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 big data to questions of responsible mathematisation and falsification of models, explainable and safe mathematics, as well as many issues related to communication and documentation. The usefulness of a Hippocratic oath for mathematicians is an issue of ongoing debate among scholars.[2] As an emerging field of applied ethics, many of its foundations are still highly debated. The discourse remains in flux. Especially the notion that mathematics can do harm remains controversial.[3]
The ethical questions surrounding the practice of mathematics can be connected to issues of dual-use.[4] 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.[5] These structures can set up perverse incentives, where targets can be met without improving services, or league table positions are gamed.[6] 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] 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.[8]
The philosophical positions on the relationship between mathematics and ethics are varied.[9] 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]