Past Maths in Society Seminar

If asked, we all say we aim to to good research and make sensible decisions. In mathematics, the choice of criteria to optimise is often explicit, and we know there is no complete ordering in more than one dimension.

Statisticians involved in multi-disciplinary research need to reflect on how their understanding of uncertainty and statistical methods can contribute to reliable and reproducible research. The ISI Declaration of Professional Ethics provides a framework for statisticians.  Judging what is "normal" and what is "best" requires an appreciation of the assumptions and guidelines of other disciplines.

I will briefly discuss the requirements for design and analysis in medical research, and relate this to debates on reproducible research and p-values in social science research. Issues arising from informed and uninformed consent will be outlined.

Examples might include medical research in developing countries, toxic tort or wrongful birth claims, big data and use of routine administrative or commercial data.

Sustainability is a highly complex topic, containing interwoven economic, ecological, and social aspects.  Simply defining the concept of sustainability is a challenge in itself.  Assessing the impact of sustainability efforts and generating effective policy requires analyzing the interactions and challenges presented by these different aspects. To address this challenge, it is necessary to develop methods that bridge fields and take into account phenomena that range from physical analysis of climate to network analysis of societal phenomena. In this talk, I will give an insight into areas of mathematical research that try to account for these inter-dependencies. The aim of this talk is to provide a critical discussion of the challenges in a joint discussion and emphasize the importance of multi-disciplinary approaches.

Computers can now beat humans at chess and at go. Surely one day they will beat us at proving theorems. But when will it happen, how will it happen, and what should humans be doing in order to make it happen? Furthermore -- do we actually want it to happen? Will they generate incomprehensible proofs, which teach us nothing? Will they find mistakes in the human literature?

I will talk about how I am training undergraduates at Imperial College London to do their problem sheets in a formal proof verification system, and how this gamifies mathematics. I will talk about mistakes in the modern pure mathematics literature, and ask what the point of modern pure mathematics is.

In recent years it has become abundantly clear that mathematics can do "things" in society; indeed, many more things than in the past. Deep mathematical work now underpins some of the most important aspects of the way society functions. And, as mathematically-trained people, we are constantly promoting the positive impact of mathematics. But if such work is capable of good, then is it not also capable of harm? So how do we begin to identify such potential harm, let alone address it and try and avoid, or at least reduce, it? In this session we will discuss how mathematics is a powerful double-edged sword, and why it must be wielded responsibly.

How would we get a powerful AI to align itself with human preferences? What are human preferences anyway? And how can you code all this?
It turns out that maths give you the grounding to answer these fascinating and vital questions.
 

Let's take a step back to understand what it means to use maths in society: Which maths, and whose society? I'll talk about some of the options I've come across, including time I spent at the US Census Bureau, and we will hear your ideas too. We might even crowdsource a document of maths in society opportunities together...

In the twentieth century we leant that the theory of communication is a mathematical theory. Mathematics is able to add to the value of data, for example by removing redundancy (compression) or increasing robustness (error correction). More famously mathematics can add value to data in the presence of an adversary which is my personal definition of cryptography. Cryptographers talk about properties of confidentiality, integrity, and authentication, though modern cryptography also facilitates transparency (distributed ledgers), plausible deniability (TrueCrypt), and anonymity (Tor).
Modern cryptography faces new design challenges as people demand more functionality from data. Some recent requirements include homomorphic encryption, efficient zero knowledge proofs for smart contracting, quantum resistant cryptography, and lightweight cryptography. I'll try and cover some of the motivations and methods for these.
 

As early as the 1920's Marshall suggested that firms co-locate in cities to reduce the costs of moving goods, people, and ideas. These 'forces of agglomeration' have given rise, for example, to the high tech clusters of San Francisco and Boston, and the automobile cluster in Detroit. Yet, despite its importance for city planners and industrial policy-makers, until recently there has been little success in estimating the relative importance of each Marshallian channel to the location decisions of firms.
Here we explore a burgeoning literature that aims to exploit the co-location patterns of industries in cities in order to disentangle the relationship between industry co-agglomeration and customer/supplier, labour and idea sharing. Building on previous approaches that focus on across- and between-industry estimates, we propose a network-based method to estimate the relative importance of each Marshallian channel at a meso scale. Specifically, we use a community detection technique to construct a hierarchical decomposition of the full set of industries into clusters based on co-agglomeration patterns, and show that these industry clusters exhibit distinct patterns in terms of their relative reliance on individual Marshallian channels.

The second part is to use industry relatedness, which we measure via a similar metric to co-location, to better understand the association of industrial emissions to city-industry agglomeration. Specifically, we see that industrial emissions (which are the largest source of greenhouse emissions in the US) are highly tied to certain industries, and furthermore that communities in the industry relatedness network tend to explain the tendency of particular industry clusters to produce emissions. This is important, because it limits cities' abilities to move to a greener industry basket as some cities may be more or less constrained to highly polluting industry clusters, while others have more potential for diversification away from polluting industries.