arXiv subjects

Maurice Chiodo

Publications and source records attributed to Maurice Chiodo.

At least 19 recordsLinked to original sources

arXiv2026

Reframing AI Loss of Control: What Control Is, How to Have It, How to Lose It

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, and even governments. However, in the existing literature, the concept seems to rest on surprisingly weak foundations, where even those that discuss loss of control extensively do not first establish what control is and what exactly is being lost. Our paper aims to address these gaps. We establish a working definition of control by anchoring it to the "setting and getting of goals". Then, we discuss various aspects of control, built on foundational concepts from related fields like cybernetics, management control, and control theory. This includes who (or what) can be in control, and the things they require to be in control, such as the ability to set goals, having a functional control loop, having requisite variety, and having sufficient goal alignment. Once a framework for control is established, we then discuss how control can be lost, how AIs can contribute to such loss of control, and offer relevant recommendations for how one can maintain control. One interesting consequence of our work is that humanity, as individuals and as groups, can lose varying degrees of control as a result of AI behaviour that is far below the level of superintelligence; the potential for loss of control scenarios (as we define them) already exist, and have existed for a long time.

cs.CY↗

arXiv2026

"We are currently clean on OPSEC": Why JD Can't Encrypt

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 spite of encryption (Signal), to deepen the socio-technical considerations when designing and deploying encryption. First, we use applied pi-calculus to formally model the boutique secure facility setup requested by the US Defence Secretary, to prove that a leak would not be prevented. We then examine how using a secure channel might still not give overall information security, as, in this case, power imbalances between personnel and officials led to the application of cryptography that compromised their operational security. We look at how cryptographic tools may have instilled a false sense of security, and led officials to "overshare". We then apply this analysis to the Trump administration's general desire to burn through political, legal, and now technical process, and demonstrate geopolitical harms that may arise from such ineffective use of cryptography in a brief use case. We conclude that, even with advancements in usability of cryptographic tools, genuine message security is still out of reach of the "average user".

cs.CR↗

arXiv2025

The Ethical and Sustainable Concerns Triangle: A Framework for Navigating Discourses in Mathematics and Its Education

The literature on ethics and sustainability in mathematics and its education is increasingly complex and fragmented, potentially leading to communication breakdowns between different scholarly traditions. To address this, the paper introduces the "Ethical and Sustainable Concerns Triangle," a framework that maps discourses based on their relative concern for three areas (represented as three vertices in the triangle): "Mathematics", "Community", and "Society/Planet". By integrating a systems theoretic perspective, we analyse discourses as dynamic systemic reactions to external irritations. Our analysis reveals that the field's fragmentation can be explained by the "location effect": the phenomenon whereby a discourse's position within the triangle shapes its perception and acceptance of other scholarship. By mapping key discourses and educator archetypes, the framework functions as a meta-heuristic tool. Ultimately, it serves not only to facilitate critical reflection but also as a call for the epistemic humility and dialogue needed to advance the field.

math.HO↗

arXiv2025

Ethical and sustainable mathematics is localised: why global paradigms fail and culturally-situated practices are essential

This paper identifies several different interconnected challenges preventing the move towards more ethical and sustainable mathematics education: the entrenched belief in mathematical neutrality, the difficulty of simultaneously reforming mathematics and its pedagogy, the gap between academic theory and classroom practice, and the need for epistemic decolonisation. In this context, we look at both bottom-up and top-down approaches, and argue that globalised frameworks such as the United Nations' Sustainable Development Goals are insufficient for this transformation, and that ethical and sustainable forms of mathematics ought not to be built using these as their (philosophical) foundation. These frameworks are often rooted in a Western-centric development paradigm that can perpetuate colonial hierarchies and fails to resolve inherent conflicts between economic growth and ecological integrity. As an alternative, this paper advocates for embracing localised, culturally-situated mathematical practices. Using the Ethics in Mathematics Project as a case study within a Western, Global North institution, this paper illustrates a critical-pragmatic, multi-level strategy for fostering ethical consciousness within a specific research community, and shows how this may be achieved in otherwise adversarial circumstances.

math.HO↗

arXiv2025

Formalising Human-in-the-Loop: Computational Reductions, Failure Modes, and Legal-Moral Responsibility

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 human monitoring (i.e., total functions), single endpoint human action (i.e., many-one reductions), and highly involved human-AI interaction (i.e., Turing reductions). We then proceed to show that the legal status and safety of different setups vary greatly. We present a taxonomy to categorise HITL failure modes, highlighting the practical limitations of HITL setups. We then identify omissions in UK and EU legal frameworks, which focus on HITL setups that may not always achieve the desired ethical, legal, and sociotechnical outcomes. We suggest areas where the law should recognise the effectiveness of different HITL setups and assign responsibility in these contexts, avoiding human "scapegoating". Our work shows an unavoidable trade-off between attribution of legal responsibility, and technical explainability. Overall, we show how HITL setups involve many technical design decisions, and can be prone to failures out of the humans' control. Our formalisation and taxonomy opens up a new analytic perspective on the challenges in creating HITL setups, helping inform AI developers and lawmakers on designing HITL setups to better achieve their desired outcomes.

cs.CY↗

arXiv2025

The Problem of Algorithmic Collisions: Mitigating Unforeseen Risks in a Connected World

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 function of individual algorithms, a critical and underestimated danger arises from their interactions, particularly when algorithmic systems operate without awareness of each other, or when those deploying them are unaware of the full algorithmic ecosystem deployment is occurring in. These interactions can lead to unforeseen, rapidly escalating negative outcomes - from market crashes and energy supply disruptions to potential physical accidents and erosion of public trust - often exceeding the human capacity for effective monitoring and the legal capacities for proper intervention. Current governance frameworks are inadequate as they lack visibility into this complex ecosystem of interactions. This paper outlines the nature of this challenge and proposes some initial policy suggestions centered on increasing transparency and accountability through phased system registration, a licensing framework for deployment, and enhanced monitoring capabilities.

cs.CY↗

arXiv2025

Teaching Resources for Embedding Ethics in Mathematics: Exercises, Projects, and Handouts

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 problems that teach students ethical awareness and transferable skills, for many of the standard courses in the first and second years of a university degree in mathematics or related courses with significant mathematical content (e.g., physics, engineering, computer science, economics, etc). In addition to the exercises, this document also contains a list of projects, essay topics, and handouts for use as final projects and in seminars. This is a living document, and additional contributions are welcome.

math.HO↗

arXiv2025

Integrators at War: Mediating in AI-assisted Resort-to-Force Decisions

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, integrators, users - and creates a relationship between these groups and the machine, embedded in the (pre-)existing organisational and system structures. In this article, we focus on the important, but often neglected, group of integrators within such a sociotechnical system. In complex human-machine configurations, integrators carry responsibility for linking the disparate groups of developers and users in the political and military system. To act as the mediating group requires a deep understanding of the other groups' activities, perspectives and norms. We thus ask which challenges and shortcomings emerge from integrating AI systems into resort-to-force (RTF) decision-making processes, and how to address them. To answer this, we proceed in three steps. First, we conceptualise the relationship between different groups of actors and AI systems as a sociotechnical system. Second, we identify challenges within such systems for human-machine teaming in RTF decisions. We focus on challenges that arise a) from the technology itself, b) from the integrators' role in the sociotechnical system, c) from the human-machine interaction. Third, we provide policy recommendations to address these shortcomings when integrating AI systems into RTF decision-making structures.

cs.CY↗

arXiv2024

A Field Guide to Ethics in Mathematics

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 this. Our actions affect what others, in particular our students, decide to do with mathematics, and how mathematics affects the world, for better or worse. In return, the study of ethics in mathematics (EiM) has become increasingly important, even though it is still unknown to many. This exposition tries to change that, by motivating ethics in mathematics as an interesting, tractable, non-trivial, well-defined and good research area for mathematicians to consider.

math.HO↗

arXiv2023

Mathematical Artifacts Have Politics: The Journey from Examples to Embedded Ethics

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 artifacts that have politics. In the second step, we provide an argument that shows that all mathematical artifacts have politics. We conclude by showing the implications for embedding ethics into mathematical curricula. We show how acknowledging that mathematical artifacts have politics can help mathematicians design better exercises for their mathematics students.

math.HO↗

arXiv2023

Manifesto for the Responsible Development of Mathematical Works -- A Tool for Practitioners and for Management

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 develop mathematically-powered products and services in a safe and responsible way. Rather than give a framework of objectives to achieve, we instead introduce a process that can be integrated into the common ways in which mathematical products or services are created, from start to finish. This process helps address the various issues and problems that can arise for the product, the developers, the institution, and for wider society. To do this, we break down the typical procedure of mathematical development into 10 key stages; our "10 pillars for responsible development" which follow a somewhat chronological ordering of the steps, and associated challenges, that frequently occur in mathematical work. Together these 10 pillars cover issues of the entire lifecycle of a mathematical product or service, including the preparatory work required to responsibly start a project, central questions of good technical mathematics and data science, and issues of communication, deployment and follow-up maintenance specifically related to mathematical systems. This manifesto, and the pillars within it, are the culmination of 7 years of work done by us as part of the Cambridge University Ethics in Mathematics Project. These are all tried-and-tested ideas, that we have presented and used in both academic and industrial environments. In our work, we have directly seen that mathematics can be an incredible tool for good in society, but also that without careful consideration it can cause immense harm. We hope that following this manifesto will empower its readers to reduce the risk of undesirable and unwanted consequences of their mathematical work.

math.HO↗

arXiv2022

Mathematicians and Ethical Engagement

Building on Chiodo and Bursill-Hall (2018), we outline that mathematicians can demonstrate what we term the "four levels of ethical engagement."

math.HO↗

arXiv2022

Questions of Responsibility: Modelling in the Age of COVID-19

When conducting COVID-19-related research, mathematicians may find themselves in public service roles. They might engage in policy discussions, collaborate with politicians and other non-scientists, and use the predictive power of mathematics to shape substantial decisions. We aim to promote good practice for ethical mathematical modelling in these difficult times. We begin with some observations about mathematical modellers, then derive eight questions that all mathematicians should constantly ask themselves, in order to develop their mathematics responsibly and ethically.

math.HO↗

arXiv2022

A useful ethics framework for mathematics teachers

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 mathematics. We present such a framework, adapted from Chiodo and Bursill-Hall's (2018) levels of ethical engagement for mathematicians, with discussion of its applications and implications. Awareness of ethical and social responsibility amongst mathematicians and mathematics educators is a newly established field, and yet it is crucially important, if we are to use mathematics for good and the avoidance of harm - in other words to use mathematics for justice, belonging, peace, care, education, lawmaking, building, creativity, equity, connection, fairness, rulemaking and order. Here, we present a way to extend ideas from ethics in the field of mathematics for mathematicians to the field of mathematics education for mathematics teachers, aiming to contribute to this transdisciplinary work and to advance the field further. We also explore links to ideas of equity, and silence and voice, drawing on the consequences of a deeper examination of the entanglements of mathematical-ethical dilemmas for mathematics teachers both inside and outside the classroom.

math.HO↗

arXiv2021

A Hippocratic Oath for mathematicians? Mapping the landscape of ethics in mathematics

While the consequences of mathematically-based software, algorithms and strategies have become ever wider and better appreciated, ethical reflection on mathematics has remained primitive. We review the somewhat disconnected suggestions of commentators in recent decades with a view to piecing together a coherent approach to ethics in mathematics. Calls for a Hippocratic Oath for mathematicians are examined and it is concluded that while lessons can be learned from the medical profession, the relation of mathematicians to those affected by their work is significantly different. There is something to be learned also from the codes of conduct of cognate but professionalised quantitative disciplines such as engineering and accountancy, as well as from legal principles bearing on professional work. We conclude with recommendations that professional societies in mathematics should sponsor an (international) code of ethics, institutional mission statements for mathematicians and syllabuses for incorporation into mathematics degrees.

math.HO↗

arXiv2019

Investigating transversals as generating sets for groups

In [3] is was shown that for any group $G$ whose rank (i.e., minimal number of generators) is at most 3, and any finite index subgroup $H\leq G$ with index $[G:H]\geq rank(G)$, one can always find a left-right transversal of $H$ which generates $G$. In this paper we extend this result to groups of rank at most 4. We also extend this to groups $G$ of arbitrary (finite) rank $r$ provided all the non-trivial divisors of $[G:core_G(H)]$ are at least $2r-1$. Finally, we extend this to groups $G$ of arbitrary (finite) rank provided $H$ is malnormal in $G$.

math.GR↗

arXiv2018

Torsion, torsion length and finitely presented groups

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 finitely presented group is the quotient of some $C'(1/6)$ finitely presented group by the subgroup generated by its torsion elements. We use these results to show there is a finitely presented group with infinite torsion length which is $C'(1/6)$, and thus word-hyperbolic and virtually torsion-free.

math.GR↗

arXiv2016

Transversals as generating sets in finitely generated groups

We explore transversals of finite index subgroups of finitely generated groups. We show that when $H$ is a subgroup of a rank $n$ group $G$ and $H$ has index at least $n$ in $G$ then we can construct a left transversal for $H$ which contains a generating set of size $n$ for $G$, and that the construction is algorithmic when $G$ is finitely presented. We also show that, in the case where $G$ has rank $n \leq3$, there is a simultaneous left-right transversal for $H$ which contains a generating set of size $n$ for $G$. We finish by showing that if $H$ is a subgroup of a rank $n$ group $G$ with index less than $3 \cdot 2^{n-1}$, and $H$ contains no primitive elements of $G$, then $H$ is normal in $G$ and $G/H \cong C_{2}^{n}$.

math.GR↗