Ethics in mathematics: Difference between revisions
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{{short description|Emerging field of applied ethics}} |
{{short description|Emerging field of applied ethics}} |
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'''Ethics in mathematics''' is an emerging field of [[applied ethics]], the inquiry into ethical aspects of the practice and applications of [[mathematics]]. It deals with the professional responsibilities of [[mathematicians]] whose work influences decisions with major consequences, such as in law, finance, the military, and [[environmental science]]. When understood in its socio-economic context, the development of mathematical works can lead to ethical questions ranging from the handling and manipulation of data to questions of responsible mathematisation and falsification of models, explainable and safe mathematics, as well as many issues related to communication and documentation.<ref>{{Cite web |last=Chiodo |first=Maurice |last2=Müller |first2=Dennis |date=2023 |title=Manifesto for the Responsible Development of Mathematical Works -- A Guide for Practitioners and Management |url=https://arxiv.org/abs/2306.09131 |url-status=live |website=arXiv preprint arXiv:2306.09131}}</ref> |
'''Ethics in mathematics''' is an emerging field of [[applied ethics]], the inquiry into ethical aspects of the practice and applications of [[mathematics]]. It deals with the professional responsibilities of [[mathematicians]] whose work influences decisions with major consequences, such as in law, finance, the military, and [[environmental science]].<ref>{{Cite journal |last=Nickel |first=Gregor |date=2022 |title=Ethics and Mathematics – Some Observations Fifty Years Later |url=https://scholarship.claremont.edu/jhm/vol12/iss2/4/ |journal=Journal of Humanistic Mathematics |volume=12 |issue=2 |pages=24 |doi=10.5642/jhummath.PXMY2159}}</ref> When understood in its socio-economic context, the development of mathematical works can lead to ethical questions ranging from the handling and manipulation of data to questions of responsible mathematisation and falsification of models, explainable and safe mathematics, as well as many issues related to communication and documentation.<ref>{{Cite web |last=Chiodo |first=Maurice |last2=Müller |first2=Dennis |date=2023 |title=Manifesto for the Responsible Development of Mathematical Works -- A Guide for Practitioners and Management |url=https://arxiv.org/abs/2306.09131 |url-status=live |website=arXiv preprint arXiv:2306.09131}}</ref> The usefulness of a Hippocratic oath for mathematicians is an issue of ongoing debate among scholars.<ref>{{Cite journal |last=Rittberg |first=Colin Jakob |date=2023 |title=Hippocratic Oaths for Mathematicians? |url=https://link.springer.com/10.1007/s11406-022-00588-8 |journal=Philosophia |language=en |volume=51 |issue=3 |pages=1579–1603 |doi=10.1007/s11406-022-00588-8 |issn=0048-3893}}</ref> |
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Although many mathematicians see no ethical implications of their research work, assumptions made in mathematical approaches can have real consequences.<ref>Chiodo, M. & Bursill-Hall, P. (2018) [https://ethics.maths.cam.ac.uk/assets/dp/18_1.pdf Four Levels of Ethical Engagement] Discussion paper 18/1, Cambridge University Ethics in Mathematics Project</ref> An instrumental interpretation of the impact of mathematics makes it difficult to see ethical consequences, yet it might be easier to see how all branches of mathematics serve to structure and conceptualize solutions to real problems.<ref>[https://academic.oup.com/rev/article/26/1/15/2919400 Slightly dirty maths: The richly textured mechanisms of impact] Laura R. Meagher Ursula Martin, Research Evaluation (2017) 26 (1): 15-27</ref> These structures can set up perverse incentives, where targets can be met without improving services, or league table positions are gamed. While the assumptions written into metrics often reflect the worldview of the groups who are responsible for designing them, they are harder for non-experts to challenge, leading to injustices.<ref>O'Neil, C. (2016) [https://www.penguinrandomhouse.com/books/241363/weapons-of-math-destruction-by-cathy-oneil/ Weapons of Math Destruction], Penguin.</ref> Thus, it has been argued that mathematical artifacts have politics just like any other technical artifact.<ref>{{Cite web |last=Müller |first=Dennis |last2=Chiodo |first2=Maurice |date=2023 |title=Mathematical Artifacts Have Politics: The Journey from Examples to Embedded Ethics |url=https://arxiv.org/abs/2308.04871 |url-status=live |website=arXiv preprint arXiv:2308.04871}}</ref> As mathematicians can enter the workforce of industrialised nations in many places that are no longer limited to teaching and academia, |
Although many mathematicians see no ethical implications of their research work, assumptions made in mathematical approaches can have real consequences.<ref>Chiodo, M. & Bursill-Hall, P. (2018) [https://ethics.maths.cam.ac.uk/assets/dp/18_1.pdf Four Levels of Ethical Engagement] Discussion paper 18/1, Cambridge University Ethics in Mathematics Project</ref> These ethical questions surrounding the practice of mathematics can be connected to issues of [[Dual-use technology|dual-use]].<ref>{{Cite web |date=2023 |title=The dual use problem in mathematics |url=https://wissenschaftliche-integritaet.de/en/comments/dual-use-problem-in-mathematics/ |url-status=live |website=Scientific Integrity}}</ref> An instrumental interpretation of the impact of mathematics makes it difficult to see ethical consequences, yet it might be easier to see how all branches of mathematics serve to structure and conceptualize solutions to real problems.<ref>[https://academic.oup.com/rev/article/26/1/15/2919400 Slightly dirty maths: The richly textured mechanisms of impact] Laura R. Meagher Ursula Martin, Research Evaluation (2017) 26 (1): 15-27</ref> These structures can set up perverse incentives, where targets can be met without improving services, or league table positions are gamed. While the assumptions written into metrics often reflect the worldview of the groups who are responsible for designing them, they are harder for non-experts to challenge, leading to injustices.<ref>O'Neil, C. (2016) [https://www.penguinrandomhouse.com/books/241363/weapons-of-math-destruction-by-cathy-oneil/ Weapons of Math Destruction], Penguin.</ref> Thus, it has been argued that mathematical artifacts have politics just like any other technical artifact.<ref>{{Cite web |last=Müller |first=Dennis |last2=Chiodo |first2=Maurice |date=2023 |title=Mathematical Artifacts Have Politics: The Journey from Examples to Embedded Ethics |url=https://arxiv.org/abs/2308.04871 |url-status=live |website=arXiv preprint arXiv:2308.04871}}</ref> As mathematicians can enter the workforce of industrialised nations in many places that are no longer limited to teaching and academia, scholars have made the argument that it is necessary to add ethical training into the mathematical curricula at universities.<ref>{{Cite journal |last=Alayont |first=Feryal |date=2022 |title=A Case for Ethics in the Mathematics Major Curriculum |url=https://scholarship.claremont.edu/jhm/vol12/iss2/10/ |journal=Journal of Humanistic Mathematics |volume=12 |issue=2 |pages=160–177 |doi=10.5642/jhummath.CXSI3022}}</ref> |
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The philosophical positions on the relationship between mathematics and ethics are varied. Some philosophers (e.g. [[Plato]]) see both mathematics and ethics as rational and similar, while others (e.g. [[Rudolf Carnap]]) see ethics as irrational and different from mathematics.<ref>{{Cite journal |last=Nickel |first=Gregor |date=2022 |title=Ethics and Mathematics – Some Observations Fifty Years Later |url=https://scholarship.claremont.edu/jhm/vol12/iss2/4/ |journal=Journal of Humanistic Mathematics |volume=12 |issue=2 |pages=7–27 |doi=10.5642/jhummath.PXMY2159}}</ref> Possible tensions between applying mathematics in a social context and its ethics can already be observed in Plato's [[Republic (Plato)|Republic]] (Book VIII) where the use of mathematics to produce better guardians plays a critical role in its collapse.<ref>{{Cite journal |last=Jens |first=Rod |date=2002 |title=THE MACHINERY OF THE COLLAPSE: ON "REPUBLIC" VIII |url=https://www.jstor.org/stable/26219859 |journal=History of Political Thought |volume=23 |issue=1}}</ref> |
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==Need for ethics in the mathematics profession== |
==Need for ethics in the mathematics profession== |
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===Issues of accuracy=== |
===Issues of accuracy=== |
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For example, complex calculations were needed for the success of the [[Manhattan Project]], while the overextended use of the [[Copula (probability theory)|Gaussian copula]] formula to price derivatives before the [[Global Financial Crisis]] of 2008 has been called "the formula that killed Wall Street",<ref>Felix Salmon, [https://www.wired.com/2009/02/wp-quant/ Recipe for disaster: the formula that killed Wall Street"], ''Wired''23 Feb 2009.</ref> and the theory of global warming depends on the reliability of [[climate models|mathematical models of climate]]. |
For example, complex calculations were needed for the success of the [[Manhattan Project]], while the overextended use of the [[Copula (probability theory)|Gaussian copula]] formula to price derivatives before the [[Global Financial Crisis]] of 2008 has been called "the formula that killed Wall Street",<ref>Felix Salmon, [https://www.wired.com/2009/02/wp-quant/ Recipe for disaster: the formula that killed Wall Street"], ''Wired''23 Feb 2009.</ref> and the theory of global warming depends on the reliability of [[climate models|mathematical models of climate]]<ref>{{Cite journal |last=Frigg |first=Roman |last2=Thompson |first2=Erica |last3=Werndl |first3=Charlotte |date=2015 |title=Philosophy of Climate Science Part II: Modelling Climate Change: Modelling Climate Change |url=https://onlinelibrary.wiley.com/doi/10.1111/phc3.12297 |journal=Philosophy Compass |language=en |volume=10 |issue=12 |pages=965–977 |doi=10.1111/phc3.12297}}</ref>. |
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===Issues of impact=== |
===Issues of impact=== |
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For the same reason as in [[medical ethics]] and [[engineering ethics]], the high impact of the consequences of decisions imposes serious ethical obligations on practitioners to consider the rights and wrongs of their advice and decisions. The potential impact of data and new technology is leading more professions, such as accountancy,<ref>[https://www.icaew.com/technical/ethics/ethics-and-new-technologies Ethics and New Techologies, ICAEW, 2018]</ref> to consider how bias is overseen in automated systems, from algorithms to AI. |
For the same reason as in [[medical ethics]] and [[engineering ethics]], the high impact of the consequences of decisions imposes serious ethical obligations on practitioners to consider the rights and wrongs of their advice and decisions. The potential impact of data and new technology is leading more professions, such as accountancy,<ref>[https://www.icaew.com/technical/ethics/ethics-and-new-technologies Ethics and New Techologies, ICAEW, 2018]</ref> to consider how bias is overseen in automated systems, from algorithms to AI. Due to its large impact and its necessity in the modern industrialised world, mathematics has been labelled as a new [[Factors of production|factor of production]] by some scholars.<ref>{{Cite book |url=https://link.springer.com/10.1007/978-3-642-11248-5 |title=Production Factor Mathematics |date=2010 |publisher=Springer Berlin Heidelberg |isbn=978-3-642-11247-8 |editor-last=Grötschel |editor-first=Martin |location=Berlin, Heidelberg |language=en |doi=10.1007/978-3-642-11248-5 |editor-last2=Lucas |editor-first2=Klaus |editor-last3=Mehrmann |editor-first3=Volker}}</ref> |
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==Disasters involving the use of mathematics== |
==Disasters involving the use of mathematics== |
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Courses in the ethics of mathematics remain rare. The [[University of New South Wales]] taught a compulsory course on Professional Issues and Ethics in Mathematics in its mathematics degrees from 1998 to 2012.<ref>{{cite journal |last1=Franklin |first1=James |date=2005 |title=A "Professional issues and ethics in mathematics" course |url=http://www.austms.org.au/Publ/Gazette/2005/May05/franklin.pdf |journal=Gazette of the Australian Mathematical Society |volume=32 |issue= |pages=98–100 |access-date=30 June 2021}}</ref> In 2023 the [[ETH Zurich]] taught an optional seminar on ethics in mathematics<ref>{{Cite web |last=Course Catalogue |first=ETH Zürich |date=2023 |title=Seminar 851-0185-00L: Ethics in Mathematics |url=https://www.vvz.ethz.ch/Vorlesungsverzeichnis/lerneinheit.view?lang=en&lerneinheitId=170861&semkez=2023S& |url-status=live}}</ref> and a non-examinable seminar also exists at the [[University of Cambridge]]<ref>{{Cite web |date=2023 |title=Cambridge University Ethics in Mathematics Project |url=https://www.ethics.maths.cam.ac.uk/ |url-status=live}}</ref>. |
Courses in the ethics of mathematics remain rare. The [[University of New South Wales]] taught a compulsory course on Professional Issues and Ethics in Mathematics in its mathematics degrees from 1998 to 2012.<ref>{{cite journal |last1=Franklin |first1=James |date=2005 |title=A "Professional issues and ethics in mathematics" course |url=http://www.austms.org.au/Publ/Gazette/2005/May05/franklin.pdf |journal=Gazette of the Australian Mathematical Society |volume=32 |issue= |pages=98–100 |access-date=30 June 2021}}</ref> In 2023 the [[ETH Zurich]] taught an optional seminar on ethics in mathematics<ref>{{Cite web |last=Course Catalogue |first=ETH Zürich |date=2023 |title=Seminar 851-0185-00L: Ethics in Mathematics |url=https://www.vvz.ethz.ch/Vorlesungsverzeichnis/lerneinheit.view?lang=en&lerneinheitId=170861&semkez=2023S& |url-status=live}}</ref> and a non-examinable seminar also exists at the [[University of Cambridge]]<ref>{{Cite web |date=2023 |title=Cambridge University Ethics in Mathematics Project |url=https://www.ethics.maths.cam.ac.uk/ |url-status=live}}</ref>. |
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Many courses considering ethics in mathematics also appear under different names, e.g. "mathematics for social justice."<ref>{{Cite web |date=2022 |title=Special Issue on Ethics in Mathematics, Journal of Humanistic Mathematics 12(2) |url=https://scholarship.claremont.edu/jhm/vol12/iss2/ |url-status=live}}</ref> These complementary approaches to the teaching of responsible or ethical mathematics often build on different educational philosophies and find themselves in different |
Many courses considering ethics in mathematics also appear under different names, e.g. "mathematics for social justice."<ref>{{Cite web |date=2022 |title=Special Issue on Ethics in Mathematics, Journal of Humanistic Mathematics 12(2) |url=https://scholarship.claremont.edu/jhm/vol12/iss2/ |url-status=live}}</ref> These complementary approaches to the teaching of responsible or ethical mathematics often build on different educational philosophies and find themselves in different traditions of mathematics education.<ref>{{Cite journal |last=Müller |first=Dennis |date=2022 |title=Situating "Ethics in Mathematics" as a Philosophy of Mathematics Ethics Education |url=https://arxiv.org/abs/2202.00705 |doi=10.48550/ARXIV.2202.00705}}</ref> |
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== See also == |
== See also == |
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Revision as of 11:17, 12 August 2023
 | This article contains content that is written like an advertisement. (September 2022) |
Ethics in mathematics is an emerging field of applied ethics, the inquiry into ethical aspects of the practice and applications of mathematics. It deals with the professional responsibilities of mathematicians whose work influences decisions with major consequences, such as in law, finance, the military, and environmental science.[1] When understood in its socio-economic context, the development of mathematical works can lead to ethical questions ranging from the handling and manipulation of data to questions of responsible mathematisation and falsification of models, explainable and safe mathematics, as well as many issues related to communication and documentation.[2] The usefulness of a Hippocratic oath for mathematicians is an issue of ongoing debate among scholars.[3]
Although many mathematicians see no ethical implications of their research work, assumptions made in mathematical approaches can have real consequences.[4] These ethical questions surrounding the practice of mathematics can be connected to issues of dual-use.[5] An instrumental interpretation of the impact of mathematics makes it difficult to see ethical consequences, yet it might be easier to see how all branches of mathematics serve to structure and conceptualize solutions to real problems.[6] These structures can set up perverse incentives, where targets can be met without improving services, or league table positions are gamed. While the assumptions written into metrics often reflect the worldview of the groups who are responsible for designing them, they are harder for non-experts to challenge, leading to injustices.[7] Thus, it has been argued that mathematical artifacts have politics just like any other technical artifact.[8] As mathematicians can enter the workforce of industrialised nations in many places that are no longer limited to teaching and academia, scholars have made the argument that it is necessary to add ethical training into the mathematical curricula at universities.[9]
The philosophical positions on the relationship between mathematics and ethics are varied. Some philosophers (e.g. Plato) see both mathematics and ethics as rational and similar, while others (e.g. Rudolf Carnap) see ethics as irrational and different from mathematics.[10] Possible tensions between applying mathematics in a social context and its ethics can already be observed in Plato's Republic (Book VIII) where the use of mathematics to produce better guardians plays a critical role in its collapse.[11]
Need for ethics in the mathematics profession
Mathematicians in industrial, scientific, military and intelligence roles crucially influence decisions with significant consequences.
Issues of accuracy
For example, complex calculations were needed for the success of the Manhattan Project, while the overextended use of the Gaussian copula formula to price derivatives before the Global Financial Crisis of 2008 has been called "the formula that killed Wall Street",[12] and the theory of global warming depends on the reliability of mathematical models of climate[13].
Issues of impact
For the same reason as in medical ethics and engineering ethics, the high impact of the consequences of decisions imposes serious ethical obligations on practitioners to consider the rights and wrongs of their advice and decisions. The potential impact of data and new technology is leading more professions, such as accountancy,[14] to consider how bias is overseen in automated systems, from algorithms to AI. Due to its large impact and its necessity in the modern industrialised world, mathematics has been labelled as a new factor of production by some scholars.[15]
Disasters involving the use of mathematics
These illustrate the major consequences of numerical mistakes and hence the need for ethical care.
- The Club of Rome's 1972 mathematical-model-based predictions in The Limits to Growth of widespread collapse of the world system by the end of the 21st century.
- The wrongful conviction of Sally Clark (1999), An English solicitor, Sally Clark, was wrongfully convicted of murdering her two children – each of whom had died due to sudden infant death syndrome – due to a fundamental statistical error in the testimony of an "expert". The error was further compounded by the "prosecutor's fallacy".[16]
Ethical issues in the mathematical profession
Mathematicians in professional roles in finance and similar work have a particular responsibility to ensure they use the best methods and data to reach the right answer, as the prestige of mathematics is high and others rely on mathematical results which they cannot fully understand.[17][18] Other ethical issues are shared with information economy professionals in general, such as duty of care, confidentiality of information, whistleblowing, and avoiding conflict of interest.
Mathematicians have a professional responsibility to support the ethical use of mathematics in practice, both to sustain the reputation of the profession and to protect society from the impacts of unethical behavior. For example, mathematics is extensively applied in the use of Big Data in Artificial Intelligence applications, both by mathematicians and non-mathematicians, with complex impacts that are not readily understood or anticipated.[19]
Ethics in data journalism
Journalism has established Professional ethics which is affected by mathematical processing and (re-)publication of sources. Reusing information packaged as facts require checking, and validating, from conceptual confusion to sampling and calculation errors.[20] Other professional issues arise from the potential of automated tools which allow the dissemination of publicly available data which has never been collated.
Misuse of statistics
Applications of mathematics generally involve drawing conclusions from quantitative data. Due to uncertainties that mathematical models deal with, and challenges in drawing and communicating any conclusions, there is a possibility of mathematicians misleading the clients as they are not generally aware of quantitative techniques. To avoid such instances, statisticians codified their ethics in the 1980s in a declaration of the ISI, recognizing that there would often be conflicting demands from stakeholders, with ethical decisions a matter of professional judgment.[21]
Mathematical folklore
Priority and attribution of mathematical discovery are important to professional practice, even as some theorems bear the name of the person making the conjecture rather than finding the proof. Folk theorems, or mathematical folklore cannot be attributed to an individual, and may not have an agreed proof, despite being an accepted result, potentially leading to injustice.[22]
Ethics in pure mathematical research
The American Mathematical Society publishes a code of ethical guidelines for mathematical researchers. The responsibilities of researchers include being knowledgeable in the field, avoiding plagiarism, giving credit, publishing without unreasonable delay, and correcting errors.[23] The European Mathematical Society Ethics Committee also publishes a code of practice relating to the publication, editing and refereeing of research.[24]
It has been argued that as pure mathematical research is relatively harmless, it raises few urgent ethical issues.[25] However, that raises the question of whether and why pure mathematics is ethically worth doing, given that it consumes the lives of many highly intelligent people who could be making more immediately useful contributions.[26]
The study of ethical challenges in pure mathematics is deeply connected to the philosophy of mathematical practice[27]. Arguments against the ethical neutrality of pure mathematical work often builds on the social constitution, i.e. the socio-cultural context of the research and the many decisions involved in mathematical proofs[28][29]. The problem of epistemic injustice in mathematical research is actively discussed in this context.[30]
Parallels between ethics and mathematics
Ethics and mathematics both appear to rely on reasoning from intuition, unlike empirical sciences which rely fundamentally on observations and experiments. That has been suggested as a reason in support of objectivity or moral realism in ethics, since arguments against objectivity in ethics are paralleled by arguments against objectivity in mathematics, which is generally believed to be false.[31][32]
Justin Clarke-Doane argues to the contrary that although mathematics and ethics are closely parallel, a pluralist attitude should be taken to the truths of both. Just as the parallel postulate is true in Euclidean geometry but false in non-Euclidean geometry, so ethical propositions can be true or false in different systems.[33]
Teaching ethics in mathematics
Courses in the ethics of mathematics remain rare. The University of New South Wales taught a compulsory course on Professional Issues and Ethics in Mathematics in its mathematics degrees from 1998 to 2012.[34] In 2023 the ETH Zurich taught an optional seminar on ethics in mathematics[35] and a non-examinable seminar also exists at the University of Cambridge[36].
Many courses considering ethics in mathematics also appear under different names, e.g. "mathematics for social justice."[37] These complementary approaches to the teaching of responsible or ethical mathematics often build on different educational philosophies and find themselves in different traditions of mathematics education.[38]
See also
- Essentially contested concept – Problem in philosophy
- Ethical calculus – Application of mathematics to calculate issues in ethics
- Misuse of statistics – Use of statistical arguments to assert falsehoods
- Prosecutor's fallacy – Error in thinking which involves under-valuing base rate information
- Type I and type II errors – Concepts from statistical hypothesis testing
- Type III error – Term in statistical hypothesis testing
- Unintended consequences – Unforeseen outcomes of an action
- Big data ethics – Ethics of mass data analytics
- Ethics of quantification
Notes
- ^ Nickel, Gregor (2022). "Ethics and Mathematics – Some Observations Fifty Years Later". Journal of Humanistic Mathematics. 12 (2): 24. doi:10.5642/jhummath.PXMY2159.
- ^ Chiodo, Maurice; Müller, Dennis (2023). "Manifesto for the Responsible Development of Mathematical Works -- A Guide for Practitioners and Management". arXiv preprint arXiv:2306.09131.
{{cite web}}: CS1 maint: url-status (link) - ^ Rittberg, Colin Jakob (2023). "Hippocratic Oaths for Mathematicians?". Philosophia. 51 (3): 1579–1603. doi:10.1007/s11406-022-00588-8. ISSN 0048-3893.
- ^ Chiodo, M. & Bursill-Hall, P. (2018) Four Levels of Ethical Engagement Discussion paper 18/1, Cambridge University Ethics in Mathematics Project
- ^ "The dual use problem in mathematics". Scientific Integrity. 2023.
{{cite web}}: CS1 maint: url-status (link) - ^ Slightly dirty maths: The richly textured mechanisms of impact Laura R. Meagher Ursula Martin, Research Evaluation (2017) 26 (1): 15-27
- ^ O'Neil, C. (2016) Weapons of Math Destruction, Penguin.
- ^ Müller, Dennis; Chiodo, Maurice (2023). "Mathematical Artifacts Have Politics: The Journey from Examples to Embedded Ethics". arXiv preprint arXiv:2308.04871.
{{cite web}}: CS1 maint: url-status (link) - ^ Alayont, Feryal (2022). "A Case for Ethics in the Mathematics Major Curriculum". Journal of Humanistic Mathematics. 12 (2): 160–177. doi:10.5642/jhummath.CXSI3022.
- ^ Nickel, Gregor (2022). "Ethics and Mathematics – Some Observations Fifty Years Later". Journal of Humanistic Mathematics. 12 (2): 7–27. doi:10.5642/jhummath.PXMY2159.
- ^ Jens, Rod (2002). "THE MACHINERY OF THE COLLAPSE: ON "REPUBLIC" VIII". History of Political Thought. 23 (1).
- ^ Felix Salmon, Recipe for disaster: the formula that killed Wall Street", Wired23 Feb 2009.
- ^ Frigg, Roman; Thompson, Erica; Werndl, Charlotte (2015). "Philosophy of Climate Science Part II: Modelling Climate Change: Modelling Climate Change". Philosophy Compass. 10 (12): 965–977. doi:10.1111/phc3.12297.
- ^ Ethics and New Techologies, ICAEW, 2018
- ^ Grötschel, Martin; Lucas, Klaus; Mehrmann, Volker, eds. (2010). Production Factor Mathematics. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-642-11248-5. ISBN 978-3-642-11247-8.
- ^ Derbyshire, D., "Misleading statistics were presented as facts in Sally Clark trial", The Telegraph, (12 June 2003).
- ^ Müller, Dennis; Chiodo, Maurice; Franklin, James (2022). "A Hippocratic Oath for mathematicians? Mapping the landscape of ethics in mathematics". Science and Engineering Ethics. 28 (5): 41. doi:10.1007/s11948-022-00389-y. PMC 9427075. PMID 36042113.
- ^ Money Mathematics: Examining Ethics Education in Quantitative Finance
- ^ Collmann & Matei (Eds.), Ethical Reasoning in Big Data, Basel, CH: Springer, 2016
- ^ McBride, [1], 2017
- ^ Jowell, R. (1986) The Codification of Statistical Ethics, J. Official Statist. 2(3): 217-253
- ^ van Bendegem, J., Rittberg, C. & Tanswell, F. (2018) Epistemic Injustice in Mathematics, Synthese
- ^ American Mathematical Society Policy Statement on Ethical Guidelines, 2005.
- ^ Code of Practice – European Mathematical Society.
- ^ Hersh, Reuben (1990). "Mathematics and ethics". Mathematical Intelligencer. 12 (3): 13–15. doi:10.1007/BF03024064. S2CID 206832780. Retrieved 30 June 2021.
- ^ Franklin, James (1991). "Ethics of mathematics". Mathematical Intelligencer. 13 (1): 4. doi:10.1007/BF03024064. S2CID 206832780. Retrieved 30 June 2021.
- ^ Wagner, Roi (2023). "The Ethical Charge of Articulating Mathematics". Global Philosophy. 33 (35): 1–20.
- ^ Cantù, Paola; Testa, Italo (2023). "Introduction: From Social Ontology to Mathematical Practice, and Back Again". Topoi. 42 (1): 187–198. doi:10.1007/s11245-022-09870-6. ISSN 0167-7411.
- ^ Nickel, Gregor (2007-03-01), Berendes, Jochen (ed.), "Mathematik und Mathematisierung der Wissenschaften. Ethische Erwägungen", Autonomie durch Verantwortung, Brill | mentis, pp. 319–346, doi:10.30965/9783969750360_014, ISBN 978-3-96975-036-0, retrieved 2023-08-12
- ^ Rittberg, Colin Jakob; Tanswell, Fenner Stanley; Van Bendegem, Jean Paul (2020). "Epistemic injustice in mathematics". Synthese. 197 (9): 3875–3904. doi:10.1007/s11229-018-01981-1. ISSN 0039-7857.
- ^ Lear, Jonathan (1983). "Ethics, mathematics and relativism". Mind. 92 (365): 38–60. doi:10.1093/mind/XCII.365.38. Retrieved 30 June 2021.
- ^ Franklin, James (2021). "'Let no‑one ignorant of geometry…': Mathematical parallels for understanding the objectivity of ethics". Journal of Value Inquiry. 55. doi:10.1007/s10790-021-09831-z. S2CID 235538417. Retrieved 30 June 2021.
- ^ Clarke-Doane, Justin (2020). Morality and Mathematics. New York: Oxford University Press. ISBN 9780198823667.
- ^ Franklin, James (2005). "A "Professional issues and ethics in mathematics" course" (PDF). Gazette of the Australian Mathematical Society. 32: 98–100. Retrieved 30 June 2021.
- ^ Course Catalogue, ETH Zürich (2023). "Seminar 851-0185-00L: Ethics in Mathematics".
{{cite web}}: CS1 maint: url-status (link) - ^ "Cambridge University Ethics in Mathematics Project". 2023.
{{cite web}}: CS1 maint: url-status (link) - ^ "Special Issue on Ethics in Mathematics, Journal of Humanistic Mathematics 12(2)". 2022.
{{cite web}}: CS1 maint: url-status (link) - ^ Müller, Dennis (2022). "Situating "Ethics in Mathematics" as a Philosophy of Mathematics Ethics Education". doi:10.48550/ARXIV.2202.00705.
{{cite journal}}: Cite journal requires|journal=(help)
References
- Aitken, C., Roberts, P. & Jackson, G., Communicating and Interpreting Statistical Evidence in the Administration of Criminal Justice, Practitioner Guide No.1: Fundamentals of Probability and Statistical Evidence in Criminal Proceedings: Guidance for Judges, Lawyers, Forensic Scientists and Expert Witnesses, Royal Statistical Society, 2010.
- Alayont, F. (2022), "A Case for Ethics in the Mathematics Major Curriculum", Journal of Humanistic Mathematics, Vol.12, No.2, (July 2022), pp.160-177.
- Balinski, M., "What is just?", American Mathematical Monthly, Vol.112, No.6, (June-July 2005), pp. 502-511.
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