about the role and responsibilities of that group, and being held accountable to the relevant standards. Whether mathematics is (sufficiently like) a profession for this virtue will be a point of discussion in Sect. 4.
Lastly, de Bruin argues that oath-taking enhances compliance to the ethical framework proposed by the oath. This is an empirical claim and de Bruin acknowledges that evidence for it is scarce at best. Nonetheless he believes that "the results that are available do tend to indicate that oaths may have some effect on compliance" (de Bruin, 2016, 30), which is sufficiently cagey to not be wrong. What is needed, however, is an argument for the stronger claim that oath-taking is effective, that it enhances virtuous ethical behaviour. In the next section, I review some evidence for and against this stronger claim.

The Effectiveness of Oaths
In Sect. 1 I reviewed some of the arguments in what sense mathematical activity is ethically charged: its application to the world faces ethical concerns; mathematical knowledge is applied to practices of contentious moral standing; mathematics as a social activity has relevant ethical dimensions; and (some) mathematical knowledge itself may be ethical. Calls for mathematicians to take these ethical concerns of their activity seriously realise that, generally, mathematicians lack sufficient training to practice due diligence in these matters. One proposal to raise ethical awareness is to have mathematicians swear a Hippocratic oath. Such calls align with those for Hippocratic oaths for scientists (Bettridge et al., 2018;Matteucci et al., 2012;Rotblat, 1999;Popper, 1971), developers of digital/modelling/etc. technologies (Strümke et al., 2021;Abbas et al., 2019;Kashyap, 2018;Derman & Wilmott, 2009), or bankers (de Bruin, 2016DeMartino, 2011). A common facet of these calls for Hippocratic oaths is the (often unstated) assumption that they raise awareness of the ethical issues at stake in a way that enhances virtuous ethical behaviour; in de Bruin's words: oaths enhance compliance (Sect. 2). For short, I will say that the claim is that oaths are effective at fostering virtuous ethical behaviour. In this section I review some literature on the effectiveness of oaths.
The literature on the effectiveness of oaths is a mixed bag. A number of social science papers argue that oaths are effective whilst numerous philosophically minded papers argue that they are not. As an explanation of this divergence I suggest a conceptual difference: what the social scientists are testing are not oaths in the philosophical sense offered by de Bruin's conceptual framework, in which the entire moral standing of the swearer is at stake, but rather the kind of pre-theoretical oaths that de Bruin would call "mere promises", in which the trustworthiness of the agent is at stake. To see this, consider the work of Pruckner and Sausgruber (2013), referred to in the social science paper (Beck et al., 2020, 469) as evidence for the effectiveness of oaths. Pruckner and Sausgruber conducted a field experiment to study honesty in honour-system based newspaper sales on the street. In their set-up, the honoursystem involved a booth containing newspapers and a locked cashbox. Customers are supposed to pay for their newspapers by depositing money in the cashbox, but there are no mechanisms enforcing this. The experiment involved different messages on the sales booths: the Legal treatment reminded customers that stealing a paper is ille-gal, the Moral treatment aimed to reinforce customer honesty by appealing to social norms that benefit society (Pruckner and Sausgruber 2013, 662-663). The result is that the Legal treatment has little effect, whereas the Moral treatment increases the average amount deposited for a newspaper (albeit still to only 25% of the askedfor price). My point here is that the Moral treatment is hardly an oath in de Bruin's (2016) sense (note that Pruckner and Sausgruber never claim that it is an oath). Even on a very charitable reading in which we assume that the customer is in some sense bound by the message of the Moral treatment, noncompliance only undermines the trustworthiness of the customer but not their entire moral standing. That is, the treatment is more like a promise than an oath in de Bruin's conceptual framework. Beck et al., (2020) refer to de Bruin's (2016) framework; perhaps they should have known better than to refer to Pruckner and Sausgruber as evidence for the effectiveness of oaths. The real question is how to test the effectiveness of oaths in a social science setting. Beck et al.'s research design is a modification of the dice experiment by Fischbacher & Föllmi-Heusi (2013), in which one group of players signed an honesty oath. They acknowledge that this lacks the element of ceremony (Beck et al., 2020, 472) but remark that this is just how they have sworn oaths not to take bribes in service of the German federal state Hesse -recall here the difference between the fuzzy folk concept oath and the conceptual sharpness of de Bruin's conceptual framework. But Beck et al.'s set-up not only lacks a ceremony. The oaths taken by their test subjects lack the solemnity and moral gravitas that distinguish oaths from mere promises for de Bruin and Sulmasy (cf. Section 2). Oaths are meant to be binding for life, but in the controlled environments of empirical experiments the binding force of oaths usually ends at the end of an experiment. In light of this, I struggle to see how the effectiveness of an oath in de Bruin's sense could be explored in such controlled social science experiments as performed by Beck et al., (2020). This is not so much a criticism of such experiments than it is a potential explanation of why there is such disagreement in the literature on the effectiveness of oaths.
One may hope to assess the effectiveness of oaths by studying practices that already incorporate oath-swearing, say the US medical profession. The problem here is that the study is no longer controlled in desirable ways. Non-compliance with the (modern versions of) the Hippocratic oath in the US generally has legal consequences. This raises the question whether the oath is effective in fostering compliance or whether compliance is enhanced by legal sanctions. To understand which of the two means is more effective is an aim of social science work (recall Pruckner and Sausgruber's Legal and Moral treatments) which requires that the experiment be controlled in ways that are likely to divorce it from the conception of oaths put forward by de Bruin.
A more bird's-eye perspective is taken in Gilman's (2005) study "Ethical codes and codes of conduct as tools for promoting ethical and professional public service" for the World Bank. Notice that he studied codes, not oaths. I already remarked on the relevant differences between oaths and codes in Sect. 2; codes are sets of rules, oaths commit to future actions. Keeping these differences in mind, we can learn some valuable insights from Gilman for the discussion at hand; his work is also referred to by social scientists (Beck et al., 2020) and philosophers (Boatright, 2013) interested in the effectiveness of oaths. Gilman's (2005) is a large-scale study of how various codes have impacted governmental practices around the globe. One of Gilman's important lessons on why these codes may fail to achieve their intended goal is when they raise unrealistic expectations. When practitioners routinely witness senior practitioners violating the code, there tends to be a spiralling effect where more and more violations occur (Gilman, 2005, 63). This resonates with Dobson's (2003) philosophical insights about acculturation, by which he means the implicit education into moral value systems through observation of one's peers. Dobson notes that the ethical norms expressed in codes or oaths erode when violation of these norms is routinely witnessed in the behaviour of one's peers. His central claim is that in the world of finance, such violations are routinely witnessed, which is why he thinks ethics codes for the financial sector do not work.
Gilman furthermore observes that codes may also fail to be effective because they try to control too much. He refers to Menzel (1996) who argues that disappointment in ethics codes is inevitable and needs to be accounted for when designing such codes. This sharpens the question of this section by connecting the effectiveness of oaths and codes to their particular content. De Bruin (2016) is aware of this (without referring to Gilman or Menzel). He did not ask whether oaths in general are effective, but rather how effective particular oaths are.
Boatright (2013) is concerned with oaths for bankers and argues they are not effective because they cannot instil a sense of a higher moral purpose. He draws on Austin's (1962) work on performative utterances, i.e. utterances that change social reality (e.g. a person taking a certain oath in certain circumstances, thereby becoming president).
The taking of the [banker's] oath leaves an oath taker in the same status or position as before, as a banker. As a performative utterance, the oath is merely a promise or commitment to act in certain ways, but it does not perform any act beyond this. The reason for this lack of change is related to a banker's role, which, as previously noted, involves a fairly routine commercial or business activity. There is nothing to change into. (Boatright 2013, 148) What Boatright misses in contemporary secular oaths are relevant sanctions. Ancient oaths were seen as a form of self-curse, a form of magic that, when violated, would bring ill fortune onto the swearer (Silving, 1959(Silving, , 1330Lasch 1908, 3-4). In religious contexts, oaths are sworn to a deity, who may again bring down ill-fortune (e.g. ignominious death) on the oath-breaker. As we saw in the last section, Sulmasy (1999) agrees with Boatright that oaths ought to contain some form of sanction whereas de Bruin (2016) is more lenient. For Boatright however, the lack of sanctions in the banker's oath means that sound ethical judgment will always be required in banking, and an oath or a code can provide only a starting point for developing this capacity.
[…] the conduct of bankers is a reflection of the whole banking system, and it is this system that must be reformed if we are to avoid more crises. (Boatright 2013, 162) .What Boatright is getting at here is what I call individual and structural interventions (cf. Introduction). For him, oaths can function as individual level interventions by providing a starting point for ethical reflection about one's practice. But, he argues, oaths are ill-suited as structural interventions to change the practices that allow for ethical misconduct. In the next section I will make a similar point about the prospects for a Hippocratic oath for mathematicians.

On the Prospects for a Hippocratic Oath for Mathematicians
At this point in the argument we have seen that the production and handling of mathematical knowledge is deeply entangled with ethical concerns. The scholarly debate about the ethics of mathematics Davis (1988) called for has picked up considerable steam, but the question how to bring about the cultural change necessary for the mathematical community at large to acknowledge and engage with the ethical issues of their practices is still open. One proposal to bring about such change is to have mathematicians take a Hippocratic oath (Sect. 1). Whilst such oaths would provide meaning-giving narratives about ethical matters (Sect. 2), their effectiveness to actually commit oath-takers to these narratives remains questionable (Sect. 3). The mathematicians Müller et al. currently argue that oaths are not effective in this sense. In this section I present their and related arguments and use the conceptual framework for oaths developed in this piece to refine their points. I agree with Müller et al. that Hippocratic oaths for mathematicians are unsuited as structural level interventions at this point. As individual level interventions, however, I argue that such oaths have merit.
After briefly outlining some of the work on the ethics of mathematics (focussing on my dimensions 1 and 2; cf. Section 1), Müller et al. (2022) turn to the question whether a Hippocratic oath for mathematicians would bring about a tradition of ethical reflection within the mathematical community. They reflect on how the Oath of Lasagna might be remoulded for mathematics but ultimately reject the idea of an oath for mathematicians: In essence, the [Hippocratic oath for medical professionals] is merely an easyto-remember reminder of an otherwise deep, complicated and well-supported system. The oath alone, though useful, would probably not achieve all of it. Mathematicians have no such systems. (Müller et al. 2022, 14) For Müller et al., mathematics is not sufficiently like a profession. It lacks the means to sanction oath-breakers. This aligns with Strümke et al.'s (2021) argument that AI development needs to be professionalised. There is a heavy-handed approach to ethics in these two papers that seeks to punish the wrong-doers. Whilst oaths also come with sanctions for those who break them, the sanctions Müller et al. and Strümke et al. argue for are more akin to the kind of legal sanctions that may be imposed of those who break certain codes. The distinction between oaths and codes in absent in both pieces; Müller et al. (2022, 2) even claim that the Hippocratic oath is a professional code.
The conceptual framework for oaths developed in this piece helps to refine the arguments of (Müller et al. 2022). It is helpful to recall the seven points that make up the form of an oath: (i) publicly; (ii) ceremonially; (iii) contain general commitments; (iv) state particular beneficiaries; (v) state the function of the oath-taker; (vi) are transcendentally validated; and (vii) contain statements of sanctions.
Müller et al. are quite right that mathematics is, at present, not a profession. 24 Mathematicians work in very diverse settings -for banks, as AI developers, for universities, for the military-industrial complex, just to name a few. There is no clear function a mathematician plays in society; contrary to point (v). This injects a conceptual difficulty into any call for a Hippocratic oath for mathematicians akin to Boatright's point about transformation: since there is no official body that accredits or revokes from a person the status of being a mathematician, swearing such an oath would not transform a person in the ways that oaths are intended to do.
Müller et al. make the additional point that the ways in which mathematics can be harmful are often unclear. Is harm to be understood as conflicting with the interests of the employer? For Strümke et al., (2021), this can lead to what they call an ethical dilemma: a situation in which what is best for society stands at odds with what is most beneficial for the individual (or their employer). What harm can mathematics cause in the context of Human Rights, Müller et al. (2022, 9) ask. In the lingo of the conceptual framework for oaths: who is the beneficiary of the oath; point (iv)? Müller et al. point out that for mathematicians, this is unclear. This is a second conceptual worry about oaths for mathematicians.
A further relevant point they make is that "the idea of ethical responsibility has not permeated into the disciplinary culture" (Müller et al. 2022, 8). Remember Gilman's point about unrealistic expectations and Dobson's reflections about acculturation (Sect. 3). An oath that asks of mathematicians to act in ways in which senior mathematicians routinely do not act is unlikely to be successful in bringing about a concern for the ethical dimensions of one's practices. This is the point about the effectiveness of oath-taking. Rephrased, Müller et al. argue that in the context of the contemporary culture of (research) mathematics, oath-taking is an ineffective means to foster ethically praiseworthy behaviour. They argue that mission statements, ethics courses, the development of an international ethical code for mathematicians, and formalised complaint procedures are more suitable means to foster ethical behaviour amongst mathematicians.
I am largely in agreement with Müller et al. Their arguments reveal conceptual worries about a Hippocratic oath for mathematicians that suggest that, at present, any oath would struggle to state particular beneficiaries (iv) and the function of the oath-taker in society (v). Without such limitations, the scope of an oath risks becoming so broad that the oath ends up being a mere call to "be good". Furthermore, their insight that ethical responsibility has not (yet) permeated mathematical cultures suggests that a Hippocratic oath for mathematicians may not be an effective means in bringing about the desired cultural change. I conclude from this that as a structural intervention, i.e. as a proposal for a policy that seeks to shape mathematical practices, oath-taking is currently not likely to be effective.
I now move to my argument that oath-taking is a suitable individual level intervention for mathematics. A core insight is the distinction between raising awareness of ethical issues and enforcing ethical conduct. Müller et al. and Strümke et al. argue for the development of social structures that can enforce ethical conduct amongst practitioners by means of sanctions. For this, oaths are unsuitable. I argue that oaths can help in raising awareness of ethical issues by means of virtue-exemplarism. This "raising awareness" is what Fry (in Sample 2019), Lott (2004), and Davis 1988) wanted from a Hippocratic oath for mathematicians. The desire to raise awareness also permeates Müller et al. (2022) and especially the work of its second author, Maurice Chiodo, e.g. (Chiodo & Clifton, 2019), but these differences are not worked out in their piece.
As an individual level intervention, a Hippocratic oath for mathematicians would be akin to the oath of the Pugwash group, which frames a narrative about ethical behaviour for scientists to which like-minded individuals are free to commit. Such an oath has recently been put forward by Abbas et al., (2019) for technologists (by which they mean "users and creators of technology" (p.72)). This helps to avoid the conceptual worries mentioned above as follows.
First, by freely committing to the oath (rather than being forced to take it, say as part of graduating), the oath-taker takes on a certain role on society; point (iv). Namely, such a person would transform (Boatright; Sect. 3) into an oath-taker, somebody who has freely and willingly committed to the ethical commitments expressed in the oath. This gets around the point that mathematics is not a profession (in the same sense as medicine is a profession), and it avoids the ethically dangerous waters of defining as a mathematician as a person who has received some specific education. 25 Second, as an individual level intervention an oath need not cover every aspect of mathematical activity. This makes it easier to determine a beneficiary of the oath; point (v). For example, a Hippocratic oath for research mathematicians might focus exclusively on the ethical dimensions of the academic production of mathematical knowledge (dimension 3 in Sect. 1) and ignore other (otherwise relevant!) aspects.
Third, sanctions would be relatively straight forward: those who break the oath would be excluded from the group of oath-takers.
As an individual level intervention, a Hippocratic oath for mathematics is also more likely to be effective, i.e. to foster ethically praiseworthy behaviour amongst oath-takers. Individuals would freely commit to the tenets of the oath and hence be less likely to break with them. Furthermore, acculturation (Dobson) would be within a group of like-minded individuals, rather than the mathematical community at large, which would result in much less observed violations of the creeds of the oath.
Individual level interventions may bring about structural change through virtue exemplarism. Should well-known mathematicians publicly swear a Hippocratic oath for mathematicians, then their social standing may help to raise awareness of the ethical issues the oath covers. The call for structural change in the current ethics in 25 Conceptualisations of mathematician can include research mathematicians, mathematicians working outside of academia, mathematics learners, the expert mathematics users studied by ethnomathematics scholars, and more. To exclude someone from the conceptualisation is to establish in-and-out groups. This is often conceptually helpful, but it introduces various ethical issues (e.g. who counts as relevant authority). mathematics debate may thus partially be answered by individual level interventions embraced by virtuous exemplars. And oaths may be particularly apt at supporting this transition from individual to structural change because they offer a means to emulate the exemplar by also swearing and living by the oath. That is, oaths help with Lippitt's (2000, chp. 3) central point that exemplarism is not hero-worship: where the hero is a type we might admire, we emulate the exemplar and thereby change ourselves.
To sum up, the challenges to the effectiveness of oath-taking practices are much weaker for oaths as individual level interventions than they are when oath-taking is put forward as a structural intervention. But can such individual level interventions lead to a change in mathematical cultures such that ethical considerations become (much) more common amongst mathematicians? That will depend on how cultural change can be brought about. I contend that a focus on structural interventions as in Müller et al. or Strümke et al. is valuable and necessary for such cultural change to happen, but alone it is not enough. We cannot "fix the game" in a way that everybody becomes a virtuous player; we cannot enforce virtuous ethical behaviour purely be means of sanctions. Besides needed structural changes, we also need accounts of what it means to behave as an ethically praise-worthy mathematician, and we need people who openly commit to and live by these edifying narratives. A Hippocratic oath for mathematicians, proposed as an individual level intervention, is, I have suggested, a helpful step in this direction.

Conclusion
Whether we conceive of mathematics as a human practice, and hence as a fundamentally social endeavour, or whether we conceive mathematics as a body of knowledge that (partially) shapes the world we live in, either way mathematics is ethically charged (Sect. 1). Mathematicians have been comparatively slow at realising the ethical dimensions of their practices and mathematics education programmes still largely fail to raise relevant awareness about the (many facets of) the ethics of mathematics. To counteract this trend, some mathematicians have proposed that mathematicians swear an oath similar to the (versions of the) Hippocratic oath sworn by some medical professionals. This is much in line with contemporary efforts to install oathswearing practices in other fields, such as the banking sector, the natural sciences, or technology development. Whether such oath-taking practices are effective at fostering ethically praiseworthy behaviour remains unclear (Sect. 3). Mathematical practices in particular are not yet attuned to considerations about the ethical aspects of mathematical work, which severely lowers the hoped-for effectiveness of oath-taking practices for mathematicians (Sect. 4). As a structural intervention, i.e. a proposal to change structural features of mathematical practices, I argued that a Hippocratic oath for mathematicians is currently unsuited. However, oaths can provide narratives about how to act in an ethically praiseworthy fashion. They can thus serve as edifying accounts of how to act ethically when acting as a mathematician. Such accounts would be individual level interventions, and given that even the best "game" requires virtuous "players", such edifying accounts are needed.