19 citations · 60 across the 25 of their papers we have counts for
27 papers
A Primer on Ethics in Mathematics
Maurice Chiodo
This is a course about Ethics in Mathematics. That is, about the ethical issues that arise in mathematics itself, in mathematical work, and in the actions of mathematicians, broadl…
Reframing AI Loss of Control: What Control Is, How to Have It, How to Lose It
Ze Shen Chin, Maurice Chiodo, Dennis Müller +1
At present, loss of control risks have gained much prominence in public discussion, particularly in relation to AI, with extensive discourse present among academics, frontier labs,…
"We are currently clean on OPSEC": Why JD Can't Encrypt
Maurice Chiodo, Toni Erskine, Dennis Müller +1
We analyse the 2025 Signalgate leak of sensitive US military information by the Trump administration, addressing why confidentiality was violated (messages leaked to the press) in…
The Ethical and Sustainable Concerns Triangle: A Framework for Navigating Discourses in Mathematics and Its Education
Dennis Müller, Maurice Chiodo, Michael Meyer
The literature on ethics and sustainability in mathematics and its education is increasingly complex and fragmented, potentially leading to communication breakdowns between differe…
Ethical and sustainable mathematics is localised: why global paradigms fail and culturally-situated practices are essential
Dennis Müller, Maurice Chiodo
This paper identifies several different interconnected challenges preventing the move towards more ethical and sustainable mathematics education: the entrenched belief in mathemati…
The Problem of Algorithmic Collisions: Mitigating Unforeseen Risks in a Connected World
Maurice Chiodo, Dennis Müller
The increasing deployment of Artificial Intelligence (AI) and other autonomous algorithmic systems presents the world with new systemic risks. While focus often lies on the functio…
Formalising Human-in-the-Loop: Computational Reductions, Failure Modes, and Legal-Moral Responsibility
Maurice Chiodo, Dennis Müller, Paul Siewert +3
We use the notion of oracle machines and reductions from computability theory to formalise different Human-in-the-loop (HITL) setups for AI systems, distinguishing between trivial…
Integrators at War: Mediating in AI-assisted Resort-to-Force Decisions
Dennis Müller, Maurice Chiodo, Mitja Sienknecht
The integration of AI systems into the military domain is changing the way war-related decisions are made. It binds together three disparate groups of actors - developers, integrat…
A Field Guide to Ethics in Mathematics
Maurice Chiodo, Dennis Müller
Mathematics has become inescapable in modern, digitized societies: there is hardly any area of life left that isn't affected by it, and we as mathematicians play a central role in…
Teaching Resources for Embedding Ethics in Mathematics: Exercises, Projects, and Handouts
Maurice Chiodo, Dennis Müller, Rehan Shah
The resources compiled in this document provide an approach to embed and teach Ethics in Mathematics at the undergraduate level. We provide mathematical exercises and homework prob…
Mathematical Artifacts Have Politics: The Journey from Examples to Embedded Ethics
Dennis Müller, Maurice Chiodo
We extend Langdon Winner's idea that artifacts have politics into the realm of mathematics. To do so, we first provide a list of examples showing the existence of mathematical arti…
Manifesto for the Responsible Development of Mathematical Works -- A Tool for Practitioners and for Management
Maurice Chiodo, Dennis Müller
This manifesto has been written as a practical tool and aid for anyone carrying out, managing or influencing mathematical work. It provides insight into how to undertake and develo…
A useful ethics framework for mathematics teachers
Lucy Rycroft-Smith, Dennis Müller, Maurice Chiodo +1
An argument is presented that mathematics teachers would benefit from an ethics framework that allows them to reflect upon their position regarding the teaching of ethics within ma…
Questions of Responsibility: Modelling in the Age of COVID-19
Maurice Chiodo, Dennis Müller
When conducting COVID-19-related research, mathematicians may find themselves in public service roles. They might engage in policy discussions, collaborate with politicians and oth…
Mathematicians and Ethical Engagement
Maurice Chiodo, Dennis Müller
Building on Chiodo and Bursill-Hall (2018), we outline that mathematicians can demonstrate what we term the "four levels of ethical engagement."
A Hippocratic Oath for mathematicians? Mapping the landscape of ethics in mathematics
Dennis Müller, Maurice Chiodo, James Franklin
While the consequences of mathematically-based software, algorithms and strategies have become ever wider and better appreciated, ethical reflection on mathematics has remained pri…
Investigating transversals as generating sets for groups
Maurice Chiodo, Robert Crumplin, Oscar Donlan +1
In [3] is was shown that for any group whose rank (i.e., minimal number of generators) is at most 3, and any finite index subgroup with index , one…
Preserving torsion orders when embedding into groups with `small' finite presentations
Maurice Chiodo, Michael E. Hill
We give a complete survey of a construction by Boone and Collins for embedding any finitely presented group into one with generators and relations. We show that this embed…
-torsion and universal groups
Maurice Chiodo, Zachiri McKenzie
For a set , we define the -torsion of a group to be all elements with for some . With recursively enumerable, we give t…
Torsion, torsion length and finitely presented groups
Maurice Chiodo, Rishi Vyas
We show that a construction by Aanderaa and Cohen used in their proof of the Higman Embedding Theorem preserves torsion length. We give a new construction showing that every finite…
Transversals as generating sets in finitely generated groups
Jack Button, Maurice Chiodo, Mariano Zeron-Medina Laris
We explore transversals of finite index subgroups of finitely generated groups. We show that when is a subgroup of a rank group and has index at least in th…
Coset intersection graphs for groups
Jack Button, Maurice Chiodo, Mariano Zeron-Medina Laris
Let H, K be subgroups of G. We investigate the intersection properties of left and right cosets of these subgroups.
A note on torsion length
Maurice Chiodo, Rishi Vyas
We construct a 2-generator recursively presented group with infinite torsion length. We also explore the construction in the context of solvable and word-hyperbolic groups.
The subgroup identification problem for finitely presented groups
Maurice Chiodo
We introduce the subgroup identification problem, and show that there is a finitely presented group G for which it is unsolvable, and that it is uniformly solvable in the class of…