** Section 1**

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Who would deny logic? Every simple person uses logic without the guidance of a logician, but logic that attempts to prove the soul, the god, or the supernatural cannot be considered valid. The common person would believe any of this without some obscurantist logician creating confusion.”Carvaka

In every age the old gods fall to new. Today the gods are data and programs. They see us. They govern our fate, and they will guide us to our destiny.

The rules of power are always obscure. Rules, fates, actions and consequences are obscured so people do not resist or enact change, even when they can. Unlike before, communication is now instantaneous. Memory is becoming indefinite, and vision infinite. We can be watched, remembered, and tracked in ways we never could be before. Digital technologies guide what we want, what we know, and how we respond, while instilling an illusion of free choice. The ruling forces of today are capital, weapons and information gathering. We might say that the Gods have a new trinity of Gs, Greed, Guns and of course Google.

When production and governance become part of automated systems, people reduce to data streams whose actions become functions that are operated on again and again. These functions are abstract in nature, but they can make the difference between life and death. Insurance, for example, is getting granted based on scores and indices that trace the history and the risk of a person and assigns a number to them. A person might be denied a loan for their education because their family has a score of 600, and the bank wants a score of 800.

This may seem to portend some sort of a doomsday scenario, where we all become slaves to programs and their writers, but at the heart of any system of data analysis is mathematics. Data processing is ultimately a mathematical activity, and it is there that lies the hope. Mathematics is a human activity after all. Like any other human activity, it carries the possibilities of both emancipation and oppression.

We live in the age of digital data, and in that age mathematics has become the parliament of politics. The social law has become interwoven with models, theorems and algorithms. With digital data, mathematics has become the dominant means in which human beings coordinate with technology.

We hope that the practice of mathematics takes up the challenges of the time, strives to bring accountability to the needs of the people. If action is not taken at this time, our digital technologies will be the new jails.

#### Section 2

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Machines were… the weapon employed by capitalists to quell the revolt of specialized labour.”Karl Marx

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The successful construction of all machinery depends on the perfection of the tools employed; and whoever is a master in the arts of tool-making possesses the key to the construction of all machines”Charles Babbage

Three centuries ago the Newtonian revolution in physics made mathematics a firm part of any technological project. Two centuries ago began the age of specialization of mathematics, where mathematicians ceased to be natural philosophers or even mathematicians, but became geometers, logicians, computers, analysts, etc.

One century ago, the age of the universalist mathematician finally closed with the death of Henri Poincare in 1912. This era marked a crisis point in the history of mathematics, often associated with the search of Universal Foundations.

Almost half a century ago, human beings began to lose their monopoly of producing mathematical knowledge to technology with the publication of the first computer assisted proof in 1976. Since then, there has been an interplay between mathematical thought and technology that has been growing.

Each year, mathematics shapes politics in new ways, through technologies of surveillance, medicine, transport, communication, media, information, identification, and governance.

Mathematics, by its nature, is contradictorily both universally accessible and accessible only in parts — this is a time to start engaging with mathematics politically.

Over the last many decades, concerns about the relationship between science and society have informed public discourse at multiple levels – both internationally and within the Indian context. Although voices have been raised by different sections from within and outside the academy, and with varied political motivation, the efforts made to understand and transform this relationship have contributed both to theory and practice – influencing the different points at which science and society interact. In India, the Peoples Science Movements (PSMs) – which themselves have been guided by varied motivation – have sought to promote scientific temper, popularize science, to aid State building and national progress by promoting science and science education among the masses, to critique the relationship between Science and Technology and industry and also to use science as a means for social transformation. More recently, studies in the Sociology of Science have also sought to understand the relationship between science and society, to critique the practice of science and the structure of scientific research, and to question the role of scientific activities in accelerating inequality.

In current times, there have been sufficient efforts to reveal that the relationship between science and society is far from benign. In some ways, this relationship manifests itself in very apparent ways – the relationship between progress in science and technology and economic progress for example – and thus makes way for it to be better understood, and also challenged more often. In contrast however, the relationship between mathematics and society, across the various levels of education and access to technology, is much less understood. However, it is precisely because of this that it enjoys a special status – one that perhaps needs to be probed further.

Mathematics is often seen as a tool to be able to learn and do science. It is what formats and determines vocabulary, and that is where it’s role ends. On the one hand, this attitude lends a sort of impunity to the mathematics community within the academy (Pure mathematicians are not bothered by what their science is used for, the applications it finds is not their concern – they study mathematics for its own sake.) On the other hand mathematics assumes a crucial and dominant role within educational curricula precisely because it is what is needed in order to engage with scientific, technological and economic processes and activities. It is guaranteed a place at the university and compulsory at school. It therefore also serves as a sort of gatekeeper, helping to shape a notion of merit. It determines, in many ways, who takes part in the development of the Nation and industry and to what extent.

To address this issue we should look at the nexus of the producers of mathematical knowledge and mathematically skilled professionals. In light of the recent debates regarding the restructuring of the University Grants Commission, the relationship of centres of research and industry, debates regarding the updating of the tertiary-level mathematics syllabus, and the composition of mathematics education up until that point.

Mathematics is also different from science as a knowledge form in that it is associated not only with skills of reasoning or logical thinking, but also with a deep capacity for abstraction. In a caste-ridden society like India, where the mind is valued over the hand, asking questions of mathematics as to how it renders itself into caste inequalities and reproduces social inequality becomes all the more necessary.

#### Section 3

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I worried about the separation between technical models and real people, and the moral repercussions of that separation.”Cathy O’Neil

Guided by the larger concerns of how knowledge gets valued in todays changed economy, what processes contribute to creating this value, how forms of knowledge and their arenas of practice serve to uplift an economic system, accelerate economic inequality or support industry and contribute to state building, we feel the need to focus on mathematics as an area of knowledge in particular. And even more specifically, to examine the relationship between mathematics and society in the Indian context.

We feel it is important to understand how mathematics serves and has served as a basis for contributing to industry and State building and in turn how the State, industry, and other forms of organisation make demands – overt and subvert – of mathematics.

This is not the first time such questions are being asked of course. Unlike in the case of science, such concerns rarely emanate from the mathematical community within the academy, and in public. They do, however, find a voice within the community of mathematics education. But as it is, such concerns have been little explored in the context of India. Across the international community of mathematics education as well, discourse surrounding such concerns is increasingly directed towards the politics of curriculum making which asks important questions but has little to do with practice. So what we are left with then is very little in way of data and empirical studies, which will help us be more concrete and pointed even in the questions we are trying to raise.

Formulating these questions to us is only an attempt at perhaps initiating such studies in the context of India. It is an invitation to those who might share these concerns to begin a dialogue.

We are putting up this initial note in the hope that those who are interested could add their own questions, ideas and of course anything that they think is pertinent to this initiative.

The questions and suggestions for study, we thought would help us situate and guide us to work through the concerns. We are looking for people to work together on questions which is of particular interest to them concerning mathematics in India. We do believe that not merely sharing concerns but even working together is still very much possible in our increasingly fragmented professional and social worlds.

Guiding Questions | Questions as points of entry for study | Sources for study |
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Mathematics and Industry How does labour get commodified through skilling by mathematics? How does the industry manage mathematically skilled labour? What is the mathematics that contributes – or is perceived as contributing to – industrial growth? | What are the employment trends in industry of the mathematically skilled labour force? How much of the mathematically skilled labour force gets absorbed into management institutes? What is the kind of private capital being invested in mathematical research and mathematics education initiatives? | Looking at mathematics graduates in industry – number, qualification, skills needed etc Looking at Microsoft labs, Infosys investments etc – when did they begin, in what economic climate etc? |

Mathematics and State building What role does the state play in terms of policy, economic interventions, education, and research in promoting or suppressing mathematical learning/research? What kind of mathematical knowledge contributes to State building? (Triangulation and private property, the mathematics involved in determining monetary policy, poverty lines, policies of taxation etc) What institutional structures form around mathematics that is commodified? | What are the employment trends within State structures of the mathematically skilled labour force? What are the kind of mathematics educational initiatives supported by the State in recent years at all levels – from school to research mathematics (ATMs etc)? What kind of funding does mathematical research enjoy and from whom? | Educational initiatives Policy docs NGOs and CSR initiatives supported by the state changing social composition of curriculum designers Trace birth of IISERs? |

Mathematics and the Knowledge Economy How does mathematics get commodified in the current economy? How are different forms of mathematical knowledge valued? How does abstraction get privileged? How much and what mathematics must one know in order to contribute productively to the capitalist economy but at the same time not challenge it? | What are the markers of mathematical skill/skills that require mathematics? (from the perspective of capital) How do these markers get restructured in light of social privilege or lack thereof? (eg: region, caste, gender) How much in the mathematics curriculum (school, high school, undergrad) is actually useful? How much of mathematics education serves to make processes of society and economy legible (and how?) and how much serves to anesthetize? | Look at the mathematics being used by mathematics graduates employed in finance/investment firms etc and compare it with the mathematical training they received at school/college/university |

Mathematics and the Public How is mathematical knowledge perceived to be valuable by the public at large? How does it contribute to asserting/shaping different forms of cultural identity? How does it link to aspiration? What constitutes the popular imagination of who the mathematician is? Of who the student of mathematics is? What does access to mathematics and mathematical prowess have to do with existing structures of social hierarchies? What social structure results from the commodification of mathematics as it has over the past 150 years? | What are the aspirations of students who study/wish to study mathematics? How has this changed historically? What is the caste composition of mathematical research community? What are their attitudes towards caste? What are the experiences of dalit students in such spaces? | Interviews with high school students, undergrads?? Interviews with mathematicians, PhD students etc |