Ethics In Mathematics
Dr Mark Hocknull
29th October 2025
What are ethics and how important are they in mathematics? Dr Hocknull’s seminar covered the ethics present in science, many mathematicians may believe that their area of expertise has such little immediate affect on society[1] it can be hard for them to imagine that there would be any ethics to consider.
Firstly, what are ethics? Dr Hocknull quite succinctly explains ethics as a ‘branch of philosophy that considers the values of human conduct in terms of rightness or wrongness’ and ‘goodness or badness’. However, as one can imagine, whether something is ‘right’ or ‘wrong’ can be overwhelmingly objective, the final decision eventually decided after much consideration and debate. Part of why there can be so much debate on whether something is ethically good is partially due to there being several moral theories that concern the ethics, theories that contradict one another. Dr Hocknull’s seminar introduces three different moral theories, in which he explains.
The first is Kantian Ethics, which states that if the action does not follow the rules, then it is ethically wrong. Whilst this could be simply that one should not break a law, Immanuel Kant’s own work goes on further to say that this should include things like lying. People have therefore mocked the concept, using the ‘murderer at the door’ question to scorn Kantian Ethics whilst others have suggested that this is a misreading of such ethics [2].
Secondly is Utilitarian Ethics, developed by John Stuart Mill, which focuses on maximizing the happiness of the majority, even at the cost of the minority. Through utilitarian ethics, something that could be considered morally wrong, like risky human experiments, are ethically good provided the benefits of these actions outweigh the negatives. Dr Hocknall’s example of this was a scientist of the name Edward Jenner. Jenner realized, that by injecting a person with cowpox, that after they heal, they would then have an immunity to smallpox. This was an amazing discovery, and the birth of vaccinations, as cowpox was a much milder disease than smallpox, which was responsible for the death of thousands. However, to test his theory, Jenner injected young James Phipps with cowpox[3]. As a child of Jenner’s gardener, Phipps would have had very little choice in the experiment and could have been at great risk both from the cowpox injection and to the subsequent exposition to smallpox that could have killed him had Jenner’s hypothesis been incorrect. Today, experimenting on a child would be unthinkable, but in utilitarian ethics, Phipps’s potential suffering, even if the vaccination had failed, would have been for the greater good of humanity as a whole and therefore ethically correct. Utilitarian ethics also gives an answer to whether we should be using data collected from morally and ethically bad situations, such as data collected from Nazi death camps in WW2. In this ethical structure, it is considered ethically right to use the information garnered for scientific developments, and it is even suggested that this is a form of redeeming the data despite its horrendous origins, though the topic is still debated[4].
As evidenced, both Kantian and Utilitarian ethics are models of ethics, and seem to have a disconnect between the model and the human. Virtue Ethics, however, is less of a structure that provides an answer, but a concept created by Aristotle, who suggested that a scientist not only possessing but living certain values will make the right ethical decisions. These values can differ, but Dr Hocknall lists Honesty, Objectivity, Tolerance, Doubt of Certitude, Unselfish Engagement, and Accountability as the six key values of a virtuous scientist. A scientist should be honest about their results, keeping their results open for all to see, including outliers even if they could skew their results. Objectivity means that the scientist should be open to seeing all possible trends in the data, not fall to their own bias and become blind to the real results. They should be tolerant and acceptant of the ideas and input of the other scientists in the community. Pride can prevent a scientist from accepting the help and ideas from others, but a virtuous scientist, in Aristotle’s philosophy, would be acceptant of their help and willing to collaborate. Doubt of certitude means that a virtuous scientist understands that humans are capable of error and willing to both double check and have others assess their data to ensure there is no errors in their work. Due to scientists wanting to be the first to publish a new finding, to have their name attached to the annuls of history and be remembered for their contributions to science and society, it can be very appealing to push through an unfinished discovery to ensure their own fame rather than to further scientific progression. Unselfish engagement means to ignore one’s own hubris in favour of progress in science. This means taking the needed time to complete research, even at the risk of someone else publishing their findings first and being willing to share and collaborate these findings at the cost of their own personal fame. Accountability is the final virtue and means that a scientist needs to understand that their work is going to be scrutinized, adapted, repeated, and used in the future, and so should not only be able to prove itself but also provide answers as to why it is important.
In the end, there is no one code of ethics that is perfect for every situation, which is why it is the ethics of science is still widely debated. Mathematics itself has avoided much of this debate in the past, as mathematicians have previously believed their work to be outside the societal scope that requires ethical accountability and regulations. It has a different impact on society than other sciences such as medical science[5]. However, there are now many papers coming out with people asking for more considerations into the ethics of mathematics, as well as it being considered when teaching mathematics[6]. Perhaps, in the future we will see vastly more considerations into the ethics of mathematics and more discussions on how not just mathematics, but all sciences, can be practiced more ethically.
[1] Ernest, P. (2018). The Ethics of Mathematics: Is Mathematics Harmful?. In: Ernest, P. (eds) The Philosophy of Mathematics Education Today. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-77760-3_12
[2] Varden, H. (2010). Kant and lying to the murderer at the door… One more time: Kant’s legal philosophy and lies to murderers and Nazis. https://philpapers.org/rec/VARKAL
[3] Bazin, H., & Jenner, E. (2000). The eradication of smallpox (pp. 83-93). London:: Academic Press.
[4] Farahani, I., Janhonen, J. Indignity of Nazi data: reflections on the utilization of illicit research. Med Health Care and Philos 27, 381-387 (2024). https://doi.org/10.1007/s11019-024-10212-z
[5] Muller, D., Chiodo, M. & Franklin, J. A Hippocratic Oath for Mathematicians? Mapping the Landscape of Ethics in Mathematics. Sci Eng Ethics 28, 41 (2022). https://doi.org/10.1007/s11948-022-00389-y
[6] Buell, C., & Piercey, V. (2019). Ethics in mathematics. MAA Focus, 39(1), 15-17.
46551
The applications of the ethical theories are good! There are some minor grammar issues, but it is otherwise really good!
17304
Presentation: Date, title and name of speaker were present. Some grammar issues (e.g., misspelled ‘Kantian’, the 4th word of the 2nd paragraph should be ‘off’ not ‘of’, and misspelled ‘emphasise’ and ‘complement’ in final paragraph). To improve check your work carefully for mistakes.
Content: Seminar content covered accurately. No improvements needed.
Context: Societal context adressed. Research context not adressed. Can be improved by explaining research context.
Style: Blog is suitable for a lay audience and engaging. No improvements needed.
External source: Evidence of external sources but no quote. To improve, add a quote from one of your sources.
63865
You’ve got a really strong draft! You’ve got all the key points from the seminar and applied all 3 theories to the case study, but with a few typos and SPaG (Spelling, Punctuation, and Grammar) errors throughout:
- Presentation (1/3): You’ve correctly included the Date, Title, and Speaker. However, there are some specific typos and SPaG errors such as: “Kanitan Ethics” -> “Kantian Ethics; “Adrew Wakefield” -> “Andrew Wakefield”; “compliment” means to praise, which has a different meaning from “complement” (which means to go well with) which is the correct verb you need to use in this context; “emphasis” is a noun, so you need to use the past tense verb “emphasised” to describe the action in this context. This is a non-exhaustive list so there are more typos and SpaG errors.
- Content (3/3): You’ve covered all 3 ethical frameworks and applied it to the thought experiment.
- Context (3/3): You’ve used both Jan Schon and Andrew Wakefield, but I absolutely love how you utilised these examples as a strong rationale for why the peer-review process today is important - this is the “aha” moment that stood out to me as the cherry on top!
- Style (3/3): the tone is digestible for a lay audience.
- Sources (2/3): You’ve cited your external sources (Deer, Stanford, etc.) well, but you need to include a relevant quote (or multiple if you feel that works better for your blog).
Overall, well done - it’s a 12/15 (80% so a solid First) but just fix the typos and SpaG errors - as this shouldn’t take long and you’d get more marks by doing so.
81177
The presentation is overall well done however there are some typos present such as the misspelling of “Kantian” as “Kanitan” in paragraphs 3 and 4. Grammar wise it could do with some improvement for example there are some areas where commas could improve the flow such as at “unlike the previous theory actions aren’t considered” in paragraph 3 which a comma after “theory” helps it flow better. The content was covered well, going over all the types of ethics gone over and the thought experiment that was raised. Context for why the contents of the seminar is important has been provided with examples of real world impacts to explain why ethics in science is important, Also the applications of the different views on ethics on the thought experiment gives context for how different views on ethics can be applied. While there is evidence of extra reading there is no quotes present instead it is only paraphrased from the sources. The style of the report is appropriate for a lay person as it does not use any terms that would confuse them.
42890
Apart from a few typos or incorrect grammar it looks very good. Clear understanding of the topic and is structured logically and fluently.